A MATHEMATICAL DETERMINATION OF THE MAXIMUM PRESSURE AND THE EXTENT OF COMBUSTION IN THE GAS ENGINE BY GEORGE THEODORE FELBECK B. S. University of Illinois 1919 THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS 1921 Digitized by the Internet Archive in 2016 https://archive.org/detaiis/mathematicaideteOOfelb *Required for doctor’s degree but not for master’i r?j • . n T-"’ r *ms’ *a_ > - MM — w — T ’< 8I0WIJJI HO YTiSHavlMU •■^ 1 *!4 aOOHQ8 aTAUQA^O 3HT '?. HT« ir ■n ^ t -u "T wy! 1? x»( . . .. XifiifijCx. '^' 1 ! ^ 'V-' , f<- ru sLmm (I3«ah3H^i 8183Ht arif* t/.ht ya^H^N i - f -i j f-'i V “ i»'- f* 'ij •/.' ■ " ■ ■ wnTttf ' "k«’Av _.»">t;' '•j^: ' . 1 ! '■ flW 3HT 30 T3AS EIHT OViUJHJrji 8A U:m333A‘ 3fl ^ ,30 33303C1 HHt ^ ^ • • w ^ • ^i... — ^ t'- WtflMJT fft. \ "V,.J m hiMn'iaqBO t» «m»H »•: J tel '., -•r'^- •• •.H' JSl^i';' it) ^ir*i!rmmoO V >'j no *i) 0 *lJsjriaTjixa (iwiri _ - lU iL i- ' Oi i'4- ‘^: M'',-i "^’■^ T- '-*' / ,-^ ij l»wii&ft rtoinA^ ^ fTtBoWltrl ^ ■ * V. V ' ■ . '‘'',v'‘.i»? "tSi*!*’ ■ ■*■ '>x ■■yi n ■ ^ »l|lllll ^ > Jn *»| | » t i'- r^r )■ -t- , ■ ,:' v:-A^i ^ -. '-ita I '.z.' '.''£’ 1 :';" '' ' ■#•:' J :i.y[ a- i^SHI^B£:i:X ■,-■ f •, , ?- ;ii?a ' ' W» iMitf •^r *6 »'to»a(ii<> Krf i'.i jtt; T:‘JBLS OF CONTENTS Page I. Introduction. 1 II. Derivation of Equation for Adiabatic Compression. 2 III. Derivation of Equilibrium Equation for Constant Volume Adiabatic Combustion involving only the Reaction CO f'2<)^->C0j_ Case I. 6 IV. Derivation of Energy Equation for Case I. 15 V. Numerical Example Case I. 17 VI. Derivation of Equilibrium Equations for Constant Volume Adiabatic Combustion involving the Reactions C 0 -t-iOj^-tCO^ and CO^-t CO + -|0 Case II. 19 VII. Derivation of Energy Equation for Case II. 24 VIII. Numerical Example Case II. 24 IX. Derivation ofEquilibrium Equations for Con- stant Volume Adiabatic Combustion involving the burning of CO, and C and the Dis- sociation of C 0j_ and H^^O ^ Case III. 27 X. Derivation of Energy Equation for Case III. 24 XI. Redustion of Equations and Method of Solution, Case III, 27 XII. Numerical Example Case III, 41, XIII. Effect of loss of Heat during Combustion on the Maximum Temperature and Pressure and the Ex- tent of Combustion in Case III, 45 XIV. Effect of Excess Air on the Maximum Temperature and the Extent of Combustion in Case III, 50 XV. Extension of Analysis to Cover G&seous Combus- tions Involving the Hydrocarbons C^H^ 0JL,Cz^yj and C ^ H^ . 54 Appendix A, Specific Heats. 56 Appendix B , Heating Values. 88 Appendix C , Chemical Equilibrium. 122 Appendix D, Determination of the Maximum Possible Percentage of N 0 Pr4sent at the Point of Maxi- mum Temperj:ture in the Gas Engine . 144 s. I» i - Jassss»ILK- I fiV \\ .’fu5 U-l-;' 3.' C ■ sJ ;VL' 'fit* TC'lpCL „ i'><. ■-. : Uir.. •‘•w -V' ii*' • > ..-rtF » > - V .• "r ' ' * «» , . ', \ .. : 1,. ; • . v.'JjflwV • .' T: «5i V .« w - : '.vl^ oT t ii « t : . . L : nk':\ r -Xtc^ « .; i.. ■>■■■. • ^ , •>» • w - • 1, »« A- V • - ♦* A ^ - V .k *■ * f w ' ;. ^ J ’ i%<6rj ^ '•::■• --i. ■ ^ c>r:^ ,':, •=!:/'. 'i '.-ii i •' .' ••• '•.0 J f- * ' •* V.f A V >> \. i, onL tt . nA . . /tiot . ^ .1 1 • fftoli - -t. ^ 3 ' J f !■ ‘ f 'T.^l.' (1 \ i:..ji;x*A •« ' C«M V .V, ;'1: '■ >u ' i> ' iiw ' ■ *'cX 1 ‘ L <■ Y '. i j « - • -rO «3i .iOitw;si. ;i 0 !!:r ^:c^ 1 ! ,•- i — ._ S'liJ I %Zi-. U4.'t>t;:^ll. l i l 1? i‘..:;j'X''^- ^ -v; s. . X A I »* f. - ■ , - '■' ’ /ax 1 « ' . ■ aiO-'-I-'flJ, 1. J>;:' •....' % ^.: \ Xo vt, .' ,;. iJ*? ■ t.' . i. t> t;n, P'Hi’ "i ' V . *• - Cj 4t. r*- -A ^ f) ' '■ ' -<- ^ iT >. ' '. •tttlv 7. ov. ■'i'i r>.I. ',’7^37,7 . > '* ♦ ■ ; ■M I ■ V TTJWrS**!^^ J; n -r.' Figure 4 LIST OF CURVE SHEETS Page 19 a Gr^hical Solution, Case I 5 TT TT " II 26 6 n TT ” III 44 7 TT " with loss of heat, Case III 48 7 (a) Curves showing combustion on effect of loss of heat during maximum explosion conditions 49 8 Graphical solution with excess air. Case III 52 8 (a) Curves showing effect of excess air on maximum explosion conditions. 53 9 Specific heat curves for C Ox. 61 10 IT 11 TT ” H^O 66 11 If It TT " H^O 67 12 It It curVe Methane 73 13 11 n TT ” Acetylene 74 14 TT TT IT ” Ethylene 75 15 TT TT TT ” Ethane 76 16 TT TT TT ” Benzene vapor 77 17 TT TT TT ” nitrogen 79 18 TT TT IT " Superheated Steam 82 19 TT n TT " Amorphous Carbon 86 20 Dissociation of G 0 ^ 128 21 TT TT H^O 131 22 Ecjuilihrium of the Reaction i-C 0 133 23 TT IT IT ” C i-2H^^C 137 24 IT TT TT " C +C0;,.'^2 C 0 139 ''i >-C3& -. - ij^gi^^ r , jfe< .i« X iafS ;iy» ^.H .„, ^I^P g ' ' WM .,. " .r- ras^'^'^’sv * nr ^■'«\*r.' -J.. > _ -r‘. . . ±: < f * y_ :!^ .«: ^,,3’ ‘- J^.i »vf.f 4 il ^ fe ^ rC'i,.? i f H Jr ■t . -;n . V » U i V , - i ■ ", -’^7; ■•. . V ■.'• ; ’■, '-iv ":t , . ■ .* . .^* ._ f. ..’4 .to itelldhti^o '■'"w •' ■'' ^/;if B. Jta >t , , ' ' ■ V 4-y" I \f' ’**' iic *tir rnaci»^ ^0 . » ‘.' HUKO 'V % £■' ”^5^.C!.-,';«- V. '’■" ' '••k ^ -■ '.i -«» v: , V ' Tpl ,ao*r::Va 1.^^, ^ - ■■ ' ‘.''su' ' . , ' I fc- * 0*3 0X.^u^oA too^tv <^riiKfC0< Tf i . ." ^f| A',;i j.Wt ■./ • ^.* ft.V JTOWii '^^■'' .... n#[f-l.r,r! Bi;Ori,,oia. % V# IM V \y * li 'jil il ■ii'V '* , A, ;- >o k iia.' •'■ ,. • 1 A Mathematical Determination of the Maximum Pressure and the Extent of Oomhustion in the Gas Engine I. Introduction. The maximum pressure obtained in the cylinder of a gas engine as measured from indicator cards is much less than one is led to expect from computations using the "air standard" cycle with air as a medium having constant specific heat. In fact, the actual pressures are about one-half those obtained by calculation. Some authorities claim that this discrepancy is due to the fact that the specific heat of the actual medium used in the gas engine increases with the temperature. Others maintain that combustion is incomplete and thus the pressure is lower. Some say that both causes contribute to the decrease in pressure. To foretell with any degree of accuracy from theo- retical considerations what the final result from a gaseous com- bustion will be the physical and chemical properties of the gase s involved must be studied and not the properties of some other gas entirely foreign to the combustion under consideration. aVhiL e air is one of the main constituents involved in the gas engine combustion process, the properties of the gaseous mixture are quite different from those of air. The gaseous mixture varies in different engines with the proportion of air to gas and with 2 . the nature of the gas itself whether natural gas, producer gas, coal gas, or any of the other suitable gases. The physical and chemical properties of several different gaseous mixtures will in general be different although they may all have the same constituents. The properties of all the constituents are not the same so that v/hen the proportions making up the gaseous mixture are changed the properties of the mixture as a whole are changed. It is not reasonable to suppose that all gase- ous mixtures when burned under the same conditions as to initial pressure and temperature will all produce the same maximum pres- sure. Each case is a special one and no blanket calculation can be made to cover them all. It is not fair, moreover, to an engine to measure its performance in terms of an ideal engine using a distinctly different medium such as air. To be able to judge the state of perfection of engine design the ideal established must be that which represents the maximum results obtainable with the given working medium. II. Derivation of Energy Equation for Adiabatic Compression. In this discussion only two phases of the Otto ( 2 ) cycle will be taken up; namely, (1) compression and/oombustion. Both processes will be considered adiabatic. At the beginning of compression the pressure will be taken as 14.7 lb. per square inch and the temperature as 190°F. Hopkinson*has shown that the temperature of the charge at the beginning of compression is in the neighborhood of 200°P. The value 190® has been chosen arbitrarily for convenience. It will be assumed that *Proo. Inst. M.E. 1908, Vol. Jan. to May. r^' I I I ’ i>l : ij ' J >J •> hf - -• V ‘ ' ‘ . C.I'O Ji ' i"* '•■, ill'll 'V diV ^0 z - , ■' I,.c. . / - * , w ; » ^ #. .' ■*. 5- ; *;. '• 7;, .' .u ■.( t. .1 -. .(!f •.'. I, .J L: :t,‘ ov.-. r. J.: -j: ;'J C £ »JO X I w, . ' • U ... (. . i,:}f. I >. '.' w t, w U . J. * 0-, - . * ’ ' * J j ,*C X ii ' '• : r .’ r '* W T Ih* V <■ 1 vi:7 ■ . i 4 'i ,’. ,* o 0 x'l li w ’ . \T (j':^ ,j J fr' --} ' * ' ■ *;. '.• ci . I i 'L IV lu 1 ‘£o 4' 0 :,' i £jg i:': 7 ;a: J;fn: 'i'.;.. ; I#; ■■j-i^: u •' s <*v ': r*.C IT !j •’'I ; .t “ v;' fiu ; XO V..;.: „ e'i I . / X 1 : ;. .'■ ' '; • A i ' ■ 0 W J 1 1» ■'.oi ',/. '.'•4.. .’.'C »' r.!.!- 'ci •I'Ox •■• 7 .'' , ^ '. X ' I VP .'. 4-> • X L; C. X4U'4 ill vu 4 o r»i''j* j,0'' • j ., V i.T' '..o V ij i. \ O \l>t"'i ■■) i,0 ^ x.V'.’.T i 'i. 0 ( X ) , , •. '■■'Ji'.V I ‘ Tv , V ^ . ' 5 * ' t' W 4-4-» K < 1-1 ^ <4 i'* .UN /. » i U . ^4 'Or': ■VI Ovf rCu^ . n£.J’4xA'/ '-X ft o'lx - j. i Of' .rilw r'. V - ,'• C !. :■.:{■< oC XJi. ' Lo r;r4itAvi.At X ^4 AiVOvi tx'XX ^.>-.l4xr o;J'i} x;,T.-?i'x Adx £,0'l,L.;i^vro;TiOi; lo 4 'c^f x'l 5 »r-t br,^ i»cxti > 4 '^' 01 . 4 “ '.Vj iviXi’J ."i - 3 ' Of"; 'lo JiTt-jix jij; /■-*. S'l J 44vrJ XIxv/ vft . . yi,axii« vx-Oij 'XOX YxXx: v'xv^ iXbo'O/iv • '<. '' x’v . t-:,; 'o . iO / ^, v.''C''.'X • •' • ••t . .!.>0'‘..i »K II II 1 / • I * 4 ** — ■■'. ■ C?: Ill' • J., .4 ,;i Ott,; CliCi? vIOii i;:xf- a ** .; ,x.u f*i ' •■ ' V -' ‘ V'' -» - ’ . ; 'i , * . f*. 3 ignition takes place at the end. of compression and that the combustion is instantaneous. The combustion will thus occur at constant volume. It will be assumed that the constituents of the gaseous mixture obey the perfect gas law PV/T “ constant.* The following notation will be used: State 1 (beginning of compression) P, , V, , T, State 2 (end of compression) P;^ , , T^j^ State 3 (point of maximum pressure) P , ^ P=lbs# per sq. ft. V -cu.ft. T = absolute ‘’P. The compression ratio V, /V^ is determined by the design of the engine. Knowing the compression ratio and with the assumption of P, - 2116 lbs. per sq.ft, and T,^650 , the values of P^ and T^ can be calculated from the following: The energy equation dq = du + A pdv (1) becomes for the adiabatic case du -h Apdv =* 0. (2) Also we have du ■= dt. ( 3) Where is the instantaneous specific heat of the gas mixture per mol at constant volume. The specific heat of a gas can be accurately rep- resented as a function of the temperature for the range of tem- perature occurring in the gas engine. This function is of the following form: ■=* ^/77 't' ^ 3 fp) ~T ^ (ft ) *Por a discussion of the accuracy of this assumption, see British Association Committee Report, P .368 , "Gas, Petrol and Oil Engines," by Dugald Clerk. ^ liV'T || {I ) /^r . I U v h I ' < if ik f 0 , , . uh ovn/f ew Oi.* .- fc-v .; u;ir.' :0;. J'i' .C’br?' *rr. - 0% •, r 5 --£' ; Vi" C •fiy'i ' i? r ' t C V I ' :■: Jr • • ■‘I CI.j C ». ■ 5» .9 ■ r^ci'Jtsi el: •‘" nr-y.i Cl.'-,) i Itu . ^ r*i : ■ :C' 1 ■ r^. lifc iltl V,’’*". ‘ ' '■ V * r,-A •* i ; *1C v:>-: «. - 'U* . ■ -'i ■ ryt-'v/v - .j'i?v«> " li* ■.? -1 i'Syii./ (,’VJ .' jO ’ i -f/. ri'.i- • - C' J v' i' ' XiAl 7 i ^ ' '•■*' 'C- “ , V' At'lilEJv 4. Combining (2), (3) and (4) we have The perfect gas law gives PV«M,RT (6) where M,is the number of mols in the charge P„M,RT (7) T" Substituting (7) in (5) and dividing by T, we have o-‘ {-^ 1- dT + AM.Tf ^ (a) Integrating between the limits (l) and (2) /Ofe ^ -f i tin +^fm( K'-T.V = A fl.Tf /<»fe ^ (V It is sometimes more convenient to use the pressure relation P^/P, than the volume relation V, /V^ . Prom (6) Then V. ^ T,. Pi, ■ T. ^ ( 10 ) oo Substituting (11) in (9) and collecting terms we have (ani- A n,l^) /•JS'e ^ t Z 6„(n-r,) -t f •= A M,nl'= 3 e ^ 0^) changing to common logarithms and dividing by the coefficient of the first term (12) becomes Z b, m {Tt-T.) 3 t m z. fe-7;V _5_ (/3) A ^ r, ‘ _ AM, F A /I Transposing all known quantities to the right hand side of the 3fr equation, we have 23ozc(am-t A/i,lf) 71 -b i/B. 2 • 2»302C(ar„ f Abf,P) _ _ AAf,/? , /> <*n,fAM,R ^ * A ■b -*■ ^ SL. 3 fr ' ^ ! m T**- fj^) Equation (14) can best be solved by trial for the unknown T^* , Gfiix. . ( ) :)^^■■ (<>> , ■ ' :.TVw ifkV ■ * 1 ' 'i, t*"’, * U fro’ (-i) • I’h . til ■ TI :.i . t, .IL * ' '■ ‘ ^ ^ » ■ r ; ' ri y V e ft,'f C‘£v:l,! * ( / } " 1 \v ; > • . r 3 > . ' *.. i '^v .. X \ ) iil ( \ ) r '• V ;4j. -r - 4 ( ' .. J. '.I. t> iOv aijvri^G ->T" • V.”.A- > » ' ^ \ (T^j. j..'i o'iir^vi^ irf* V r '» ,o.i: V, ..' r.I-Ov'it'i: ui dl (•j) /.I -S ' v\ : .v" \w / r,i:ujLG7 Il'dd y‘i\/i - (■.X) •V . /. ao;i? * « rt - ^ .T" ,V sY-.i ,®ii ^ 1 !.: . - .; Gti J. - . < . ; -u (I/! > ■'' ‘r»5^ K - ft 1 . !>y V »' V ‘ ■ > X.;.i ; i ' - I > .. ii u.- . r^^' \C.i. ilC * ■■‘l'‘■, * >1) rii:’!- it<.:Zi . to >' ^ J ^ 'i S ,'» • I >* ► ^ ; - . t ^ r^ y <'.% ^ r\ 'r m'' Lil;^A . .' ^ . ;■••;•.’ oi, eoi . ...v rj ..; 'rcAOt. ' ' .' ^ PV:' :■;■ Oi,' , ^A K V ., l^^ :. ^ '><' t V| ^ '.^ . - . ) T fr. ^ ■.v.,-v,v-'^ " ■ ,,^ i A '‘A.\,ir.^r I. .; \.x . .'. .' z^ i/cvioc c > , ;t'-‘.‘ ( i*I ) ,.r '’ ■.v.,-v,v-'^ r^jtxsr-sssssraaei ■ 5 . The accuracy of the value of derived from eq.ua- tion (14) depends on the accuracy of the value tafcen for T^ and upon the accuracy of the specific heat equation a t ZbT -hSfr^ The value assumed for the temperature of the charge T may he accepted as accurate within 20° S’. This temperature varies somewhat with the load but as the value 190°F was determined at full load and this treatment deals only v/ith full load we need only one value for this suction temperature. The equations for the specific heats that are available and that may be accepted as accurate for the range of temperatures encountered in the gas engine are as follows: 5’or the gases GO, 0;^ , For G^H^ = 4.51 + 0.5556 e Tp * 6.5 + 0.5556 & 7p * 6.19+8.1 0 yTy ' 4.20+8.1 0 For 4.51 + 0.0005 O = 6.5 + 0.0005 0 For G^H-y rp> • 6.67 +6.8 e ■jr'y * 4.68 -f-6. 8 0 For 00^ For G^H^ ' 5.42 -^3.5 6- 0.48 a’’ }Tp^ 6.43+11.3 0 y-p- 7.41+3.5 0- 0.48 0^" > 4.44 +11.3 0 For H^O For G^H* ( vapor) 5.04 + 1.250 +0.2 0^ T’p » 4.00 + 31.8 0 7.03 +1.25 & +0.2 Ty ^ 2.01 + 31.8 0 For G Yy- 4.04 + 5.0 0 •y = 6 . 03 +5.0 0 Vp V/here Yy - instantaneous specific heat per mol at constant volume and © » where T =r degrees Fahrenheit absolute. ./:TJ ■.'j .i. . .. ^*T ' « fJi-' ’ ■ •_ -* : -%J t - i . * O *• - rV ^ 'I 'J -■ ■ . -, -' - ' . . • .l>i■i^ : '■T-w; L f ■: -.i.i':.: J'lfi C ' j .-i ,- rr ei ‘ - ., I- ■. '» ./ . ' i j.'.i.J. aJ -I 1 *•»* !*■. V ^ \ i’ ( V . .' c> . > . i , “ # * # : / ■! .•) r, > '• i.< J ; l. i' : .1 •■'..• ;.;rlcv 6 « For a discussion of specific heats see Appendix A. While there are not sufficient specific-heat data to give accurately the variation of specific heat with temper- ature over any considerable range of temperature for acetylene ethylene Ethane and benzene a large error in the specific heat equations of these gases intro- duces no appreciable error in the calculation of the compression temperature. Talce for instance an engine running on acetylene (C^H^) with the theoretical required air; Acetylene burns according to the reaction ^ /Vj i- -h S /V^ ^ z COx. -*• 9. S'A/^ From the above reaction it is seen that the acetylene consti- tutes only 9.1^ by volume of the original mixture. If the specific heat equation we use for acetylene gives results that are as high as 30^ in error, the specific heat of the whole mixture is then only ^ in error. This error is less for the other hydrocarbons mentioned above because the ratio of required air to gas is greater than for acetylene. It is doubtful if any of the specific heat equations used give results which are correct to within Knowing the compression pressure, temperature, and volume we have the initial conditions on which to base our cal- culations for the combustion phase. III. Derivation of Equilibrium Equation for Constant Volume Adiabatic Combustion Involving Only the Reaction CO . Case I. . K ' jJ..,:::, J i-> b V ^ f >- ■- -. V* t' * -H*' - .'■ * > ». w '...( . ’k .. s.'.. 'v> L'.‘. (Y ~ 1 C.' ,. . .*•. */ • ;■ ./ i 1; - X* ■ ir U ' .. t. , .. s t» ^ a 1 V .. Ci^ . V i.i (;>•' ■ T. . j. ' «. • <- *’ V* T’ • *v 'X . r ; ; -' ■ 0 k'k I .. C MOTC irx ;, •' • » r V i C *,-'•< :ir ■' I . * / V. i L ; 1. ) 1 ...w . ^ ( <^U ) " i. J ; Ob;?. . . .. : .i . '.w ,J_ L i J.. m;..< ;;I *l.O\'C© 0' •V. -•■ '■' 0 u . . \ '' .1 .U .. 1 t*. •- ' * . '^ t . t , 'v i • C V X‘^, u- Ti ‘ i ' :r- - k’. ..r f ■ ■ ' . 1 . X - V.;. < 'lj •', o:’.i7 * • wk. - ' .-i •; !• :’vi7 {^I: - *, 1* Lcr/ ^ ..I ■ w 1 ^ ..J 1^, V-' . V*i 1 t>-X^ V? C-‘ f* I. L: .:i/ ' ' K- - .:., • V i .M ^ V rv j-*; sfiJ * i. \* '• i • - u > «»• ; .. j, :'.i ^ f.'i. ft Y v;,-.o .it.;;;.: U * K, . *• . J. r . • • " - ' « *ri ’ J‘" ‘ ■ ' ■ u '': f! ^ 07? ;r''i,? . ;*; o v.;i xi.*i :cffr/ i) Oj j I .' r. i' r 1 :i CO L •;.: :.; '©-. nr>ir( ‘fe ’ »o.. OfC ■;• : rf' : ' K '- - /:i ‘ ci r)r.- . J 'J r :: • ■. 1C * '« ** e' r »'rC(fn -M-.O'. ■ •■• .. ,' L.rii •;;, c' f • * ^ 7 • # . .'i Cw t *1D1 l;.’ :2l trS'^-C^ o'lj :. V V • y ■,'vi. , ^ r- i.C^^aw, (511 Lo'. k'.i on.,-: 'I'C -X>3 0 V ! i.; f>d;t %J‘:< et ' ,' »•< ■' - ■ ^ I J iurfuiiR’ y.. .t;;t»'i'i;:,f || 1* •• . -;- 'r'^ ')!> r- 1-^' «Vi -"• , t:- ■/ 6i dc.ii.y* .■(’ crfJ ’' , ''j';"? uOi j'aycfj-ito ‘to. '^r?> i j-^ Ok) ^r'.;I. V a Mv fAii'- ’ . ■■(■/*<: i;vAi.;rft: .• '* ? 'f' /■'oO’- vi':\-'^ .^11 7. We will ta^e first the case of an engine rimning on a simple gas such as CO. It will he assumed that none of the products of combustion of the previous cycle are left in thecylinder so that the initial charge consists only of carbon monoxide (CO), oxygen (0^), and nitrogen (H^.) . Upon ignition of the charge it is possible for the following reactions to take place; namely, C0^i0^->C0^ (1) U^i-O^-^ENO (2) It will be shown later that reaction (2) does not take place to any appreciable extent so that it may be omit- ted from the discussion. (See Appendix D.) Reaction (1) progresses until chemical eq.uilibrium is established at which point we have the maximum pressure and temperature attainable in the given case. The proportions of the various gases present will remain the same until some change of pressure or temperature is made. This is what occurs when the engine piston moves forward. The gases expand doing useful work and the pressure and temperature decrease. At ordinary temperatures reaction (1) will go nearly to completion while at the high temperatures attained in the gas engine cylinder consid- erable CO and 0^ may be present. As the temperature decreases during expansion a greater part of the CO present burns to CO^ so that at the point of exhaust the reaction is practically com- plete. When a chemical reaction between two substances is first started the vigor of the reaction is great. Depending ^ I . -to J.\l. ' J^xif ;v : ouCi. j- ,j ■<-■.• . jt;;j', Jr. .0; t.: itiv. a/2, .'i i..:j /a .: X .U-u fT' ■ ■ ..iI,ircX Col erf;i (..) L‘. ■ - V. ' . It { ' 'i / - 1 ^ cr • 1 ^ V ‘ V 1 i .. . -, '■■■ ♦ • . w . . *) • i.' -•■ J- .:. 0 J ^ u . ^ ^ - w • ^ ' tiiJci ; w'l J ■l[.i .!■ '.'u jC-rt • 1 , .•J - 'ji fc'D«r Ii>.y 0 r .. .U V. \ ...'C / - ■’.*, .;» 'i ' -■■. ■ ;• ■ ( i. ) K>iJ t .'/.' 1 ^ w- *riirf •> -b . I .‘x'r.Z :i ? £■ ;V* .: . ’ . .' iii'iMr.' J , :..r^ftiX.fbcfe;6 -' . .-.i-, j> *•.•_. <.".:•* 'r'c.-,i:' .c £ C ■:> . Cu /i ■:, . ' •-, ^ / (£} ilvC O . :'C i' J .’i r>{iC f. f ~ i J. , I><.'.i' . ' ^-1.. 8 on conditions, the reaction tends Id go one way or the other. This tendency of the reaction to proceed we may call the driving force of the reaction. As the reaction proceeds this driving force decreases and the reaction slows up. YiHaen chemical eo[uil- ihrium is established this driving force has been reduced to zero for there is no tendency for the reaction to proceed in either direction. If a reaction should acquire considerable momentum and proceed past the equilibrium point, the driving force becomes negative and the reaction is reversed and proceeds in the reversed direction until equilibrium is established. c We may represent a chemical reaction by fig.l. The point a represents the constituents in their initial state. Point b represents the reaction completed. TaJcing the reaction 00 ^ at point a we have only CO and 0;^, while at point b there is only CO^. The progress of the reaction is indicated by x. The ordinate of curve n is the driving force A of the reaction. The amount of mechanical work that can be done by the reaction up to any point P is represented by the area between curve n and the axis a,b between the limits a and x. This can be repre- sented by the equation aW;, = = E (is) 9 . Differentiating eqi.(l5) dW =Adx ’■dS A dx ~ (16) From equation (16) the equilibrium point can be determined by putting A^O, This equation involves the varia- ble S and X. We may proceed as follows to express E in terms of X* Since the laws of thermodynamics are applicable to chemical reactions we have the following: dQ ® du i-dW «du-l-dE. (17) dQ - heat from external sources du= change in internal energy dW e external work done dE. Also for a reversible process, dQ=TdS (18) Combining (17) and (18), dE ^TdS - du (19) Substituting (19) in (16) we have T ds du , , dx ~ dx ^ The variables S and u can be expressed in terms of T and x so that at a given temperature the value of x at the equilibrium point can be determined by putting A “0 in equation (20). To transfer equation (20) into one involving x and T as variables we proceed as follows: For the reaction under consideration; namely, cot (a£) {•t^ - -Si », t ' C *i ^ • f'- e' ' •.. .. v"‘>‘ ^ ■' . ur . L 2 U^ h blu . to V L ■ • " t‘ ■ '.‘.‘i u :©rX ' 7 £ ; . .' ^ u;: » -o pi) r f r r •» jjr .1 ^ r aL'C'xi J.’trd - i i' v:rvv, A-..;!.* t ■ •.Jt ajm»idQ )/0 . .ij V . t; :,;•!( ri 7 I' .<;’^ 0 v^^'^ - . > , . V '.. N ■> ‘- i. 'J'^^'V *V 0 ^ X^'- ■ {o,n ^^ 5 T ii *s I . * W KJ •_' V* *< A I * 1' Tv c>>'X''V C'CliC ; :f:IJj‘r ^ v .‘ .'3i ^r; , -Mi l . 't ) Xfv . (V.:) 0 (V.: )■•';: ., jji} '• -Xii' <•. - • . 4. C . • { 'Xr: •. : 1 .X) ■■,.,,..i,;JX.r5vi k ‘.J Nat iiSJ '^' XV XvV- X • • C f liiT ' t ir. y I :i ‘ '.'. .v.:v e 4 ^ •* k /*»’«*" t f ♦ A 1 M» * ^ W •) . li* k.' ’ 1, L . V,’ y .:, X 1 'X. ^iUi ' ^ . t/ H* ^ ’ * • X.7ri;: : : 0 i! J.o't as y c » cj . iv ■■••.,:. /■ ■ r , ^ L CtP -V’ it J jlfv i l5-i> X *.* 0 *0 V ^ C J ^ V* '& ^ ^ O-iV 00 10 . the initial mixture is as follows using an e xcess of air, CO 0* Mols 1 e f sum m The gas mixture at any point x in the progress of the comhustion is as follows: Mols GO*. X GO (1-x) 0.- (e-^) .1 , sum m - isic m Let P he the pressure of the gas mixture in the state x; then the partial pressures of the oonsituents are p --P CO 1-x m' = I.P (£ 1 ) The energy U of the mixture is the sum of the en- ergies of the constituents; that is, U =XU (l-x)u f fu m differentiating and multiplying by -1 iS. dx CO + iu - U c V V 1^- •€>. ,, - -X •i.,j . ii.: V X Xi i cXoM X UO X '■ ^ ^ ^ _ -- J, u ii • i ' » 1 * ’ ^ ■ • ‘ . • ■* • >• - . t , . s^ ^ * \ ^ “* 44 *■ * *' ■*' ' ' t i *. '4 i., ^ ‘ ^• i-hA' * O' 0 jw J. c> J. ' : ' •! X fr - nr" i ' ‘ I* • i J vj., ‘.-I- ■».• r,, ' '' ^ s.. J 'J > i, ’ ‘ , ;i J".,- ; c rio,Liv i J4r'.vi> e.'i’ -;.o ■ 'i i.'-i. ) “i' ir • 'J \ , ■ I II - u n - Ub X*;, . .V .. o J Iwj . i. f V •'- V'' }f XK-* 4- 4 ' 0 X ^ ^ ^ '^.4 . '’. V » .7 j{.;riX'' X I H ( 0 vf«J , -V q;’J- rfXiw:. y 'i ,C ,;;'0 ^ ',s; •’, N 0J5 :-f;J lo O’Xv^'i' Y‘ A iji’. ‘j;:.)- .'■nxoi.i "ii. Jy;r>ri .;;:sot^'^ rji,;xa .oovXOYO;. cX .*.4.., <1 ,oX_ .A difiX J‘uc>'iXb 11 . path ABOD in fig. E. Starting at point A with the initial gases at a temperature T the combustion is allowed to take place at constant temperature T* We then have As a second process we first cool the initial gases down to ab- solute zero and then allow the combustion to take Jilace at abso- lute zero so that So = 'Jo - Finally the products of combustion are heated back up to T®. The net result is the same as going direct from A to D. Then we may write Let the instantaneous specific heats per mol at constant volume be as follows; For CO, 0^ , a, -f- 2b, T -f 3f, t’' For CO^^ * a >. -t- Sbj^T t- Sf^T’" Then for original mixtures; i.e., CO with just sufficient oxygen |(a, + Eb,T tSf, T*') For final mixture after complete combustion; i.e., for 1 mol CO^ : ‘"a - - Sc) - - UJ Sv = - S,) - (Uo - Uc) (23) - U 3 = |(a,T + b, (24) ^ ^ + 2b^T tSfjT*” 12 Then - Uj. = a^,T + h^T’--^ f^T"^ Substituting (£4) and (25) in (23) (25) dU =H *H (|a -a )T (|b -t )T (|f -f )T (E6) The instantaneous specific heats of the gases are B.', -t 2b, T 1 3f , T a/ = a , + AR^ a^ 2b^T -^Sf^T** a^ = a;i v-AR' The general expression for the entropy of a mol of gas is s = s, + = log T -h 2bTf ^ fT^ - R log p (27) Taking each of the constituents in the misture and multiplying the weight in mols by the expression (27) with appropriate constants and adding, the expression for the entropy of the mixture is S r xs. -b(l-x)s« - 1 -(e-ix:)s- -f-fs^, <-o^ cc ^ + [xa; +(l-x)a; f( e-|x)a/ log T + 2T[xbj^-h (l-x)b,+(e-|-x)b,-^fb,J + 1 T^ £xf^-h (l-x)f, r(e-|x)f, + -a[x (i-x) ( e-|x) fj log P -R j\ log 5^ f (l-x) •log e->|x) -log^ozi^ff-log ^ In getting the derivative ^ it is convenient to take the six rows as separate functions, obtain their derivatives and add. For the first row = s dx (CO, - s. ''CO = -k For the second row (a) fb) V X 13 . For the third row * 2(h^- )T (c) (d) For the fourth row ^ ^ The fifth row is -R(m-|x)loS ^ * -Sm^log P Since the volume of the mixture remains constant during the reaction the pressure varies with x and in accord- ance with the following relation at any constant temperature T: P s m m' ( 27 ) where P^ = pressure of mixture at temperature T with x Therefore, log P log s t log m and the fifth now becomes P -Rm log log in' Tai:ing out the term log m' in the sixth row, that row becomes R j^m^log m' - X log x - (l-x) log (1-x) -(e-|x)log( e-Jx) tf log fj Adding the fifth row the sum of the two is -R j^x log xf-(l-x) log (l-x)f(e-l^) log (e-ix)^f log f + (m-|x) log The derivatives of this last expression are as follows; Terms X log X (l-x) log (l-x) (e-|x) log (e-ix) (m-l^) log ^ m Grouped in a single expression -R log Derivatives log X - 1 -log (l-x) - 1 -I- log (e-|x) - ^ -i log log f 'r I Z1 (t) (:>) :;{ , 1 ^ ~ = J u S- f - \ - /: ,ls» jw C? i Oy^v ‘ 4 .^ - r f ' ' ' ‘ ► »,■ J- “V > • ■ T~, f ■ IV I . —c f '. V - r... ;ii i.: -X/ -',■. ...Ow ti'T-l .; t 'X .‘. Ji. wHu .'.V. C ; * ;. or,A\- •„ ;.i A ; liw ' io ejS* nidtr./i. \^:'. V ; 'I. t OC-n. * • • *,..** • ‘ » * r* 4 -'-W v 4 ..y «»«i> V *i it ♦ ■«■ V .. 1 - i C'.; ■ .‘■“ ' ,•!*■ iv 'io 3-auct'i , « 0 .*?^' “ tvX =» - 'SOI , w -iii'-a uo -’X'xx iWill: uoil let- lH i; r ;.ti “ TX 'X it- ■* , f 1 f{?C 0 ..: - eV. .' y , ->'X I'w 1 ' » ^ ; ,C ( ti'v •" J ’ ) ■* ( -'“ - ^ ' ’ ' - ( X i - tsf o V ni ic ;:oI iX': v» oii-J 'XyQ ^rxXJ^-'. r t:X X : Cl r* ’'1 . ;v;I I t , •■ » k wf ... lu 0 y '■ D'r 'r q;;J‘ :-viijjX/. i' -ol 1 (.-. ; .nti' (iC- Ci nol (:f' C) '• >. ’-'I r. ' ■-- K .L (a - ) • ^ ■ ■ :.. ; . ii!^YX.ri 3 v XisJi yffX C? T ' ■ C /•i’-tiC ■ Cfi.'x.5V L „ t!cl '■'t X J. •• \.. -X) i'i'. i*‘ ... vu>. . ' 30 X (j:-X) :^oX (.''*• X) 30 X (x..'- -' ) ••oX {*’--) lit x:i. i i :j c u q;: '•> r X-^Tv.! i a £ii U © ' 1}' ^ v.,-. I H'A X ■'*— --I— — , ^ j x-i sol f-'' 14 Collecting all the derivatives, multiplying by T, and adding, we have the following; - -kr-(|a; -a;)T 2 (|b,- - |(|f, - f^)T -HT log . IjV i RT Prom - S ' + (|a/- a;) T +(|b, - (|f, -f,)T’ A- T^- ^ , s^i-T (Ja/- a;) - kj - (fa/- a;.)T log^ T - (ife,- fjT^ - RT log (29 X Z'/n-jy ^ l-Y. \e-ix ' r J C<7x 'CO, At equilibrium A =■ 0 and — ^ 'i P Substituting these values in (28) we have R loggK - ^ - (|a,'- a') log.T - (^b, - b^ )T-^(-|f, ' (29) Where G •=■ -l-R (fa/- a^/) - k. Substituting the expression for Ep in terms of x we have R log, 7 ^ (-1^)^.^, . (ia/- a;) log,T - {^b, - bjT -ft ZlN-C <30) Prom (27) 1 ^ ._L xi _ /_2SL P*- ' 7^ > ~ TiT Substituting this in (30) we have )^ (30 a.) »» v' 71 A H logeT^T- - <5 a;- a;> log^ T - (4b, - b,,) T - fj.Zl’+O (31) The value of the constant of integration C can be calculated from equation (£9) since values of at various temperatures have been determined experimentally by various in- i ^ L.- , -OVJ. s : 1* > V -‘- »' 1. w Tv 1 C^O - T;'U:X r c i: ■ -t L.ol r; v» '1 - .. * *sr<“ *' “ — ^*'" rac'i*'' f- { r. ■J. , n( X. : ( ‘o - Ip ■') ... } •:. ( t. . ^ f ul 'a.- -* 1 5. .. ?Jb ■ “ I.T - ■ - : . -':i^ - A '"P. ^ -i- ; u.T ^ hi ;/"•} iX..dn; ■( V : 7^,\ ^-y',' V' jr *’ •• ■* • :’.• ’ -.1 r - * ' :. ( \ ) tl'^M 0 ® ^ UL'i'l / ^ Xi.r* r ! , I y 4 c « V .- » ) *. » X v *1 r ij ),-7{ •\,’sox (< • - ■.') -c '• „4f ■ . { c •' -i-i ) V Jlh X M .X , ~ V{ ':t' L ,^^ r .. ;s . ( ^*- ) I. ( .^' ) . ri r: : -..u-tu L^- ...f .*:: lirfuo r .. V ' * ' W T 4. i t • I (*'f:) r.-'r'-L > I (CX ) £i.l.ti-.ri^ 1-iiXHrtUbU/c '.'■ ' ia “ T • / - ■ ! :: -■'1{,-- - ■:;) - 5,, >,^f,-> '■3 1" I k.'.'H cc* :* ''u r noi .0 A i ..i* ,iO •/ n/ v-'i;:nvo v*- uf/X ;,y * '■ . -4 .>>'' < 'iJX _' ' i< ■ -.^Uv . OC..I,. {‘h'O 4-4 ■-".•r^IiLO ’; .' i : iyp .;yo //ofi-fijry. - ti jr**' i v,."' ' ' .( , ' ■ '-pr '.-'ay - I ii;'- i^. -v Xl 15 vestigators. (See Appendix C.) Also the specific heat con- anal famperature TJ. stants and the initial pressure P^^are known so that for any given temperature T the progress x of the reaction can be cal- culated from equation (31). IV. Derivation of 3nergy Equation for Case I. In the problem of the gas engine, however, we do not know the temperature T so that for us equation (31) has two variables, T and x. A second equation in T and x is necessary to de- termine the values of these two variables for the given constant / volum€»i‘gaseous combustion J This second equation is derived from a considera- tion of the thermal and chemical energies of the initial mixture and the mixture of gases at any point x during the progress of the reaction. In the states 2 and p, Pig. 3, we have as before the fol- lowing gas mixtures. State 2. CO Ov N,, Mols 1 e f m State p Cdo- CO 0«- N, sum Mols X 1-x ®-|x f m-4x F,^. S. At the state 2 the total energy of the gas is fj made up of the thermal energy and the chemical energy. As the reaction proceeds to the point p, part of the heat of combustion is liberated and being an adiabatic process this heat of combus- tion serves to raise the temperature and consequently the * II . ' i '< / 1. ro;. '. .0 s'^^r OJiv) . L- if 0 r J .* v’V •.I t^. ., » i 1 vv^;.JW^- \ ritvi I. t CC U V.:- '.l,l- 4 . ... :.u m-v..';: c'l.*"'.. ?.'‘ t; 1 vA-j - '*“£ 'J.rw /i t.'J . ,y . T c. w ^ .1 • ' - ; -^Px ’ 1,’- k << « ■ j .£< ;• .• j L L .1 - *« • V J, - ' 's i i U-i. 7'. ' * 1 ■ « » . ., £«■'• -v i , ■/ .1' X . ; ij'i... C'/i- ‘VO'iui Jtvj • A 2 ' , w ..' ‘i .... ■ V//- ■ .1 ; ■ J X , , ■-' O' if 1.V 1' •>-. JixiV OLV Slu.iLn”I fn.* .’iv u.?.C v Ci/-. i/’'^C:>;ruV - > i j':'-. r,l A.%iv. t/. i; :.H,.u%ii Liiix ■ ‘ }j x-.i.ii. i.'. L w ; u.v i r.J. •■ o ■ / .'v &j « adz io, n; .‘‘■'io- v^-.' ;:•• it- .iv •.v,.;'Vy .rr CAJ .;/•. .V ■ s Miv i,t . Iiclj P'.y’I ri.Isj ..i-C' L' i -p'j • '..i i.' . . ' '.'.'.-UJ i -Cj. n^'. ovp.'i ©Mr .'il'S , q[ .» f i -V* V ‘X' — r*f . Dwi J C>^.- CL 2 ri -L . .1 X oc X' f- */: J Li. L P.Lx iviut ’i'p t:CC:J 'h!w - Jt:, oiU J'i cdi' rrtr:' iyi\z io Iv 4 j.Qii b:\Z V\y nc::;o.:c'H Hll; xC •:fpO''L ::r;p;-C7.: :uL ,j';L'‘j.-/i.. l>’ liL J.7.P0UiI tii 0 /iJ LXj*'A&£i^ L . lAk'' . iJ, Xi'tiJi (/' 4 .■J*.'; 5 *r.O X j.'J* yLx~'. V . fiij-' a rv 7 .i j L;jU'.:vc i 16 pressTJre of the gases within the cylinder of the engine. The energy equation (l) holds for this process; namely , dQ a dU + dW . Since the process is adiabatic dQ^O and also occurs at constant volume dW = 0 so that our energy equation becomes dU=0 (32) Let us assume the following arbitrary path. First, cool the original mixture to absolute zero; second, let the reaction proceed to the point x at absolute zero; third, heat the gaseous mixture at x up t o the temperature T at point p. From (32), then. - Ob)+ (Ug - - Up)-0 °8 - - {U^ - Ug) Ug - U„ = xH, (33) Substituting the above values in (33), we have Solving for x we have - > rf. - f ,-.i/ .... ij. Iv t-Xi .■ 'i . .w a ■- - •.•■•• 'I f - “1 J. ‘ it . .i . . ; ) i. . . ; . j. ^ C> .vA- % . i) ■ i. y...v‘ it'ji *- i tin ^ \ I 0 it V >4 J. rh • o j I'J V/; t.'- Or k.. .. J tj 'J kJ 0 :.i i • " U .i n .i* » i *, i. w f. . >' w n.iM 'tr \ M ‘ . 0 •• I J *1 J » Si V • , i. »SO j) ( ‘XJ ) (V. ) ;} - . 'i -iJ ^ X.: n ■ V. - li - u . • ^ ( (f. / V \ i (. ■•• . J ^ ♦ r. ] ( r lH G ! » ( ... t, .4 ‘ I ^ .. J. cf t,'.j iw- ( - i r (, ; '■i-Vi.: I ^ V u. - :j - j ■ ■*' ' •' ■; - ,J . . ! •• f.:) i - U- IJc iJsL :■} If-- / ' - / ■!, I ■: v<: • vr >. 'i }.:J.rlo2- ' I •. ;■ 17 . _ _ m Tf a,+b, T-f-f, t"*") -/ r? T^( a ,+b, -f , TD I'ta\ "" • H TCa b"*!? f T )'-T| a b ¥ f "T ) ' Equations (31) and (34) determine x and T; that is, the condi- tions existing at the equilibrium point. We derive P as follows from the law of perfect gases: PV - m'HT P,.V, - m RT„ V P where m' m-ix . V. Numerical Example, Case I. To illustrate the preceding points the following example is given: Assume a gas engine running on an original mixture of CO with the theoretical amount of air. P, =-14.7 lb .per sq. in. absolute. T^ * absolute .Compression pressure =160 lb. per sq. in absolute. Find the maximum pressure temperature and extent of combustion in the adiabatic Otto cycle. Original mixture is Mols CO a 1.0 0». e 0.5 f 1.9 m •= 3.4 For adiabatic compression we have equation (14) for which the constants are as follows: = 3.4 X 4.51 =15.334 Eb^ ^ 3.4 X 0.5666 -10^^ 1.8890-10"'’ 1 r • . X •f V . V - ^ . U ^ - V SI ■. c -lx W J. .* . . X - *‘ V * ' •^r♦’. y. c » t.' i -- A tj >. ’,‘J} • \ i A/il,-. \ -Ui- t ' U'J I. J , J : u t'i.'j v*-J lurl? y A . . J. ':oaj n , ..-I.'fffrjxl.. *v -';;ir ’.lO*;. uiivT t.w.'ii. ■ ,'i i. c.r. „.i>i.IXi. m ,I;‘. i- .ii i-iv' :..:v.i ^:’S o :. * , I* T . ^ ^ xi. # - »♦ .. •■ *jJL' ; iiovi j « i ^ iM ^ *( *-• ^ ‘ iy it ^ ' V ' * 0?.l ii; ro*"- •,iiix.JL(i.< ;' (;.)h * ./i ■■ A-f I . ' . ^ i f .’*»•» '"’. 'i • »\ ■* ^’ * #c» / .1 w j» ^*'1 U J • V.* .i 4 . l» , k '» *> ■j.’jiiJ 0 /W i'.J'X'*’ 00 Ij • i)v> ** t !. Q w.^t ' • i'iX .MjJXocf.,' r.' 'Cv>^ .ill . J!;. (.r- C- wvJv' :.. ■ J •: X'^.i ;<• t/w »Ja nv .f..t C ' u-; v:g 3uC i.: i. o ' w « 7 : 1.13 1 Sill i 'i 0 -■IdIJ ft - " <1 r 'i: QO - 0 t; d ii no *i,o ; (-^T) ••■.i,n & ^.v . ::. or, iroXt..i/C-,'XC 7 -;oo oXij 10 % ,‘ Utt‘ t-'-d ! T I't'' .Ji Xj.- X 0f\ i • l * (.1 00 ‘e-c.x (;I‘ dcdiil . C r 0 18. AH ^ 1.986 mAR ^ 6.749 Substituting the values for T,P,an(i Px. equation (14) reduces to §.5699^Tx =^ 3.14536 Brackets indicate logarithm of the coefficient. By trial = 1£50° . The constants for equation (34) iriiioh is the energy equation are as follows: a^*4.51 a^-5.42 =121. 250 b, = 0.2778'10'‘^ b^= 1.75*10'^ m -3.4 f , = 0 -0.16 'lO'^ T^- 1225 Using these constants equation (34) reduces to 3.4T(4.51 +0.2778-10‘'^ T)-20.643 l2T72gtf + Tri. 345-1. 333i 'lo’ T +'0.16 -W** 5>-) By substitution the following pairs of values are obtained from equation (A): T 5200 5300 5400 5500 5600 X 0.738 0.759 0.781 0.803 0.824 Equation (31) reduces t o the following with the substitution of the proper constants; (See Appendix 0.) log 7 ^ ( = -6.5661 log^„T+1.335-lo\ -0.08*lo'V-13.1+iJlog^ tlog tJ (B) To obtain pairs of values from equation (B), assume a value of T which then definitely determines the value of the right hand member after which solution for x is accomplished by trial. We have the following pairs of values from eq.(B): T 5100 5200 5300 5400 5500 X 0.825 0.802 0.777 0.750 0.723 I ( vO t .'S ‘ V.. f V • w , *.1 V S 7 • oX j . i. t. ii. .'u. I - ,, J.f! X ‘ X < -i W -i»* 'J O ^*4 V-' : c •VOxi.!.'- . '■ X ' .(J 0 .- .1 .-TOc ?c.oiIu >u*ir;iwf . t: I A « .. U ; ► rrf <•' ULi^r. C .'.'j : : ' > i ' V J.V -• c •r '■; 1' 'f. J... . : / - 0 •liiA!', -.a : ; -.I I:-.. . V ■i'.viX -. .. i\ L. r : cl| ; X. . '. i. • ■ >. . ' . 1 . ' V V , .)* V r V ' u", V' <,t ’ < (.? ’ . .’r.v .t;< i ;.i -'■) iff:--... J:. L .< V 1 i ‘ . « J. J ,/i J. X- it v' V - . J 11 ^ It 1 ( 19. Plotting the values for T and x from equations (A) and (B) as shown in Pig. 4, page ISa, the intersection gives T - 5335 X - 0.767 Prom equation (30 a.) we get P = m ■ Substituting values P - ^ , 1^0' 5 ^3 S 3.V ' P = 568.1 lb. per square inch. VI. Derivation of Equilibrium Equations for Constant Volume Adiabatic Combustion Involving the Heactions CO-^^^-j-CO^ and C0^-^C0+-^0^ Case II. In the case of the actual gas engine running on carbon monoxide and air we have the additional reaction C0j^-> CO^-i-Oa. from the fact that some of the exhaust gases are left in the clearance space. As the combustion proceeds, CO,, is formed by the burning of the CO, and some of the CO^ in the initial mixture is dissociated. We shall let x , denote the progress of the CO burning and (l-x^) be the progress of the CO, dissociation. Initial Mixture Mo Is CO a 0 e f m Intermediate Mixture Mols C0>- ax,-f gx^. CO a(l-x, ) + gd-x,.) Oz. e-i’ax, f-i-gd-x,.) = e N,. f m-'i^, -^-t^(l-x^) Let E/ be the reaction energy of the CO reaction. tt n COjj^ dissociation. -1 ^ 1. . - - * ■| V ; -v: ..vi^ » J'i Hi ' a I ’J •« f 00 ) O Lv'. - nv ^ V^A u • \% i \ ' L-:v '-f J.J L-y iOj^ui/O s' it -^ • - V u V/- , .0 a- : ; • . U '/ b fl*.' 0 C. ' C' V J w J1 _ ■'©' 01 * '.I .'t ■ * ■ . ■*! C i.'.' .■ 0 "i* .' V ] J._ /] 'v.v.- . j i:t) 7 ,,. , •'/,. V, i -O.^ wo -^n • »w : ^ .1 .. ■ J Pi' -. *::: L o.v»iJ c O •T' »..'' iULD , - ‘' . CO l/ful *C T ;; ;; t i V Oj- cTDi.; ..',v-J' aroi^ « • ^uo A< 4 f *V • i.i ''-f.(..;'r.' iit^J X’l '•••-•c " =i , •.-t.V i . .> , i.; .! ..'V 1 V ' liioir;- j*i;J ni ,..0 : ;•... 'IC «nO '* • ndS '^0 ; : ■ X .’XUd c,-.e1>0T 0'‘4‘ . :i ?< " r ■■- *£>0*ifi ii- oi -•>- -^-J ^ U V- ■■ , ■•• - s r*^f " 4 '<■*1 ■ V ; ^ M ur ■ ( n 'm ji, i >''t ^ ^ .. i r .*■ *• w*. k i ■'. .ki .• ^ VJi JjblXisil ' • !*• ‘ .. J, '’ {.--I)' ■ . , * - * i; \j- iJ 00 ' ^-X;a r fj -»0 ( ,j. - £ )7;i X f = w > 4. n- ^00 ^ ^ ~^«3 •H ^ ♦ a i);50'’X OO A -f •w . ■ 1,* 00 05^- ; i' r ' , 1 XI c I »ifx ad 0 x%i' Xh .00 »» n , *» i> H “ n 1 \ » ( Fig 4 Case 1 r"- — f - page fSa\ 0 ^ 1 § CO .Ll.Lt._l. CO !5 s 'X $enj&/\ t: te J5 c> SXF. 'Z! -a *'• p • ■> N. 1 . _ . c?. ,.f;; rcf \Si! . ’i,Ti ,;i> r^. <• b t "il' X‘ V? it i^.'j s £> ' b- - -■' * ''V !V'i 20 Let S be the reaction energy of the combined reactions. Then B -B , + Prom equation (15^ y, aA, dx, ViThere A, is the driving force of the CO reaction per mol. Similar ily E X /' Xj, gAj,dx a where A^ is the driving force of the CO dissociation per mol. Then we have E = E,•^E^» J -tj gA^dXi Taking partial derivatives of (35) we have (35) if = aA, (36) (37) Since at equilibrium the driving forces A , and A^ are each equal to zero, we have two distinct equilibrium rela- tions established. Prom equation (19) we have ^ ^ _ T-^-^ - ^ ^ ^ ~ 3 a, 3 X, Since energy and entropy are additive quantities, the expressions for the energy and entropy of each constituent of the intermediate gas mixture can be obtained separately and the desired partial derivatives taken of each expression. Like partial derivatives of all the expressions for the separate (38) (39) V 21 . constituents of the gas mixture Vvlien added together Vfill give the partial derivatives of equations (38) and (39). Sco, = a ^ log T -#• 2b f^T*' j - r[^ , -f- gxjlog Let s a/ log T 2b^ T f-Jf, T*" log T 2b^T From equation (27) / 77 ' J: p (40) m' ra Substituting these valies in (40) we have - a|ax,+ gx^Jlog J ■ -°s ox,i-3^i. fir P - aR ax, l^*" = log - gH For CO = [a( 1-x , ) ■^ gf 1-x^ )J ^s,^^ + f,J - s[a(i-x,) t g(l-x^)J log p Hr - ^ J ^ “ -s[s.^. + + gR log - ■ — p+gj ^^<5. a Ax aR For 0, 3^, = [e-iax,t Jg(l-Xi)j[s.,^ i- ,J -H[e-l,aK,<-te(l-Xi)J log g.. -i°*- ^i3C--x. ; ^ nr H: = -H H: = For R b _ 0 3 /, ^ -^Vx 3Xx tT) / -^' ■(’ 'si •ga - 0 The energy equation for tho total intermediate mixture is Vi, .v :;VC' c-*, Ln e^'T; w';: :• Ut-tv {, •\-‘' ^ (-V. ) -tr.T. Zc . > *io-- - "j Vi ^ ■-ni.fio Lcl^ia>. r ;’ '.,i- i ' c - Ov- X wl . -r ? ?::: * ~ ^ ,£ .q, .> ^ . • * ' ' ■- (id 'S 4, '^.ij;; ^ ,ua -• :: ^ci' is > * { ■ i ,.: „oi ■: 'viuJ' ' * ...sfii JUiibi;.. cX r- J i 1 , ' -'i cl .-' '■'.V jtil 1 * - ii ! 1 3 ? '" 1 .^ _xT OC lo'i ( fit i l;^/i.,..lL {fi V (, .“nnj ;,iC>X .,k' V ' «r C 1 - £ . 3^-1 ) ». / -j ^ - V ■ ftr* ..’vTj- r ^ w * 10 ^ . -A ;iX:i =-i).. ,■ r ■■-■ tf »i - ,tr:, C-' -' ‘V ■ , ^ *. , 4 . r ^ , «. ra • rv • ^ •' I ■••" 'L • 4 .4 al * I ' 4 ’irMlI- ■•T?. r. \ J\ r H lola 0 aJ j^xM;r- iTj-fti L^Co. .-.,« '• . CiX i'.c Si erfT 22. -h j^e-i-ax, t ig( f " ^ ^ "2 ^<^3,~~ ^Co^~J “ ^ ~ S -t ^Cd)^J - 3 ^V Collecting the various results we have If,- ^ RU, T-R] -1-r[-|« + <^, + /?/^3 ^t^±s0i2^r +7?J + T [-i S»^-i i+in/og^.P+iR] C^3a) a[R'3x,~ §x,J ~ -(R-i^)T-+(‘fxi‘l>OT-RTlf J-fr ^ j ^ 1 - saml „;u*- 0 ' .t* 'V. .,«! V t'CaJft'WoJ m i^^ s^ ■= ^li . ' L '-'"J'' ,xs, ‘jvr.if uiwitay feJl ‘5ni^o#lj:«0 ♦ 1 is - «d i. .K' y 1 ,- •r'-^ ,-■*! f( .f’ ■ * y V?'^ - y k « ’ * ' ' r c-t£j V <; 9*. ] I ‘4: . ??i ,<,r 7 k. e-^ 5 , . — «— « . wiiS?,^''. •«“ J- . ■‘ " ' ♦» ' ... .fc ■ .t , * ' . 1^ ■ f,v^ iy’. vji (» Cl) (a ^S) mo«i*f ^a «*Vi 4 A %• -* -'r-.'.,t •m ur.uj n? * “ ‘* * M'l ■ '' ' «> r| • • i!’ ■' •» iv^) bsm im) -r: e. ■ ■' A'*' ^ 'V - ^ .x& . ; ^ o?sx( 0m iX>) d’AJt^i 00061! ignffl tiitei 0 O ' *yf ' ^ M yl‘ '0^^S^A Jtk .Ui,>il‘'Xf. m A 1^ ; ,l0Myc i»au sitoij'uja^'t 0*1^ to tto'ioi"'?«»iTiyii nib ii XXjtw «n^i /& I ex ov^j ■ e in>J;#t'ii^ip ,«E(tf iforf^ £*w •tnifi iKfi !lap0 gtii»4 9£f^ 23 Therefore at equilihriuin X - X, ^X Prom equation (39) at equilibrium we have 0=H,-(h-iR) i*.) T-RT lojg Co X p /TV ' ' /-X [g'fJ (a -f-s) /-X -p/ e' 'R ,p- 'CO 'Or = /T, • '• F( /05, /Tp = f? - C/r - i i <^0 Substituting the expressions for (^^and + r+ zi,T+^f^T- J a,%r-3Ar-^ )jr' -(A - 3 ^) Collecting terms H, - ^ -(ia;-c:)/c>3T-{ii>.-b,) T-i(i tor -\k -in -(fa, -02 The above equation is identical with equation (29)* The equilibrium relation between x and T is therefore ^ / - 3 tC« ^ /r? ±3 ^x(F-^3)^ mt = - x(orO/<=>9r-^i,-OT~i(ifrn)r^ c i^Z) 1 fV^ . “ ► ^ V, * ^ V ^ ^ ** ^ Q ' 0 w t oii T ■] eT*«i ew mXiu-tllifpo it^JlSt) aoi; .t^v^S > i-. , . tX*’ . A > • 1'*!.. ■■• ‘ .1 • -‘ .1;' •*'% fl lluW ■ ... , ’V •. ■ . ■'>!•'.* mm ml y- ^ mUi'^9 A^l'»*.l^ulXn>jpX iK^iXaojpt eYorfa *.{t _ „ dXOlbiOilJr Bi r JbniB 3c cr^Bv-XatT aot^.:Xe%. fSuixdZXXii^fl ©nT -.(SSl { ^ C**'' -«-..■■■ lltilM^^ lt |l ■ •"'' ,. \t;^) ^ \ ' ' i^'" ”''' f ■■ i''^ (.VV)- ^ ; M . ■ Vs5v* ■ ■lIK ' - ' r7» i‘Nt.. > ,!» * , ®^3liitf a’S . '" V- ^ , J > ' j ./:.. 1 .wt' VII. Derivation of Energy Equation Case II 24. The energy relation between x and T is oxtic,-^g 0-^) /ia= (a+£)y.T(a:,-h bjTif^T") [nrfig-iCa-fgJ yJT[a,+b.r*f. T'J-u^ U^.(a4eif) Uo.^hlHV) + {a,^- 4 T, f ^ T^) •>< [(‘^ -^• 3 )He ~(p-t3)T(a^,-> bj-i fj^) + l(cn-3)T{a,-t = g Ha- Uj, i-(m ->i:g)T(g,i-b,T-tf, T'^) (a-tg) -(a^-i-b^T+fj,r) -t^(a, + b,T+f,T’-)J The solution of equations (42) and (43) gives x and T for the combustion of the gaseous mixture containing CO, COj, , Qj_ and VIII. Numerical Example Case II. The following example illustrates the procedure: A gas engine runs on CO using the theoretical amount of air. P,*14.7 lb. per square inch absolute. T^ = 650°P. absolute. - 150 lb. per square inch(«^5>. Assume that 10^ of the products of combustion are left in the clearance space. Find the maximum pressure, temperature, and extent of combustion in the adiabatic Otto cycle. The original mixture in the cylinder is as follows: Mols CO 1 . 00 a 0> 0.50 e N, 2.09 f CO, 0.10 g 3. =• m T *■ ■ 1^1' : X ■ w ,. I njiv.* .C,* ti'-'v't i.- / Cr:^a V „tA y'n ' . V f V J. ^ .1 J^.v) i ;■,^^ 'q)- * ■ I ■ ' ■ ■ ^ S'.-'.- ^ ■ -,• ! ,('T :'\ A t i "T^) t i ^ ^ ^ fai f i'T' 9 : .'- \ iJiilce ©rtT ->j • i ,■^> 'rf. li.iv -X/u -...'tJ 5.,J 'XCa a 0 ,^j 0 ;.; ’ ■•■■-' V.' . “tn ^ J.,U/Ctfie • S>lJ »/ .. irii, ijQ • i Oo 0 - • v^'*' ' 1 . :^■^V • r ., Cl ^ .'-v-ivUi .„ cv 'i.,/ Cw...v*‘iq t,^.a,^o.%X Xu.*"fJ cj . 1 -^ ,, ..^ . ..jisrxiiil. aiiX Xiil'i . jo-ite , V U\» V V( ^ j. ■- . UilJ* 'TCiXuuClV.OO V - * , w {,*•£'. o (it „':£xc: Xc iU: 5 i'iO v.i'X ■ -:XoM' ' * s’/' C. OC.. £ OD ' 0 \c ^ • \ 1 -.‘ •■* ’* • -.OC' ,•• ‘ \ * . ». , t 1 !•' ' VIT ■■ '« SJ 25 The constants for the adiabatic compression ectnation are = 3.59 ' 4.51 tO.lO • 5.42 - 16.633 2b^ = 3.59 • 0.5556 *10'’-^ 0.10 •3.5*10’^^ 2.345 'lo'^ =-0.024 10 m4H - 3.69 - 1.985 = 7.325 + mAJR • =23.958 Substituting these constants and the values for P, , T , and in equation (14) we have: (Brackets indicate logarithm of the coefficient.) log.^T^ + [ 5 . 6284^ T^- ^0.6385^t2 = 3.14879 By trial T^ =» 1250®P. absolute. Substituting the numerical values for the constants in equation (43) we have -JO^Q^ ^ 3 . 7 ^ S'! O.Z778 /O'^T) UO ^ ^ -/.3333 /. i ..V •• .:,c % ci- .. Ll I A > , I - - 4 . \«* V '.-I *' _0 TL . r'C 'J. 5' u J ^ y '. J. )';' ■ rroi.' j-i* a: J i.)'. / / i# . j.v »[*'? Uedc. ■ ■ ,. • •; : - 0 . (&'». • » ‘ • i "■'•♦v' , •. ( T \ S .« ■ ■ • 2 ^ V ^ A 1 V <,.N V 51 " 2 -.*^ • I r^,.VA ' /* v' \ ' \ >V ( .;• i j ' j J .iit.o >fi> - i.'t nc^'.’ u i^acfira fS . « I I c "€^ Ooa^ ■ CK la ‘.0 ci,-^o T z . ijv ;;i I . • { :■. i ) r.clw 4J* u *.l . ;rv-.-f:A»^o I;«ol"ref: fr V •'’• .,'.>■ ■i. •■ ■ ■ .. . ■ r."*' -t' .- V. >-■.- ‘ •V, '■-'>' ^ ^ . ■ .ii' (ij) ;;' ,cvi»i.’pt> r. ct,’'' ['i:' \:£ CrOW CCc'. 001 '^ I..V.C 5 :OE.O or..‘.o T'. $■ 1 ,;'^ : ■/ • I . i 27. The intersection of the graphs of equations (C) and (D), fig.5, page 26, gives T = 5135 X 0.819 ' m ‘ TZ 71 •p - - -k(l’0 i) 0,8 13 /5~0 -^/35~ 3.6 7 * izs~o P * 549.4 lb. per sq. in. absolute. Equations similar to those for the reaction CO +-|-0^ :^C0^ can be derived for the reaction -l-O^;?. H^O by the same method. IX. Derivation of Equilibrium Equations for Constant Volume Adiabatic Combustion Involving the Burning of CO, and CH^ and the dissociation of CO. and H,0 Case III. Y/e have available experimental data on the equil- ibrium constant for the following reactions only: CO ^0^ ^ CO^ -10 CH 20. H,0 CO^T- 2H,0 Y/e are therefore theoretically limited in our discussion to such gaseous mixtures as involve only these reactions. The most general gas mixture that involves only the above reactions is as follows: Constituent CO CH^ 0,. CO^ H;,0 sum Mo Is a b 0 e f g _h m E8. In the comhustion of the methane constituent of the above gas 00;^ ejid H^O will be the products. St the high temperature produced some of this and also the H-^0 will dissociate so that in reality the products of combustion of CH^ are CO^ , CO, and 0^. V/e shall use the follovang variables to denote the progress of the various reactions; (1) X, progress of CO reaction (E) y/ TT tr (3) z n n CH^ " (4) (1-x^) Tl T! CO^ dissociation (5) TI tl H^O (6) ( l-x,) u n CO;^ ) Produced by )CH^ combus- (7) tt tl H^O ) tion In determining the intermediate mixture consider first the CH^ combustion. (o)CH^ f- ( So)0j^-» ( Ecz)Hj_0 -^-fczjCOj^ ■+• c(l-z)CHy ( Ecz)H*0 ^ Ecz[yj Hj.0 -^^(l-ys )0^ (l-yj)H^J foz)C0^-^ czjxjCO^-f- i*(l-2^0,. -h (l-x^)CO^ We have from the various processes of the combustion the follow ing: o o o CO^ H CHy 1st reaction mmmmwm a(l-x.) -iax, ax / - — End Tl b(l-y, ) -|by, — by, — 3rd IT — “Ecz c(l-z) 4th disso. --- efl-xj 2 g(l-xJ gx ^ — 5 th IT hd-y^) ihd-yj by ^ — 6th TT — _ — cz(l-x,) i-ozd-xs) CZXj — 7 th IT Eczd-y^) oz(l-y,) ZqzJj --- u i I- •: ,0 ^ i •» . , r ♦ , ri- . uXIOJ. -Jj w - W S 4 %J '- - .'7‘-* t X i.hf‘ i.‘^ vh i.T 'v' uv' ilil-. v-V.H lr.r. ^'.0 t>i(' «>yc f'.^. -Xc; pli.; . . e*r .‘X P/m. ot? igaiuf-sr? • Li . , . . L . ■ ■N i . . . .1 Jt. '13010 *. J J . .ri(j ,.)w (X) >• ‘ f , iioiJ ^1' ' «' •. x> ^ ^ ^ •» .. f .1 1 f ^ A. i> w « i / i. V '' X (o) " ( (M !• .-X). (:.) '• ( -.:) (a) (.-X) ..•) nl ■, ' A 1/ v”< {.T!*!*C y ‘ ^ X ) L ■'■ V. , / ^ 'J^ i "t>S ) 'V " ,'0 { f;^ ) r ( 0 ) : .- - ) • \"l)' ’ ^- ,-i LL'i ' ; • V -'Ll ~ P’ “J. J. » , ' ^ .J. » . • W-' ^ • H' i» » ' ' ■ -0 %}Ji 'X L / 4 ). . . klq-x'z a>vjx i o-i ■ -,yi '■ y ‘ ';nl u i ■'i > I 'iff. ' 1 '' 'f f , -5 ~ li /' ' i f 0 U. u -y=a;iog T +2b^T + |f^T - aj-log T + 2bj-T -f -^fj-T i.e • i.e • i.e. i.e. i.e. for and CO. for CO,^^. for HjO. for CH^. for H^. n S!t9fJ0Xi ktioo j^OO ^ ■A ♦*ir i -i r :1 /??■ i 1 ?>r [ 5 ^S 3 - [ JAito/ii^’WiOO Oj)i &d4 ict 4 iJV H 4 - \ H A 5 ^ios-[ K.V 5 S-[ * • . _ $ 1 ** 1 ^ i 11 S ,'.J OltOO Wf^ -XO^ jr r - F '‘j I ^ ^ ” v*=^ '1 ' •*,1 'V 1? ■ . ■. - '- ,/tx; .», i ra . - I I anuarx: 31. For the CO constituent s„- ^6-x.>^g(l-x.)^ C 2 (hx,)]ls.,.i 4,] -R[ J log pj Ifr* -9 l -C2 I lj‘°= 3 Sco <3 X, 4,] 4 aTi log [ " ] -ioR [ ■ J /og [ " ] L ■ ] iCzR log [ •■ J -tczR L - ]-c(/-xjl^/og[ •• ]-c (/->,>? Por tne constituent, ^ CZO -(/,)] [ 5, 4 J -T\[ J -n,)p j ■■ J -/? [ " J 4 /i R log [ - ] 4 /? 7f •• ] +ZCZ~R/ogl .. J 4^czK, <3 5 . ;m. = - -^CZ [ For the 0^ constituent 6f-|a(l-x,)+ih(l-y, )+igfl-x Jf^hd-y, )/.ioz(l-x,) ■f c z ( 1 -y^ ) -2c z -i-( af b ) «./ hi'. J . . J I o -C. . . ^ * 0 = 2 * t A ■ ' »► ’>'- ♦ j \-\ji n ' ■ '^_ ) ^c.VrVs,3-i- ^ \ / l f ' ! '■ ><; .vc: I ^ ]>-. X - fc- ^ ^ ? ^ J . •* ^ /; ■ ,r » ]<- j r ‘ •44 t , ] '’'X- r ■' 1 ■ -S,-!- i •.4 4»^-4 ' V 1 .-».'> • jr . .1 \ ^ , J- . -..i: . .JvT '. ^•^,'^l^^“*‘ r^. « .. .. .. ' .KO.-. Ifi07-i .' - ’M .. i. y; iA-ij ^ vfl'-XXol \. ^ V.: r- w - . . )j. - ir,,'if:a • « ■ <■ _, . jf •• - . , i . • < , u -* i •: n ' ^ :::» i 0 -* I 1 li ' ( i ‘ r I .. ■'■ d i V , r* ( ”, y j V . . if O' t»: ■ 0 - u^; u- 4 ^ -•* » I i' I ~ H 34. Equation (46) plus two times equation (47) plus equation (48) gives H - Py 1 L J -E<^, -^) (49) CH^ CO^ -2 s. Equation (49) is tlie equili'brium equation for iaethtjae coia- bust ion. X. Derivation of Energy Equation Case III. The relation between the thermal and chemical energies of the above gas mixture is derived as follows; The chemic^iL energy liberated at absolute zero is Prom CO reaction axHo <^0 IT II II Oli^ IT n 00^ dissociation IT H^O II IT o o II -cz(l-x)Htf ) Prom c.e> ) CH^ II H^O II -2cz{ l-y)H^ ) combustion Adding we have U -U, ^ xH^ ' (a+g<-oz)f yH- • (b•^h^2oz) f H- ( -g - cz) ( -h - 2cz)-f czH^ U^= thermal energy of initial mixture j'ust before ignition. U = ’’ ’* at equilibrium point. I . » / i T ' ; w i.* ■ ^ ' ( 1 ►. ) I - OiU - ' { . ) :'i i V JLftjUi - H» • X Y.' r • i * V V-. i. * * (:.:•) !u.i r *•-. Ol K ! J 9 i 1 I U liO I I t f>rfT j i I I 1 , I 35 The thermal energy of the mixture at the equilibrium point is found as follows; U = / 2TydT == T(a+bTtfT"') ■'o The following notation will be used: « a, + b, T + f, T^' mean specific heat for CO, a,^ + b^ -+ f ^T’" If n If II CO;. n n It II H;,0 y^=a^+ b^T ^-f^T" IT II IT n GH^ >;^=a^ + b^T -f f^T"" n If II n 00^ present at equilibrium point; (a+g+cz)x H^O present at equilibrium point: (b+ht2cz)y OH^ present; o(l-z) GO + Oj. t present: CO = (a+g+oz) (l-x) ^ f OjL - i-(b+h+2oz) {l-y)+-|-(a-+g-H3z) (l-x)t |e-2cz-4^(ai-b^ Sum -g-(b+h+2cz) ( l-y)+^( a-^-g-foz) (l-x) +[i-2cz-i-( a+b) + :^ H present at equilibrium point; {b't'h-f2cz) (l-y) Total gas present: m+i(g+h-c) - 4 ^(a+g+ 02 )x-|(b+h^ 2 c:^y t /' ? Ox' v f :.l, • r-i' . .* < ■ •• tn'J’ ton- z-r^oJI-, . nr. DrjuDi { '" . r 1 r Ml. . 1 r V { t; .’ 1 M.. 0 • * ' fT '• - V*- X.,t' 1 f* tl *. •'' r , -V T w 3 ,.}»T r i - ' V U l»’ ? . u^-\q : - ■ i- ■ ' • v‘ ii U-E '•( J 0 ? 4 !C< fO I f.-Di) ( .V,t «) ^ •^. Jl h.-.r.trti ,0 ' ■ '; ; - C / f rd ) ’. “ fraur& : J. ■ nn .i..-"o jd ^aatoiq; H (i-X) (- 0 ^* r^fC! ) : inm .r'-J'-f’; v' ■•- ) ■' ^r- . :*3> rj )v- f m - - ,:.r/ -- ■ -i= I 36 We may write for our thermal equation: ( a-tgfcz)xHa,^^ -f(a+g+oz)|:(l-x)T(a,+b,T+f , T^ + ( a-<-g+cz)xT ( a^-»'bi.T-^f,,T’') + (g+hr2cz)yH^ -i-(b-+ht2oz)-|-(l-y)T( a,+b,Tf-f, T*") — f-{b-f-ht2cz) (l-y)T( a^-Ha^Tf T^) •+{bfhf2oz)yT( aj+b5Ttf3T’^) ■foz(H^ -2Ho. ) +c(l-z)T( a^-Ha^Tv-f^T*') -{gH +hH ) CO n f(eff-2cz-|(a+bj|T(a,-/-b,T-#-f, T^) - (50) Combining coefficients and transposing: (a+gtcz)x^-g-K}z) (l-x)f^i•(b-^ht•2oz) (l-y) a•^b-f4oz)■ p e_^_ X fm' y /^m' {— = Tty ?; = (atgtcz)x (b+htEoz)*’ y’' „ tTr^ otl-z) • (e^)‘' “ ^ j i, , i4. -la: fi,^ii‘7 ^ . I * • \ <*• ) (.-.I) ( :t>^^ ,. )■; V •! ■ i; ^ r»’ { _• ;- . • f ■ ■ ( I I I ' £J ) T \ f .) ,X -■ 0 ':^ ' d > t ) ■' * V B ^ \ 1 . ( :: -i > •■ r i , )Zyi:i/Vii d)r I ( .•’ (. •'£) d ^ } -i 0 ^v‘‘. C, • fi'A/ ; ’ )V( ■- ^4!:':- .n)soT^ 2:^ :' 4: ■ c .: ) ■ /•> r .5 0 > : ■! i:.c ^ > ■'‘•x'3 : 1' •1 - ( '.s' 1 ' , 0 - .O'" ; ' ^v:(*. 0 - " if ) )'. • C'T.'Sfc'rV X .-ocf) V • .'f% ( '; ? 1 .-3 ) £ ;r:o il '. v'* 'Ji > - ■ ji' ^ 'i )y »» .1- ’"n^ . jO ' r ( "V a , )D ( *;C'a’ >d ) ^ •V- lo , U 0 't©::'.V iipvi . (Iir A . ,:• ,yd'( o'-ir, • J , -.M ^ -5 , V iit.- ;. s.\ *1., . . -v^l #*44 -^nJ .v flo't fexiir ? (fry S^^!£jL ''h' : njL^*oJIot .V 0 . .) '■ J .: ■ /ICt. : ;.|J1: 1 ■ i \ ■ ■ t» fv. e r." x 7 ai'!Co •010X54^ ( V f ♦ *»* ■ • 1 ) ti) ' fT 0 ^ h i . ': , - ( •••X 4- 1 . j . ... .... .5 ■f-- 4 » •» ^ . J -T . 1 . ( “'Os'-'.' cl . ■/) / ■ H 37 . XI. Reduction of Equations &nd Method of Solution Case III. Equations (46), (47), (49) and (50) are the four equations whose simultaneous solution gives the valies of x, y, z, and T at the equilihrium point. Substituting the numerical values of the specific heat constants and expressing in terms of and T according to equation (26) v/e have 4.671 4.571 log^K,^^=12|iOO -> —6 *. -5.3881 log^^T+1.3335'10 T-0. 08-10 T-13.1 (51) -6.2621 log,^T+0. 2361 • lO'^Tf 0.0333* ld^T+1.1 (52) 4.571 log,^;. ^-^Z2^ + 5.6183 log, T-0.0552* 10 "t-0.0133*10”^T-22.4 ( a+g+o z ) X ^.1 . 34-1 . 3333 -10^ T+0 . 1 6 •IO^T'J -<■ ( b+ h+2oz ) y 1 . 72-0 . 2361 ♦ 10"^T -0.067* lO^T^'J - c(l-z) |5.04+2.500*ld^:^ + ^+ffa+i(3g+h+c^|4.51-K).2778*10'^T] (54) , 121250g-H02100hj;cz. 21570 - Uv ' T The solution of the above four equations would be much simplified if the value of one of the variables was known. We arrive at the approximate value of z by the following method: The maximum value of z, of course, is 1. If we establish a minimum value for any given case, then the vflue of z is known to be between this minimum value and 1. When z is a minimum, the partial pressure of the methane constituent at equilibrium is a maximum. Prom the equil- ibrium equation we have at any temperature T the following: n i: 10 ‘ ^ ^ • 2 a ... ■> '. iiv .1, ^‘•■^ ) -'.- \ . . ) , ' » , V J. . fi 1. 4. ' • '‘ 1^ Vt ‘ ^ ^ U i. ' T t . \ • *W ^i«T‘'’:'5’l^i:t' ijpo Ow I X. I J. ' 01 ■£; .^OX C . 0* .I:::X . i: ‘ r t' I j. ■ V'. 30.1; n .i. OX' « O’ • "* - ^V> J. X> (■ • . 0:. .. - OX xva. ^ , - jTl - u.r*^ * 1 0. . .* .1 0 t ‘ .. ./ -. - ox - . -■* ' •■.( J-v- - ' j .. ytjJJ O M'O J. !;:i;::.^^SrJj:JixJ-. ' .. •-. .• ,, •••;<. . 'io ii X'f^'IOG ojr.X ; V ;• ■/ry xo o:V* _i .oei . .LlJp; i:o ^xixr* t*..j.O' ijx ..\’.:.»c * ■ ■ ,i: kj; : ^ cvi i'.:.j os'- , r .7 *0 tfi.J orix^ro oc^l. „ 7Vi’'l ■\. - ,. , . ,:wVi ,’^. c* ?r.-0 fe.!.:!.;'/ "iirr-tn.lrj ^0 -• 'r 7 i -.‘.X ';«■*. . . • .«/ , . '■>. I . . Xt ^ «4» .. ;.i. 7/L . ’/ .iA . .A . . t> L - K QJ .A c .t . V - iKOt 7a w . r>ju^Xj stroo --S^xfXdm :••• .vA’dxXol t’i'j 4'7-.;X .i'A©.. ::.vJ v.fX; jo :;v,ri .-w ar^io'dl \- r . A , ,t ir "f' 28 . If we consider that there is no dissociation of the CO3. or H^O; that is, x =1, and y ^1, then the partial pressu of these two constituents will he a maximum. Also, the 0*. par- tial pressure will he a minimum h ecause more 0^ is required to completely hum the CO and than is the case when there is dissociation. We may further decrease the 0^. partial pressure at equilihriurn hy furnishing in the initial mixture only the theoretical amount of oxygen required for complete combustion. Under these conditions the right hand member of the above equa- tion is a maximum which will make the partial pressure of the methane a maximum. Substituting the values for the partial pressures with X »1, and y -1, we have, using the required oxygen, the following: V { a+gfcz) (b+-h+2oz) From which ( 1-z) | ( atg-fcz) ( " I 4c^ cz) (b+h-hScz) X If By putting z 1 on the right hand side of the above equation we get an approximate value of z which is slightly smaller than the value indicated by the equation. (1-z) ■E (atg+c) (b+h-f-2c)' 4c'^^ 1 (55) From equation (55) it can be seen that z will be a minimum if c is a minimum for a given value of • Of the gases used in gas engines the methane con- stituent is the lov/est in producer gas. An average producer gas has about the following composition by volume: CO 22 mols a CO^ 7 mols 8 " b 61 ” f CH. 2 ” c total 100 mols Substituting these values for the constants in equation (55) we have ( 1-z) r(5i)(iE)"7 L' 32 n/ J (56) e * .. - .!. Iv‘ ■ 1 .' ) c. • •ij. . ^r*: i i*v ' c i G * t* - 1. vv ■■ i ' , J- .. , ' ■ ' , ' I - ; w. ' 'io ,1,1 oc '.i-, .t Jl ;.;' L 0 ..r.^ .l ’ '■ ‘.,1. :'i i- a IV :• XII> . ■ X io' . ; .• -cTJ i.Li !. ri«>i •. tuv ."Cv/nic.: w < L. “I'i :.V -:;6 .1 -iJ 17 tV . jioi '. 1 ■ : : ' - rJ i >-:v^ *r; .. , i.-'ciXi:;! » c.. • T 1' ?>t - -'7; . * .r. .j;,i ..' i • Li'J'o'iC'orij ■ ;?i.,A- s': ;» ■ 'J r ' isOi-Ii X..U" ,n , ' » * r::ri7x^. A ei rtoiv . :■ -. . a /.V G 4 . o/J , V « V : * l^Gci u frsv' . X - jr' » C - it d^XV'- : yii'.vc X lO-t ! • y I * Cf*- ' ■ ) ^ { Tt •: ) (;., o* r^ )' I j rc'x'X ( *i < , - • ) - : .r c‘ ... X ■; f ^ L -V i X r . ?.c*: i.' ♦'rf I r‘ , f;; w vVs'Ji . ,, j .» ;f i- Tkv i ,;f. f 1;: £ • £ v#XXji;:'\-: (;'-X) ou . : .<-5? i. I 1 : L *■■■■— i ' X '■ ( ' i V XJ,„ V,: t i iJil- .: vtv aurjr. w. i* „u.‘* .1.1 f^(T) -0.8750.1og,^T-1.0972'l6"T+0.1133'l6^f-M4.20 JZi f, (T)-M^^tl«34 - 1.3333 *l6 Tt0.16*10’^T*' fj(T)-i9|i22 + 1.7E - 0. 2361-10 T-0. 067-10 T f,(T) f,(T) '3 4.51 + 0.2778'10 T 12125Qg-M021001if21570Q - U, From (60) we get, using notation given atove: & For any given temperature 0 is fully detemined. (61) Substituting (61) in (58) we have = log"' flitL2)l= x( 1-y) |^4.57:y Gx log /o ^ nOx __ f*(T) . 1 n__m.l Pi, /,»v 43^ ^2 '^^+2 (62) x(e-i) ijj Substituting equation (61) in (54) with z 1, we have the follow- ing, using the new notation: x' j(G-l)L f,(Tjjtx{L-f,{T)-(G-l)[s-f,(T)+f,(Tf| + iiG-f^(r)| -js-fjCD+f^d)] = 0 (63) To solve equations (62) and (63) proceed as follows; In equation (62) assume a probable value of T sons- where in the neighborhood of the expected result. The right hand member of the equation and the value of G are then determined* 41. Solve for x by trial. Plot the curve of (62) with x and T as coordinates. In equation ( 63) assume values of T which then reduces the equation to a quadratic in x which can be solved by the quadratic formula. Then plot equation (63) with (62). The intersection of the two curves gives x and T of the solution, y is then found from equation (61). To detemine the maximum explosion pressure we have P^m'T P = (64) XII. Numerical Example Case III. A gas engine uses a gas having the following anal- ysis by volume: CO 20^, CH^ 1(^, GO^ 8^, 2^, N^ 20^. The thecretical amount of air is supplied. Assume 10^ of the products of combustion left in the clearance space. Initial pressure and temperature of charge in cylinder 14.7 Ib.per.sq. in. absolute and 190°P. Compression pressure 150 lb. per. sq. in. absolute. Find the maximum temperature and pressure and the extent of combustion in the adiabatic Otto cycle. The gas mixture in the cylinder at the end of the suction stroke consists of the initial gas plus the required air plus 10^ of the products of combustion. The charge in the cylinder has the following composition: Mols Mols CO 4.00 a 0.62 h H;. 2.00 b O- 6.00 e CH. 1.00 c 23.10 f GO^ 1.38 g Total number of mols - 37.10 = m. 42 The constants for the adiabatic compression equation are 34. 10'4. 51+4. 04+1. 38*6. 42+0. 62-5. 04 -=168.435 2b^ = ( 32.10' 0.5556+2.0 *0.5 +5. 0-hl. 38 -3.5+0.62 -1.25) lO'^ -29.440-10'^ -f(-1.38‘0. 4840. 62*0.2)10'^ « -0.2692-10'^ mAR ^37.10-1.985 ^ 73.643 aj-mAR - 242.078 fn Substituting the numerical values for the constants, equation (14) reduces to the following: log/,T^+^.72277j T - 6839oJ T^ = 3.15392 (Brackets indicate logarithm of the coefficient.) By trial substitution, T^^ - 1230°F abs. The constants for the energy equation are as follows: L= 6.38 f^(T)=. . ; n =4.62; 17945 “TT" r = 5.50; s= 34.98; U^=234,252; Substituting these constants in equation ( 63) we have x" [6.38(G-l)f, (T^+x[6.38 f, (T) -(G-l) ^34.98 +4.62 G f jTjJ - |34.98*f3(T)tlZ|i5j :^0 (E) V/e have the following values for the various functions of T in equation (63) according to definitions given on page 40. T 4700 4800 4900 5000 5100 Log G 0.9320 0.9479 0.9646 0.9804 0.9965 G 8.551 8.870 9.217 9.559 9.920 f< (T) 84.411 23.891 23.398 22.928 22.481 f;, (T)22.041 21.527 21.030 20.547 20.082 f,(T) 5.816 6.844 5.871 5.899 5.927 It) 3.818 3.738 3.662 3.589 3.519 ' .L J r i - i M t I f . j ( .i.i ) . .) A ?* ;j 0. ■ : , { ;r ) JC> ■*a V... . . i . J.l J ( ' I 43 . For T 5000 equation (E) reduces to X*- -0*6935x-0.1677=^ 0 By quadratic fomula x = 0.802 We have from equation (B) the follov/iiqg pairs of values: T 4700 4800 4900 5000 5100 X 0.707 0.738 0.770 0.802 0.835 For the second relation between x and T we have equation (62) which reduces to the following upon the substitution of the proper constants: r5.50-3.19x-S.3l6x li L L inm-rj For T =*5000 the value of the right hand member of equation (F) is 0.78662 Solution by trial gives x = 0.800 Similarly we get from equation (F) the following pairs of values: T 4900 5000 5100 X 0.849 0.827 0.802 The intersection of the graphs of equation (E) and equation (F), fig. 6, page 44, gives: T- 5050V <>^ 3 . X =0.816 For T -5050, G -9.751 Then equation (61) gives y-0.977 Equation ( 64) gives P- = 543.3 lb. per. sq. in. absolute = f^g^ '^-ilog 1-0.16241 (?) u i . • >' ; . . i ... ■. j I '• •• > V ^ V ^ ^ w • * » ' V . ■ U', . i' u 1 . . - .s V I r ■ C ... • , r : •• !' . ; • ‘ .'V iU ^ i. i < . I ■! L' ■ V. • ! 'j .-r. I ; ( L ) ■■ .'■'.ne r > 1 t .1: ( ■’. I . '■ > • . r, r- - 45 ZIII. Effect of Loss of Heat Luring CornLustion on the Maxim'um Temperature and Pressure and the Extent of Combustion in Case III. To show the loss of heat by radiation, conduction, etc., during the combustion phase on the values of x, y, and T, various percentages of the heat of combustion ^all be assumed as lost and the corresponding values of x, y, and T calculated. The only change necessary in the equation for the adiabatic case is the subtraction of the desired amount of heat from the left hand member of equation (50). This results in an additive term in the numerator of f^ (T) .TAe equilibrium equa- tion is not affected. Let H= total heat of combustion of gaseous mixture at constant volume and 6E^P. 100 K percent of heat of combustion lost. Equation (63) then becomes: f,(T^+x|L f,(T)-(G-l)[s-fj(T) +f^(T)t^]+nG-f^(T)j -js f3(T)tf^(TH^j = 0 The above equation with numerical values for the coefficient^ that of x being equal to 1, can be obtained from the simplified equation in the adiabatic case for a given temp- erature by subtracting from the known term of the quadratic KH T[;iG-i)L-"f7nrr| X the value of this fraction multiplied by (0-1 ) and from the coefficient of equation the value thii If values of K that are multiples of each other are chosen, the quadratic equation in x and T can be immediately 1 r j •>/ 'TV ’ . 1 X A ^ ^ 4 • .JL s * / , .* ■ w r» ^ '; .0 i i; ' \ » r** ■*4 '• I *' .A. 1 r 4i.S' V- . ■ X . *lv* rVO./^t> ' \ • M . I* , *■ 1 1 ' ’ or.', .* r i Jt^i^L-i -. t;i>rX;.lf r il: '. ;■ io « ■>■, \5r,J :... ^ a^joi’i.-v * -''':.■ I', ol -t '■ i;:r. , 1& ,c;c:;.C.v ’;■ I^..;y';,'J‘C'^ oJt c.. J ‘xo - ). i,;,....: :.' .'..J'l.l V- oru:« o UV' f 5 ';X :.(• { .*. - * i '-'f.w 0 X *..• i L < ** ' *D ••• i 1.' V X ^ - X t ...I .,' u L ! .i<\ i. i . • . \>v . / ii A J C 1. 1 '.) IT' '» 0 f.’JOl.'J i; k. iOJ. Ollk' i'tO*; il - ::■ i- '•;. .( ) 1 'to '-C^ -■*;. . a.,;'. oi-J^ r *'f- • y ^ V 1 ‘ .L • ^. Aj \ ^ ' i,» ^ * ... i.’ - ,t. ^ -,►/ *i . * K ^. ■ u ^ w 0 ^ ^ 0 - •vj.u c -I ri*^' xu Ij J jt t!i if-^ .i {• '> M > V , :, « ' Ir.C -l L.. ..'.) »j; : ;.o I"' -•• .j'i, ^ OCI .' .ii. . C i. ■ t y; <> (f'iv ) f'C C'^’ 'ir''<^ H ♦ 1 ■ > (■'it. f{-] •.. . ,. / /■r’l \ -i / .^ • J I -s . } UT'-v ., (■: ).1 0 - ' I, :^r{ X^K. !.*.•::/• uiTJ.v/ rv. ^ t.<,.'. f,-..T , V . ‘ T r / , ' > <* ‘ \ , .' t *z i ri*l _ X.- J o . - iv .' run) , X Ow , w‘ i':w7‘ 01 •■ :> Li j.~ ' c."^ ivl J -i .3 c'f/j v,.iw* .i' r-xf-s;' to V nt '. f . .'I- t.£'. i.'.u'l !, (l~ i ) . ■ ; c /; iw’ i X <• A. tu 7 ^ »ji « ■; :X 0 X /aV r.''j ■<..'). :.'■. ‘it '-.'/pfj- li. uiti acw -j ■ V / . , /'i J' J Qiiv . X"‘ O'.. »-'-■ I '• ■ '’' ' .i .J ' A- -**•)... , ', iw 'x.Oau;.. •IJ aimut ••■ ■• ■ ---5«ea(Beaf5»v--'^.;?£=: -..r 46. written down from the equation of the adiabatic case after the correction terms have been calculated for the first value of K. The following values of K are therefore chosen: Case No. 0 1 2 3 4 0 2.5 5.0 7.5 10.0 H 1,038,070 from analysis, page 41, and heating values given in Appendix B. For 5000°' and Case 1; 'm 1 _ 0.026 • 1038070 ^ tr‘ ((J-l)L - f, (DJ 5000 • 8.559 - 6.38 - 22.928 " j(G-l) = 8.559 ' 0.00415 ^ 0.0355 For Case 0: 0.5935X - 0.1677 = 0 For Case 1: X*' - 0.6290X - 0.1718 =0 For Case 2: X*" - 0.6645X - 0.1760 ^0 For Case 3: x^ - 0.7000X - 0.1801-0 For Case 4: x’' - 0.7355X - 0.1843 -0 For the other temperatures we deduce similar sets of equations. Solutions of the various quadratic equations give the following table of values for x; * •'“iw . . •: ► I- Cjt'iVI \ } V* .'I - a t . » J " I 1 < • • j J. * - I 1)1 o f. 'fO‘j 47 . T 4700 4800 4900 5000 5100 Case Uo. 0 0.707 0.738 0.770 0.802 0.835 Case No. 1 0.738 0.770 0.802 0.835 0.868 Case No. 2 0.772 0.802 0.834 0.867 0.901 Case No. 3 0.802 0.834 0.866 0.900 0.934 Case No. 4 0.833 0.866 0.899 0.933 e.967 The following pairs of values satisfy the equil ibrium equation (P) , page 43*. T 4000 4300 4600 4900 5000 5100 X 0.970 0.945 0.905 0.849 0.827 0.802 Plotting the above values we have the chart, fig. 7, shown on page (48). The lines for heat losses from 15^ to ZQfJo were obtained by extrapolation. The following values of x and T are obtained from the chart. The values bf y are then calculated by means of equation 61 and values of P % loss of heat: 0 5^-/- from equation 10 15 64/ 20 25 30 T '^I.abs. 5050 4930 4810 4680 4550 4410 4260 X 0.816 0;.843 0.868 0.892 0.913 0.932 0.949 y 0.977 0.980 0.983 0.986 0.988 0.990 0.993 P#/sq. in.abs. 543 529 516 500 485 468 452 The curves on page 49 give a graphic^ representation of the data given in the above table. Prom this curve sheet it can be seen that x and y increase with heat lost during the explo- sion phase while T and P decrease. X 0.36 ii!i -p.- \ ‘ I’i'^ ':.1 . ' ' , ' i ■ .r' -pr - ‘ % y-^ i \ e* ' mM-i: [4700:^ s/0 460 Oxi 4m of Heat Dun/ 1 ^ the Mmimurn Expios f on on Te imperature and Pr^ssute the €\ient of Corpbu^^tionj^ j/fe/j-ce/it Z.05S ■\V.) V ■'tH-l-p . 1 .. p- \. — • Mii -Li- X. !*i. ti|:rrl' i4- ' ‘ f: ■ X.. -. N, ! ' i > ' h 1 , J.J, ' aliX : H| 4 ? !;:, ^:h:1S 1 , [1 lilliiii-' S : ' ! i\, / I ew X l;:n ■ : ; . : 4 jJ ^ 1 / Ha ' '/ H - : HTV "T ■Ci'\ I u<' 2a m a : ■-:: am “ » 1 jr 1 \y j^ |:3 *' t ' ; 3 tL. i > ' ' ' ! ! >: 'Icxm \ ..^.a aw «s«JiSV \ :jj'; 50 . ZrV. Effect of Excess Air on the Maximum Temperature and the Extent of Combustion in Case III. To show the effect of excess air on the values of X, y, and T, the preceding problem will be recalculated using various amounts of excess air. It will be assumed that the compression temperature is not affected by the excess air. Let 100 B ^percent excess air. To the analysis of the charge in the cylinder it is necessary to add to e, the amount of oxygen, Ee and to f,,the amount 3.8Ee. In our general notation the following changes are made: r is increased by the amount Ee S ” n Ti If n 4,8Ee f^(T) is decreased by the amount 4.8Ee T«.( a, T^. ^f, Tp This change results in subtracting from the laiown term of the reduced form of equation (B) the expression 4.8e fj(Tj - CGrirr’X' f/n?') E and from the coefficient of x the above expression multiplied by ( C -1 ) . Having found the value of the quantity inside the brackets of the above expression for any given temperature ^d having the reduced quadratic equation from the solution for zero excess air, the value of x is easily determined for any percent of excess air. 61 V/e have from the solutions the folloiving values of x: Temp.°P Percent excess air absolute 0 10 20 30 40 4600 0.678 0.682 0.689 0.694 0.700 4800 0.738 0.803 0.867 0.935 1.002 5000 0.802 0.873 0.945 1.017 1.090 The only change in the equilihrium equation (62) as given on page 43 is the addition of the quantity Ee to r. Making this change the following values are calculated; Temp • °P absolute Percent excess air 0 10 20 30 40 4300 0.945 0.968 0.977 0.981 0.983 4600 0.905 0.934 0.948 0.955 0.960 4900 0.849 0.881 0.900 0.912 0.921 5100 0.802 0.835 0.856 0.872 0.883 Plotting the values given in the above tables we have the solutions chart, fig. 8, on page 1 are obtained: 52, from which the following ^ excess T abs. air 0 10 20 30 40 5050 4975 4890 4790 4680 X 0.816 0.866 0.902 0.930 0.952 y 0.977 0.984 0.989 0.992 0.993 P#/sq.in. abs. 543 537 530 522 512 The values of y are calculated from equation (61) and the values of P from equation (64) as before* The above table is presented in graphic^, form on page 53, fig. 8 a t- : - ■j’} a> Vi n i r Of. 1 ' rO< i'V> a ■i * k*'a «4 i O' ’.• . . O^L- 0;/ (0- I ... iif" . I'j C.1 ■ X' V. .i .■ .. ..:»i ; •', iu ' ' V'. % . , > : * ' • • ii ■ < ’ f - '*.■ * -*- . ..■ , i.i..' 7. , \ w'. V , ‘ ' C. ■• . .’•if: • ' ♦ !,' .. ,' ... ' 1 . V \, i .'■'. \ 4 ’ . I t: . J.'vi ..; Up© uiCA.^. '; '1. ■ .i ■/ u^: *'■ r \ 035 O ■I \ \ \ I I r i ' / , ' } \ \ ‘\ o \ & , J Q X CJ a ty U-. ^ r' % iP J 3:' U . 1 -^ i^ C7 -t j. rs •r^ > - > P* rj % y i# I ti ■ f ^ r . ,p o M L' - f *d '' ^ / / / \ : !/ A 1 f . 1 f Oc)^ Y ?» Vi’':»^''iJ'^ a; ^ VV'"'-'-'! L> !V ' ■ ' 0 ■■t o> <0 ^ i o 'p P . . a . ^ £? ,V _.' i^,i.. A :''::v.r ■ -. L ,' .'. ■ - * t ‘ ".■■■■; '' ■ M ' : St ‘ ‘ ; . , . L til' • ■'■ i c? iV I ''.IV. rv* /"> ? U.:-N‘.- . '-' K I ': 'Mm IjJiy i : uiiiiiL±iiJ-^4iiL ^ ' '.O' 54 The effect of excess air on maxiraum explosion conditions is the same as the effect of heat lEt by radiation, conduction, etc. , namely, to reduce the amount of dissociation. In the case of the actual gas engine where both factors are present we may conclude that there is very little dissociation of and 11^,0 . ZV* Extension of Analysis to Cover Gaseous Combustions Involv- ing the Hydrocarbons C^H^, and C^H^. We can extend this analysis to gaseous mixtures containing such hydrocarbons as C^H^, C^H^, C^H^, C^H^ , etc., if we assume that the combustion of these hydrocarbons is com- plete and that the reaction proceeds in one direction only. In other words, the final products of combustion are 00^ and Hj,0 which establish an equilibrium with respect to CO, and 0^ without regard to the nature of the original hydrocarbon from the combustion of which the CO^ and H were formed. The basis for this assumption is the work of Professor W. A. Bone and others* on the combustion of C^H^ and C^H^ each in the presence of its own volume of oxygen. In the cases v/here the initial pressure was sufficient for detonation the products of combustion of both the mixtures C^H^fO^and were CH^, CO, CO^ , Hj_, and H^O. According to the previous discussion, if sufficient oxygen had been present the methane would have burned completely so that the final products would be CO, CO^, H and HJD. Since there is always sufficient oxygen present for complete combustion *Phil Trans Roy Soc v215A (1915) 55 in gas engine mixtures, we may accept the assumption of the complete combustion of the hydrocarbons as being very close to the truth in gas engine explosions. It has been shown previously (page 6 ) that lack of specific heat data at high temperatures for the hydrocarbons introduces no serious serror in the calculation of the compres- sion temperature. We are not concerned with the specific heat data of the hydrocarbons above the compression temperature be- cause in the energy eq.uation we consider the thermal energy of the final products which with the above assumption will not energy of the initial mixture which is at contain any hydrocarbons and the thermal/compression temperature. With the assumption of the complete combustion of the hydrocar- bons the conditions at the maximum explosion point of any gaseous mixture ordinarily met in practise can be calculated by the methods of the preceding pages. * •»Qi to e^*r oO’itv;a •ti- oi^Jt4fe»iJrfiaco i^nXqjljoo «or.:. dd^l^re u«% rtt :#it4 r. -wt' ■■' ;: \ - ■* ‘ 3tl U ( 3 ti oooU mixl^'41. '^ * ^ ^ Baodxoco^fr^ eriJ^ loTc xi:- -'xciw»4 cijid 4-i «4«Ji 4^od ol^-toeq^ io i -aai ffiiot' l4 isci4. luol o &:i‘4 aX •xci'xos ?jBOii»a on 8eouic«4nl ' • ^ • • 4a© I QlsXa&cru itdUiiXtw i^&niat^ffco 4 ML. •* hcIb -® ©rotfa ©44 d4iiai doJtrtw 84ofrX>o^q XsnlY od4 Iko 4« ai liolf^w gtp^tjUm X*iUini frfu to \;3ioa6 oi«j4ai©qmt'4 noie«©*i*ncoo\l3o;*iad4 ©iCr i)na ttnoji9oox5^ w> nJt©4aot , -inooxtiii ©44. to acl48^ooioe tO noi4.(aiyi«© od4 44jtW to ittkoq aoliiolaxt s-asil-^a ©44 4© im©i4iMoo ©xU ©^Ou jbeJcXuoXi O od ii»io ©e44o#^q «i 4$w niiiiuxlAio ^Ofiuejs , . , .30^^ snXfceoouq od4 flJyofI4oa|i ©44 56. Appendix A Specific Heats The following is from manuscript by Prof. G. A. Goodenough, and gives specific heat equations for 0*_, CO, air, H^O , CO^ and CH^. ”In the analysis of the processes occurring in the internal combustion engine an accurate knowledge of the specific heats of the various components of the gas mixture is of first importance* The specific heats are required (1) in the deter- mination of the variation of the heat of combustion of a fuel with the temperature; (2) in the calculation of the temperature ' attained v/hen the fuel mixture is burned; (S) in the establishment of the equilibrium equations for the various reactions that re- ceive consideration. At the present time it cannot be said that our knowledge of the specific heats of gases, eppecially at very high temperatures , is satisfactory. The results obtained from experiments are discordant. Any expression for the specific heat of a gas must be regarded as conjectured and subject to change as more reliable experimental data are obtained. Experimental methods : Two principal methods have been used in the deteimiination of the specific heats of gases. (l) The constant pressure method in which the gas under con- stant atmospheric pressure is made to flow through a heater and then through a calorimeter where it is cooled. A comparison I ' i \ • i ^ , • -..in fiXJ. . • X U:e I-nr*' fi [1 r;-‘. . ’’ c. 0 ‘•p. . : I t - - .!. 'J J O .. . ' L-t \i k .ft 0 u {'. / i ' “ ‘ .■ t .'HO , r j . -I. 0 r l- . u jj . -t' :-i '.. j.' -I. i j. — ... , . I .. ' * ^ .1. \ I OJ U V/ I ' ; f i. w ■1' rx-.'. ■du X/j' ; ; s (i ' H ' I'i' 67. of the temperature change with the heat rejected gives the specific heat. This method was used by Regnault and subse- quently by Joly, Holborn and Henning, and others. It is ap- plicable at moderate temperatures. (2) The es^losion method used by Langen and by Pier. A combustible mixture of gases in a closed vessel is ignited and the rise of pressure is determined. The change of temperature is calculated from the pressures, and assuming that the chemical energy of the original mixture is all transformed into thermal energy, the mean specific heat of the gas mixture for the temperature range involved is readily com- puted. The explosion method is the only one applicable at very high temperatures. A comparison of the results obtained from the two methods shows that the explosion experiments give specific heat values somewhat higher than those obtained from the constant pressure experiments. A critical discussion of experimental methods and results may be found in the Report of the British Association Committee on Gaseous Explosions. This is published in Clerks ”Gas, Petrol, and Oil Engines,” Vol.l. T he Matoiaic Gases. Experiments on the diatomic gases as nitrogen, oxygen, CO, and air, appear to establish two facts. 1. The specific heat is a linear function of the temperature. 2. The specific heat per mol is nearly the same for all these gases. ■1 ti. . (.'-1 « - ■'/ V'f ^Ct^! fl. Vf :;vV . . oi; wi’*’iD3f „ -■*£• ~.c • ■ ‘:'’C ■’ ’ • :!• , fxi.\ , .f'»“i. v.. < ■ ■ '•' ( '-' ) • Jt- ’i. 'll ‘i’.icJ ' r: :,i., J’ii •. ■ ■- ■ ‘'.i. ' -X.'.^. J.: ... ; 4 . /;u. yo^ii;-..' *’,d = J i* * . ^ J . 1 ’.' ■ V S i» t '^ - ■ 5'- • c^;”^ k! .'C .*,.J<% Ci.v Xv-i.1 tJ j. V !..'.* t' 5 i.w iO ; !. I J< t; -< a.v; qtl . a' .'. ...i 2 iv. vr - i.i x i ,..j : e. X . .u\ • JLL 7driJ • - X'. I -r;Ci. >^i*: •.: , ...V. c-vnl . :ixji f-i x ‘Xu ov J ;; oX.- , : xi .'■ • ;.r.c ; : < ^.X oc;;^Su; .-XX .?i " d-a^' . ‘jOCUlo c 'vX r*C'. : . . ri J .-o': &i'x 1', .too : r; ‘ *0 "A s, • w' X : / vj v_t'. ?"7l . bj... i'j. i:cXuO'i,p:o v.'’ : .i 3t X ^vt: Hr: i>X>oHXvu. tr '■. . 0 ucOf* ;ii 'w • ;.i X :\ .»- .. J . :c>r:.X. i .- jO ''. o X.': ?. l',,i‘'!'^ cn J. V. r»v ^'ii‘<,. .iC .f. otii.. j *y .x^o.i.X.1 '.' j Xi. ,'^.01 :.■ Ov.:*rr-.-. ,‘OlXf'iu pXX xv tJX iX .‘x i; >'i ei v;-n ..Ju;:iC'i:'- fc. .* i A JI'ijxrfT ti *:jO A • -' ' -< .'i .. X C fft OsXX A..^.:^pO, . t. Co'.' .t,rv: IX J _JX:r- .loilei- . axsO” 'J- - '' V If!^' ' o "' .f. CL F^ti L J ':i.^ r*/' V.-X /LniX A.J.'.e L>J h:n ,1. , , aox-o'^Xx/i ti > : . •■ 51 . .J X >: !.' V orii *t.: riv xXo."j:i'r -i.c^j^TX! l: ?i i. I XX oo <:>;?2 ortT .1 c:n;:x n: ' mcX cH* rS-: i lo;n *iy « ol'IXot>-;2 oXl? -X ' . ■'.r * ' . ♦ ij *j ^ •>*’ '* . » .7 > . . • U-' • - ■ 58 The equations representing the experiments of Lan- gen, Pier, and Holhorn end Henning are respectively, Langen +0.0006t Pier y -- 6.9 -|-0.00045t * ty) Holhorn and Henning 6*58 +0.00053£t In these expressions t denotes the temperature on the C scale, and denotes the mean specific heat from 0®- t^C . Expressions for the instantaneous specific heat are obtained by doubling the coefficient of t. This we obtain /p = 6.8 + 0.001£t 6.9 +0.0009t Vp=6.58-^ 0.001064t Lewis and Randall* propose as a compromise the formula 6.50-t-0.0010T in which T denotes absolute temperatures on the C. scale. The proceeding formulas apply to all the common diatomic gases except hydrogen. Eor hydrogen Pier gives the mean specific heat ifp - 6.7+ 0.00045t • m whence ^p= 6.7 + 0.0009t That is. Pier makes the variation with temperatures the same as for the other gases, but tikes 6.7 instead of 6.9 for the abso- lute term. Lewis and Randall propose for the specific heat of hydrogen the equation 2Tp = 6.5 +0.0009t to Chem Soa vol 34. 1912 59. which agrees quite closely with Pier’s equation. The formulas of Lewis and Pandall may he accepted as a fair compromise of the conflicting experimental data. To transform the formulas to the P. scale we multiply the coeffi- cients of T hy 5/9. If we let T/lOOO = 0, in v/hich T denotes absolute temperatures on the P. scale the formulas become: Por 0^, 00 and air, Por 6.5^5/9 9 (1) yp = 6.5+i9 ( E) Carbon Dioxide : The experiments on the specific heat of carbon dioxide may be classified as follows: 1. The earlier experiments of Regnault and Wiedemann at low temperatures. These have been supplemented by the experiments of Joly and Sv/ann also at lov; temperatures. 2. The experiments of Holborn and Austin extending to about 800° C and the later experiments of Holborn and Henning which covered the range 0® to 1400° C. 3. The explasion experiments :0f these the experiments of Mallard and Le Chatelier may be left out of consideration as the results are obviously inexact. Langen and Pier have also used the explosion method; the latter’s experiments extending to 2100° 0, There is little doubt that Pier's results should be given considerable weight. The following are some of the formulas that have been proposed. In these denotes th mean specific heat per mol between 0° 0 and t° 0. r r if.;' . vTiJr.: .- " V. :. ■■ ‘ vr-t.'i.i: :'i /; . • i ■ ■**' -tw Tii t’ IlC 6 u 3 . /..., .»i .;-.T xO .:; i'.;- V,.' ■■' e;‘fx iw i‘ ' 1 . c 1 a r_. < ::x ca . ' o.r •,, 'Xc-;.'*: j’! oui’ {- ■• r,": J*-! ..T ■ 1 ’^c e i I k V L i .) (I) - ♦ : L un. <:. ,. u - 1 -ii. jjfc. f.. : . .. Iwx lv{:JxC> -U ., . iO i.Ljf •. •,* * T u' . 4 . X %.* , rf*' iV ‘ - V o tlv , if; j j. '■ JL) ' t' .. l.» . C» ij -4 V ©ft ll? V V ,.o^ v it /.' j vne t Ivl Xo »j v'.j. ■ .V • Ci i K, » 0 jf I . ' i> » ■'.■ , \ t, ,', i V f' t: C ^.^.i ■ r* (fs' • 1 ; I :} Il i.’i ?. ''I ?>C^ Zi.SOOi) ■’ 00 £'f. oJ- II .. i; . i r :i . . ‘ // c j: ; i i, .Cq ^ - '<•. /• , , oxiJ V i i\c;ivJ I -T «/ :; t i, v^:,r' '.r'l. lXi;-j -j/. ,ba^ JjZlII i)oai! kjvJI d • : i • • J r. ' 41 A I- I *■ • ,* * ' '* oXi'J ... ;. ~.x fc»’: Oj • r, 0 001 :: t .' J" .„.■: r l!;;; xo’;: t'du ^.g • i i . »»4 .J i. I / ■’ - V*.J > — t * C/ J / J. ^ IJ,f ^7 '-aT ’'i ' 1 f. !l I ? * t/C’’ '■ n.T , tti B'O-fi a ;-vQ d i I . 0 J&xv; 0 ^'0 rrt'*o'i(J «) :f Ic ra aoo 60. Holt) or n and Austin, ^ = 8.923 + 3.046 -ld^t-0. 735 -10^ t' Holfcorn and Henning, 4 = 8.84 +3.267'ld^t-0.792-ld^t" Langen, 4 ^8.7 + 0.0026t '‘m Pier, 4-8.79 +3.3 -10"^t-0. 95 *10'^"+ O.l-lO^t^ Lev/is and Randsll have proposed the following formula "based on Pier's results at high temperatures and Holhorn and Henning's results at the lov/er temperatures: >^-7.0 + 7.1‘ld^T - 1.86 'IO^t"' In this formula T denotes absolute temperature on the C scale and Yf, is the instantaneous specific heat per mol. A comparison of some of the proposed equations is shorn in fig. 9, page 61. The points of temperatures 500-2000® are obtained from Holborn and Austin's formula, the points for the higher temperatures from Pier's formula. It v/ill be ob- served that at the lower temperatures the increase of specific heat with the temperature is quite marked, but at the higher temperature the rate of increase becomes smaller. This decrease in the slope of the Cp curve is clearly indicated by the experi- ments of Holborn and Austin, and Holborn and Henning; and the indication is strengthened by Pier's experiments, which give points on a curve continuous with the Holborn and Austin curve. Langen' s formula represented by the straight line gives reason- able values up to 2000® but for higher temperatures cannot be I' page 6f lOOO 2000 3000 ^OOO \ d 'tlli '■• I accepted. 6E. For convenience in subsequent applications, the equation should be a polynomial in ascending pov/ers of T, and if possible of a degree not higher than the second. Our problem then is to frame a second degree equation that will represent with fair accuracy the experimental results at the lower temperatures and also Pier’s experiments at the higher temperatures. Obviously a second degree equation v;ill give a maximum at some value of T, and at higher values of T the cal- culated values of C p will begin to decrease. There is no exper- imental evidence that the specific heat attains a maximum and then decreases; hence, at temperatures exceeding the temperature that gives the maximum specific heat, the values given by the second degree equation must be regarded as approximate. Holborn and Austin’s equation gives a maximum for Gp at a temperature of E883° absolute F; from Holborn and Henning’s equation the temperature is 2982°. For temperatures above 3000° values of C p calculated from these equations decrease rap- idly; hence, the equations are not valid for temperatures above about 3000 degrees. Pier’s third degree equation gives a max- imum for Op at T =» 4100, a point of inflection in the Gp curve at 4767, and a minimum value of Gp at T -5433. The second degree equation of Lewis and Randall gives a maximum value of Gp at T ^ 3436. By a slight change of constants it is possible to move the maximum to a still higher temperature and still preserve the accuracy of the formula at the lower temperatures. The « • • • h r'^ .* 1 j ». ' t'S oi.’, » X ' W w - v\ . t IPf.'JC 1 *ii .‘-ir'/-- I . . • J. v< . • 1 w. c ' Tjvv'- r. .1 'is.* '. ■. r r'-^ j . : » S» *1 ’j' '' '■>.. L 9c*. • . y r vv' 'i , » - • ■ . . : •• . . )•* , ’,i i .'. ' .■ 1 . ->c ilU T0q •• i. 1’ i . ■L xC’ o .? * ^ - V 1 f ^ < • i... - / ;>.T . ■'. u‘ - . — ‘Xv . ^ ' > i f>-. . ; •' 0■■■ *} 1 : 1 . ' ■.'i;. .. , . i ;i aJt tl. 6 .'. *Ji W a .riv ry^;o^;«u ■ 1 ' • . zf:iK .( w . ■- ‘ - \ .“.Vw .* ' .4 t) ■ f:a‘io * V# Z,* • . _ Ij i r *r • ■.' ? ..ti V ,• ■ i-- -' •■ V ', A. , • \t i .’ 0 n i.e. .'1 VO a ^ U1/ ^ .. > . • * / . - - s. -'X i-’X C'.’v.M JX'Ot* •} 1 1 z r::;v 'J cil- iii /!f • .; w’ Q 0 rt‘ I'i • , , L X. % ' ^ X n? i. s> .*1 ; '10 t fp'*"'. i* ’ t 'f • i . -- ’.1' f ■ * C- :.'| ; X V f:ii ' n •' ’1 N , . j » V • . f- . . > #. - . • . . . r , • L ,> . - -.jcj i, l| 'X-.l- » •j :.'■ -C.-LL',. r. ' ;: CJ'nfJ'li:!' 0 xQ 0’^~J/X<::.c «;• ••> V-’ ;! -^ ■ ■ iv k • V ■-:. * ' ■' i ' .. r f : < . - . . . « . .w -.. . 1. - 1. T . r p • I. i • . .f j. . .1 ^ 62 ec[uation finally developed is X," 7.41+3.5 9 - 0.48 9^ (A) r in which, as usual, 9 '•T/1000. The value of 9 for a maximum is 9*3.5/2^0.48 =3.648 or T =-3648 degrees absolute F. The graphical representation of this equation is shown by the full line curve of fig. 9 ,p. 61.The dash line curve represents the equation of Lewis and Randall. The agreement between the proposed equation and the experimental values is shown in the following tables: Calculated Mean specific heat Observed Holborn Equation (A) per lb. between & Austin 20° - 200°C 20° - 440°C 20° - 630°G 20° - 800°C 0.2168 Regnault 0.2173 0.2180 0.2306 H. and A. 0.2312 0.2310 0.2423 " " ” 0.2410 0.2403 0.2486 ” ” ” 0.2486 0.2479 Joly found for the mean specific heat between 10° - 100°C the value 0.2120. The equation gives 0.2116. Values of the instantaneous specific heats per pound at the lower temperatures: Temp.°G. Regnault Wiedemann Langan Holborn Holborn Equation &Austin &Henning (A) 0 0.1870 0.1952 0.1980 0.2028 0.2009 0.2049 100 0.2145 0.2169 0.2100 0.2161 0.2152 0.2169 200 0.2396 0.2387 0.2220 0.2285 0.2289 0.2282 400 0.2450 0.2502 0.2517 0.2488 600 0.2690 0.2678 0.2706 0.2665 800 0.2920 0.2815 0.2829 0.2814 Pier obtained the ne an specific heat at constant volume from 0°- t°G for five temperatures. The results are given in the following table: 64 Higher ^ ^ temperature Observed 1611 9.976 11.966 1725 10.06 12.05 1831 10.27 12.26 1839 10.28 12.27 2110 10.47 12.46 Galoulated Pier’s formula Eq^uation(A) 12.059 12.168 12.261 12.274 12.463 12.059 12.173 12.266 12.273 12.456 The proposed equation gives with fair accuracy the specific heats at the lower temperature and represents Pier’s results with nearly the same precision as Pier’s formula. Appar- ently the equation may he accepted with confidence up to the limjt T = 4500 Op. Water Vapor ; It is well shown that the specific heat of water vapor near the saturation limit varies with the pressure as well as with the temperature. However at these lower temperatures the pressure of the H^i^O component in a gas mixture is usually small, and some low constant pressure may he assumed. At the higher temperatures the variation of the spec- ific heat with the prqssure is negligible. Data for the specific heat at the lower temperature are furnished hy three sets of experiments. 1. The explosion experiments of Langen, from which is deduced the formula a; X 7.9 t0.00215t r TT) for the mean specific heat between 0° and t°C. 2. The experiments of Holborn and Henning, #iich are represented hy a; =^ 8.43 - 0.3815 -lO’^ f 0.792 'id^t*" 3. The experiments of Knoblauch and Jakob; and the later exper- iments of Knoblauch and Mollier extending to 550^ C. i 65 The discrepancy hetv/een the experimental results is shown by the curves of fig. (10), page 66. In this figure the points marked-fare obtained from Goodenough’s formula* for specific heat of superheated steam taking a pressure of 1 lb. per sq.in. The straight line that represents Langen's eq.uation runs entirely above these points, and the Holborn and Henning curve from 250 degrees C. runs far below them. That Holborn and Henning’s results are low due to systematic errors in the experimental method has been asserted by Callendar and others; and it is likewise probable that Langen’s straight line runs altogether too high for the lov/er range of temperature. The results obtained from the experiments of Knoblauch are however worthy of entire confidence. For the higher temperatures the only re]iable evi- dence is furnished by Pier’s explosion experiments. Pier’s form- ula for mean specific heat per mol from 0 to t degrees C is -3 -f V 8.065 4-0. 5-10 t 4-O.E'lO t The curve that represents this formula (see fig. 10) is almost coincident with the Holborn and Henning curve for temperature above 300 degrees C. At very high temperatures the third degree term in Pier’s formula assumes importance and gives rise to a rate of increase of with t that is scarcely credible. Curves of the instantaneous specific heat from 1000 degrees to 2750 degrees G. are shown in fig. 11, page 67. It will be seen that Pier’s curve crosses Langen’s straight line at t - 2050 and then rises rapidly. *Principles of Thermodynamics,p.l05. 3rd ed. /vC JL • IdJ -rn ^ r . ^ ' Ipi’ ''.'O' ''dr ■ \ .1 1 ‘ ' ' - ^ • . ■ 0 j t •• I u*I V J » V • e . . 4 .'- 1 . ''■ • -.J. •’ •TfvXiil {»•. '•£ r :iL eL.i , ' ' " ' . . .1 ; 'i:f o U 4 -'. f*V : rip ^ ® ! * i •...:: I'a .i ::t; V--. ' ol^i.bo •. oT. .f J :.? J J'liTi. . ./i *-SQ , l^,iOvi->.WP ■ ■/ li :rit> ^:VJ'.: li »..r/'v . '.' ■ ^ot'c iVi^n bi:t aJ C t'v :v’,. • .. • i*,.^.- -loo.f • X'f'' J ftWi 'l'>.i;av ,,;.•! ' . v' ^ -wi' ^ c. I* I bius > r-v *i9\ cX si’ ‘ICC : ,irt • < .V4 «♦. ':'/ nt> .> J uv tjJ‘iV:.rT: ( • Si iJC K‘ » ‘.'IL' ■> V ; .1 -s' ' '^.'\ j u ’. . -s r u » r' * '• ^i‘ , i ; . si' ‘.I '.i ■■ : alV^.^L'X'. i\ : t, "'.4 . . i J’i •: . ; :. A ^ H7 i :. X ij r.ri £ i) 4 - w o ;V V ■■ n 1...C* • J A’Z • 0 .0 ‘ * Lh ^ i ys, 1 ;I - •. ' '. . . xJ .•;J '••. >c- V -.4f £ o'ri. o ©fi'A viv ; t j" luu ov‘;. .;j ’ r,. '.n.''' t\'V' -infXtir:; loo •;i - 0 -,’- i 'l.s.'- '••■-' . ' > ■ . 'i *,6 ovoJi 5 .- i*r :^cfV!- .iiT ! I ' 1 fxi ricJ ^ ’.. * l. 6 VVsi' -AC ,J.x*:riJtys o’ . .. X* tl./ At) .1 iQ oJ'v'A . 4 £- w'-j’i '-t; cool' fii -;! Jyfi. ; ct': drf.- >0 •i .T”i 83/ or , .?: -v. 7 ' . ao»i30J& .»•» • . ‘ ..a l :. ■ w' tci ' 'at-’.a. !i.i >iiuwiiO':o eYUO ri'TOil »» • • ** * 1 1 ; 1 ■ ;':',.i.c:.ri 8 xiO It c%,lJ 7S Temp 0 too ZOO 300 400 Sroo 600 GT.F.'Z) C)\ %\^ • \ \ '■x*i. ^nxtvft'i'd w^ia r,>cA\ckV.^'^ \ 6 Tetnp ^C. /OOO fSTOO ZOOO ZS'OO <^r.F.ti h 68 Lewis and Randall have proposed the formula: ^f^=8.81 - 1*9'16^T -^ 2 . 22 'IO^t'*' in which 3! denotes absolute temperature on the G. scale. An- other formula used in the Babcock & Wilcox tests on heat trans- mission is Yp = 8.174 +0.Q576-10^t -f-O.BOSBt^lo’^ in which t denotes ordinary temperature on the R scale. In both these formulas 2Tp denotes the instantaneous specific heat. The Lewis curve, fig. 11, agrees with Pier’s curve to 1750 degrees G. and then runs somewhat lower and the B. & W. curve runs still lower. An exanoiination of the original data of Pier's ex- periments discloses the fact that various other expressions for ^Tp will satisfy the requirements of the esjperimental data quite as well as Pier's formula, provided no attempt is made to sat- at isfy/the same time Holborn c:nd Henning's results at the lovsrer temperatures. We attempt therefore to construct q second de- gree equation that shall(l) represent fairly well the Knoblauch values at low temperatures; and (2) give values of mean speci- fic heat that will satisfy Pier's data at high temperatures. The following equation fulfills these conditiona: 2Tp > 7.03 tl.25 ©-f-0.2 where 9 ’=• T/1000, and T denotes absolute temperature on t he P. scale. Reference to figs. 10 and 11 shows that the curve of the proposed equation fits the Knoblauch points very closely, and that in the high temperature range it shows only a moderate ■w 69 , rate of increase of with the temperature. The equation is a fair compromise between the high values obtained by Langen and the obviously low values of Holborn and Henning. Methane : V/e have the following values for the mean specific heat of methane per mol at constant pressure for the range 18 degrees to 208 degrees C. Regnault 9.507; Wullner 9.106; Lussana 9.483 For lower temperatures we have the recent values of Heuse: T^C -80 -55 -30 5 15 8.08 8.08 8.14 8.42 8.50 For the instantaneous specific heat we shall take the linear equation: = 6.03 t0.005T which T is in absolute degrees F. The agreement with Heuse 's values is as follows TOF(abs) 348 392 438 501 519 Heuse 8.08 8.08 8.14 8.42 8.50 Calculated 7.77 7.99 8.22 8.53 6^62 For the range 18 degrees to 208 degrees 0. or from 524 degrees to 866 degrees F. absolute, the equation gives for the mean specific heat 9.504 which agrees with Regnault and Lussana. Data for the higher temperatures are entirely lack- ing. The equation chosen does not give an unreasonable rise in specific heat v/ith temperature and when used in the equilibriu m equation for the reaction C + 2H3^ ->• GH^ gives an equilibrium curve 70 that agrees as well as could he expected with the discordant data available for the equilibrium at high temperatures. We may, therefore, accept the specific heat equation for methane given above as being the best possible in the light of the meager experimental data available.” Experimental data on the specific heat of gases other than those treated by Professor Goodenough are so meager that we are hardly justified in establishing a relation between specific heat and temperature. Hov/ever, for the gases acety- lene, ethylene, ethane and benzene v/hich appear in small quan- tities in ordinary fuel gases, a large error in the specific heat of any one of the above gases introduces only a small error in the totsl specific heat of the gas and air mixture burned in the engine. Being guided by the fact that the linear relation for the specific heat of methane prodiJces an equilibrium equa- tion that satisfies the high temperature data fairly well and also by the fact that the experimental data on the specific heat of benzene which is a'VEtD.able up to 350 degrees C. is also sat- isfied by a linear relation we shall assume that the specific heat equations for acetylene, ethylene and ethane are also lin- ear. Acetylene ( 0 vH : For acetylene we have only the two points by Heuse for the instantaneous specific heat at constant pressure as follows: j e(U . ■ : . «4 . u t r '• > * .0 C'. ''l;j *o a, V ot-tca* .. aiid* , rcXoificit • y •i : '- r-j ,-:v t J :i!, '. J 4- sVDit* r -ii .’ r . rj n . i. j :-T#; ^ « k '! t! i' It ^ • .•; j'ili-. ( «?*• If' <- !j •’i J > or»j)c t I i 4.^.1 4>'- ^ J’l'i 'u j n> ' I - 'iC-"’' 01 J , ./• •’- ■ 'r . -.i- r .. '., li .’ w". ai' •-' « .i ^ «-f ^ c I I w < 4 4 P i ' T. ,1 n ~: 'I ' • ■ .“. u'\T, .' -i*. i t> 1 *;i4 t'- ' u ! '. OW J"' . -■ I e t :.;r • fc"'4 - oJt'ttoo o ( ; ■ A X !, t? • ' Tx^ iT j. '. 9 C • *• •:-> IX .' -'I-.o 'ooy./' ' •.• X 'f- XI « X. j WA«i T X.. ';'f.*.niij’i"o fix efiiJxJ ■a' '.c _ ’XI < ’uW L'flo ii.' • wx*-» *yTd . *x *3 la/ i.ol.f - jIv-v -J-'t. : •• i. Vx;X .. - ■ u .\. 'i oX - - ^ j . -x;I*i'ri X Xiij i.»* i . e< *4iu . o .- Ot * i I vii.-.' xl'y-: rCt'-Jx J o 91 'Joc xa«;r r M f '.r.,, >a J .;'C^ x^olJ Oi - . : u I '■.. - *■• - f - o X&i)t fc'flJ- «>QX.'5 .a (■*,'I.-. .1 -J i.. ’lx .' C"l.x <: u '-y t^i** O'.t i'jxX” e-iisnsq t ■ 'i IvjXi.;.. j M rx ' .;jiu :C*..'T •: -*•■ X' £ *' %€ -*»j.1Sx - wtX ' t'l.i "'fiftfis/xi x -. 3x'V;i J , 'iCi o 4^,vfj . iJC f :.V 1:7 7 S)’. ■ .,?<>■£•.; Of; i A. : ; ) lJ It' ■ ' J t».. ^ ■ J" C‘ .1 -*C» , V 1 -^- 1* ’iX . V ”i 0 £ ^ W». frt / i r^j'^ t°G T^P.abs. + 18 524 10.43 -71 364 9.13 The straight line through these two points is given by the follomdng relation. T is in degrees Fahrenheit abso- lute. ZTp = 6.19 + 0.0081 T Ethylene For ethylene we have the identical values of Regnault and Luss&.na of 11. 3E as the mean molecular specific heat at constant pressure for the range 10 degrees to £02 degrees C. and the following instantaneous values by Reuse: t degrees C . T degrees F.abs. y^observed. Yp Gal culated from eq below + 18 524 10.22 10.22 - 36 4E7 9.17 9.57 - 68 369 8.79 9.18 ~ 91 256 8.64 8.41 The proposed eq.uation for the instantaneous specific heat of ethylene at constant pressure is iTp = 6.67 +0.0068T with T in degrees Fahrenheit absolute. This equation gives a value of 11.31 for the mean specific heat over the range 10 degrees to 202 degrees G. as compared with the value of 11.32 given by Regnault and L^ssena. The comparison with Reuse ^s values is given above. Ethane :Ca.H. . ufiJ **' • ' ) - ^^i od^- 7 j: V or- r-. ■"•* - r^ '■• ■ ■ * ■ •’ . :. ' lu r cr' " • :.‘V" ' ; . ) ; 5 /. L'rv t • ' ... ; r '■*■'9 u » c . • ol. • « . . r •». _ 4. ■* •' *. £ * ^ 7’'. *'<*T f:ct * •* * V*' r .r c'!? . u^erT... j- 1 f. » p r e o • • _ :io - «• • ' ' £’. . i -- ^ m ^ w ^ W « w — ^ w;k 1C'.: br^.ocL-L ■* ff • * . - X .. _ 0 r .* ; :l ; .. 4 a a . C i.> ? * j » *■ • » ,-V - ■ • ■ t • »> » f ■ '-0 .Jift-sit': ■ ' :.'-‘:n6 ,:i 'i :ij In £ w # , » i L * V f •: lU' . 't To '^rXi ^ 2 . r Jm <, ■‘ ‘t ■.- * t -;[j2 -. J- r a ■ •' ■, :*r . '. ■ Jl w' J!': ;r‘f*r . /v»-Q ;j|^'£r,y '1 . 7 ;? '^V.0 OM' TC? ; s.'-aWvfff 4» iS^M* tm •- • •> •• v r: c'lii jsr.f -+',-!»'rr^r o).'« f \ • i u c*) .> . '■O'- y< ■ '~n * Cl /t* * v«^ 611- • ^ X. 72 The equation that gives the above calculated values is * 6.43 to. OUST Benzene Vapor. OgH^: For benzene vapor we have data over a wider range and can therefore place more confidence in our derived relation. The experimental data are: Temp.rangg F ( ab s . ) 34- 115 653-699 35- 180 555-816 116-218 700-884 350 1122 observed. 23. 337 (mean) 25.913 " 29.270 " 38. 947 ( ins t.) Investigator ^Calcu lated Wiedemann 23.34 " 25.91 Regnault 29.27 Thiabaut 38.95 The proposed equation for the instantaneous specific heat of benzene vapor at constant pressure is ?Tp'4.00 t0.0318T with T in degrees Fahr. absolute. A comparison of the calculated £jid experimental re- sults is given in the above table. Graphical comparisons between the calculated and experimental values of specific heat for methane, acetylene, ethylene, ethane, and benzene vapor are given in the figures 12,13,14,15, and 16, on pages 73, 74, 75, 76, and 77 respectively. In the preceding discussion on specific heats it has been assximed that the specific heats of gases are independent of pressure. While this assumption is not correct we have the fol- lowing to show that in the range of temperatures existing in the gas engine the effect of pressure on specific heat is negligible. For the more permanent geses we have as an example the specific heat equation of Plank* for nitrogen expressed as a *Physikalische Zeit. 11-633 (1910) V % F i ► VO 1 9 C . I «, ( 6 1 .■ \ X. . . ' * r J .1 J.U J *, » . • • ' ' ■i}' . : I, . ► : : . ., •- -U ;■ 'Hi: i. J” , ■•'D ‘ •j J. J\ r- '■ : • ..•;< .; : ' i ; U: t*Ci 4J ‘ j - ’J..-;;^ rif'trj V .. !'. , C' j':.: ’j i: I . i. V " i:, - . J VJ.it • «'»v- ; 'i. :: ^ :■ I- ; ^ v- ;■ >;oI ', ; ;. .: !i 1 t s . .r. : : •• f . ■: . iv;n« c ■' .; r ; O'.* ■:'••. ; -i’-'-J' -a '. :. O’J Oi ■";> i.fi - ■ u ^ •'•'•’ -'-'i * i. ii' * ’u: t.- . -. I.OC* '. j;-;::) " ( i - 3nO BOO isoa 78 function of pressure and temperature; namely, Op = 0.2246 -^0•000038T -f- 0.905-^ where 0 calories per gram T Centigrade degrees absolute P pressure in kilograms per square meter. Using this equation Plank gives the following table of calcu- lated values of specific heat at constant pressure: Tsii^>« Pressure in atmospheres Op nn 0.0 op; t o oo 0.0 o • to 0.5 1.0 2.0 3.0 4.0 -150 0.2293 0.2303 0.2317 0.2342 0.2390 0.2439 0.2488 -100 0.2312 0.2316 0.2321 0.2329 0.2347 0.2364 0.2382 -50 0.2331 0.2333 0.2335 0.2339 0.2347 0.2355 0.2364 0 0.2350 0.2351 0.2352 0.2354 0.2359 0.236S 0.2368 60 0.2369 0.2370 0.2370 0.2372 0.2374 0.2377 0.2380 100 0.2388 0.2388 0.2389 0.2390 0.2391 0.2393 0.2395 200 0.2427 0.2427 0.2427 0.2428 0.2429 0.2430 0.2430 Sat. temp . — -207 -201 -196 -190 -185 -187 Co at sat. — 0.2334 0.2395 0.2473 0*2591 0.2681 0.2759 temp. The values in the above table are plotted in fig. 1*7, page 79t At 50 degrees G. the variation in specific heat for the pressure range 0 to 4 atmospheres is less than one half percent. As the temperature increases this variation decreases. In no case will the pressure in a gas engine by greater than 4 atmospheres when the gas temperature is below 200 degrees C. so that the error in neglecting the pressui’e effect on the specific heat is negligible. We may safely assume that this statement holds true for all diatomic gases. The Lewis and RandEll equation for the specific heat of diatomic gases which has been chosen as most accurately rep- \ ' / !: 3 * .1 i L^r. .1 •HI'fT: ; ' 1 ;i i .< ’ 80 resenting the available experimental data gives values fi)r the specific heat that are about three percent higher than those given by the Plank equation for zero pressure. Since the ef- fect of pressure on specific heat is less than the discrepancy in the experimental data the introduction of the pressure varia- ble is not justified. It v/ill be noticed from the graph of the Plank equa- tion that as the gas approaches the saturation state the effect of pressure on specific heat is greatly increased. The ques- tion naturally arises as to whether or not the effect of pressure on specific heat is appreciable in the case of the more easily condensed gases such as CO 2. c■> - b-'J^Er f\'jf ■'■ y *r r 7 _ %T » £> l’« Cv i cl'.xv ■■y^s j.‘., ..• .1 . »> i. Jr. i'i : , f f.ru^ i u P'; :j ■ L' i" 'f 'i ».■< * I . :; 7 f / ^ X JL p • fc* '*•*«. V A i t " I? y \ Jat J hrilJ • M W V* r. UH D {■" J (; J, o 0 e*. r.; 'r j i‘ U4 u » or i .. A j 1 Ui J.- > ‘ . C *?i/I.ua*'i ' «o.; lw •' \;I,( vP v .’jI.jOo -! - ' - i i'JUOC' ' • ‘ a .'c .*! i •;» . It' ■ .v.-« . c \r <\ ti'iA pr .jQUPo ciir t|* C*.'\ •%/ • ''hj... oi'i^oX y'l. ' ' 1^1 l•■r • vX ■i. J ; ^ 4 1 « frii' il(', j ' X k ■ !’*•'' j .{.■■*} '.’ .( X f ■J t.:c7x>i , .. ro J Ai rJ’ -j : J :^'£i '.>3 ie ^.r ’ ,J J -.IUM- 81 Temp • Pressure Kg. per sq. cm. °C. 0 2 4 6 8 150 0.457 0.490 0.527 200 0.460 0.479 0.498 0.522 0.545 250 0.466 0.477 0.489 0.S03 0.517 300 0.473 0.480 0.487 0.496 0.504 350 0.480 0.485 0.490 0.496 0.502 400 0.489 0.492 0.496 0.500 0.504 450 0.498 0.500 0.503 0.505 0.508 500 0.508 0.509 0.511 0.513 0.515 550 0.518 0.519 0.520 0.521 0.523 1 Kg per sq. cm -14.223 lb. per sq. in. We have the eq^uation deduced in the first part of this discussion for the specific heat of water vapor, e function of temperature alone, as follows: * 7.03 +1.25 'id^T +-0.2 -IO'^T"^ Changing to the Centigrade scale we have for the specific heat per gram C^ - 0.3905 +0.125 *i 6^T +0.036 ■loS'^ From this equation we have the following calculated values: TempOC. 150 200 250 300 350 400 450 500 C 0.450 0.457 0.465 0.473 0.482 0.491 0.500 0.509 Plotting the above values we have the curves shown in fig. 18, page 82. The dash line is the curve of the function of temperature only. Above 550 C. it can be seen that the effect of pressure on the specific heat is so small as to be negligible. All temperatures in a gas engine except in the compression phase are greater than 550 C. so that the pressure does not effect these specific heat values. Assuming that the initial mixture of gases in the engine cylinder contained lOfo of water vapor, vh ich is probably above the maximum in any actual case, the partial f I ' I," J .. i ■i. J \ I p f' ( t I I I 'J ti c " ■ 9-r -' ^ r- 0? O r Jijr:;.'. 1 82 pressure of the water at the heginning of compression will he about 1 Ih. per sq. in. and at a total compression pressure of 150 Ih . per sq. in. fahs.) the partial pressure of the water vapor will he only 15 Ih. per sq. in. The temperature at the end of compression will he in the neighborhood of 400°C . The specific heat equation chosen, v^hich is a function of temperature only, represents values of the specific heat at very low pressure in the neighborhood of 100 G. and at pressures of from 10 to 20 lb. per sq. in. in the neighborhood of 400 C.,or in other words, the probable range of pressures of the Hjj.0 along the compression line of the gas engine indicator card. The equation can be used in gas engine calculations with the assurance that the error in- troduced by neglecting the pressure effect on the specific heat will be within the experimental error of the determination of the specific heat at any given pressure and temperature. Since the equation previously derived for the speci- fic heat of carbon dioxide is based at low temperatures on exper- iments performed at atmospheric pressure, we may say following the same reasoning used in the case of water vapor, that the error introduced by neglecting the effect of pressure on speci- fic heat is within the limits of the experimental errors. 84. Specific heat of amorphous carbon : The experiment- al data available are as follows: 1* Regnault’s value of 0.2415 for the mean specific heat of one gram of wood charcoal for the range 18 degrees to 98 degrees G. 2. De La Rive and Marcet*s value of 0.1650 for the mean over the range 6 degrees to 15 degrees C . f or wood charcoal. 3. Bettendorff and Wxillner's value of 0.2040 for the range 24 de- grees to 68 degrees G. for gas rhetort carbon. 4. Weber gives the following values for the mean specific heat of wood charcoal: OO-24OG 0.1653 0°- 224OG 0.2385 0°- 99OG 0.1935 5. Kunz gives the following values for the instantaneous spec- ific heat of beechwood charcoal: 435OG 0.243 1059°0 0.362 561 0.290 1197 0.378 728 0.328 1297 0.381 925 0.358 From the above data the following eq[uation has been deduced for the instantaneous molecular specific heat of amor- phous carbon. T is in degress Genti grade absolute. Yp =1.60 -^2.84«10~^T - 0.57'10"^t'^ A comparison between the experimental values and the values calculated from the above equation is given in the follow- ing table: r. : ^ I’O f f ^ i :. >‘i 'i a . Yf ' . .L w->. C * b 0'.»'i '.♦*.' at .: '• -icZ / L' .V, V' • ■ >’ £.V c’ . :A bE • :o . . 'Tt &f»<' •:r - f." . - • :0 < ’Tf'/’ rx'?- . *. . ! XiOvO-i': • bVftoTJ t :• ,:.• 0 ^ i'i . . r , .• .:r •■'.t ':o1' r.auj' v A y - i!.i ; Y- X. > c . » . - .1 r ... 1 . ♦. .1 •' > o ow ^ 'erto ‘ Ti : . ' OXj d - '-• 1 W L ' • .t vi ,- ' letc.e : Ci : i - 00 w - 7*^*1 ^ Cf \ •„. , ' . , i : Pk . , «-• ..» li 'io: abj.rijv . ,> siOJ-i ' T '' ^ ^Xi lyi ll .. j ‘ . ij r • ■ .0 .[‘ri ^iSV ,1 *-•> l « •> ■ r ! Xu - • Xsi > fsvo . i.j If I 3,;c >, ;i:'. o ( *■ .Ui.-.i c: J Tfs'lt » uu Siy *” : ' i '.-:. .3 05 * 1^*10 r f - 0 i ! :■ Cl V .. - A 'm j • V.*- *. L Jii i.b;!'.r<;d n Fji'T, 'j.roo A' J| .. . iT ,',/) atjod ^. ■- 1 J '' f ;, - (’• ,i 'T*- ' :xUj:ir,c- tvoJ^ r-ollt < : . vfrfi ,; 85 . Temperature Molecular Investigator Centigrade Specific Heat absolute. calc. Observed. 291 - 371 2.477 (mean) 2.898 Regnault 279 - 288 2.359 11 1.980 De La Rive & Marcet 297 - 341 2.447 n 2.448 Bettendorff & Wullrer 273 - 297 2.363 tl 1.984 Weber 273 - 372 2.456 ti 2.322 II 273 - 497 2.607 If 2.862 II 708 3.337 ( inst. ) 2.916 Zunz 834 3.573 If 3.468 II 1001 3.869 IT 3.948 II 1198 4.187 II 4.272 II 1332 4.373 II 4.345 n 1470 4.543 II 4.512 II 1570 4.654 n 4.584 II At the low temperatures the equation s trikes about an average of the experimental data and at the higher tempera- tures agrees very well with the Kunz values as can be seen in fig. 19, page 86. The equation gives a maximum of 5.138 at T 2490 degrees C.fabs.) or 4022 degrees F. Changing to the Fahrenheit scale, the equation be- comes for the instantaneous molecular specific heat of amorphous carbon =1.60 +1.58 'lO'^T - 0.176 'lO'^T*" " i. : i , - j f ^ ■• '■’ ,JT V '/ :-■- .1 6V-’X . ^ ,t , ! 0- . r. i ar.i . . . ^ n..- i:, r : . • 3 -■: .: ■ ij; J V. 0( .30 • V .r ■x^4 LW'.- u V- ;.a 1' J-:-‘ . ; ..x.J S«WC':. . /XOU'IoJ. u. :■ • i. r / ' ■ , ^ V / 87 . References on Sipeoific Heat 1. Bettendorff and Wullner, 2. Be La Rive and Marcet, 3. Groodenough, 4. Reuse, 5. Holborn and Austin, 6. Holborn and Henning, Y ^ n « H 8 . J oly , 9. Enoblauch and Jakob, 10 . Knoblauch and Mollier, 11. Kunz, 12 . Langen, 13. Lewis and Randall, 14. Lussana, 15. Mallard and Le Chatelier, 16. Pier , 17. Regnault , 18. Swann, 19. Thiabaut , 20. Weber, H.P. 21. Wiedemann, £ 2 . ” 23.V/ullner , Pogg Am vl33, p293. 1868. Landholt and Bomstein Tables Principles of Thermodynamics, 3ed. Bul.#75, Eng Bxpt Sta,Univ of 111. Ann derPhysik, v59, p86. 1919. Sitzungsber. der Kgl Preuss Akad. (1905) pl75 CO^. Ann der Physik(4| v23, p809. 190*J H^. ” ” ' (4) v23, P809.1907 (4) vl8, P739.1905 Phil Trans vl82, p73. 1892. Mitteil uber Porschungsarbeit ,v35,pl09 Zeit der Yer Deutch Ing.v55,p666.1911 Ann d.Phys. (4) vl4, p309. 1904. Mitteil uber Porschungsarbeit , v8.1904 Jour Am Ghem Soc , v34. 1912. Huovo Gimento (3), v36,p5,70,130. 189< Ann des Mines, v4, p379. 1884. Zeit Elektrochem,vl6, p897. 1910. Mem. de 1' Institute de France, v26, pl67. 1862. Proc Royal Soc 1900. Ann der Physik (4), v35,p347. 1911. Phil Mag (4) ,v49,ppl61, 276. 1875. GO^. Pogg Ann,vl57,pl. 1876. G^H^. Ann der Physik, v2,pl95. 1877. Landholt-Eornstein Tables# '( i • V t ’ ■ r ? ' < it I 88 Appendix B Heat of Combustion Hydro, gen . Leaving out of consideration the work of investigators previous to 1848, we have the following brief outline of the methods used by the various investigators since that date for the determination of the heating value of hydrogen, and also the results obtained by each. Andrews, in 1848, first used the bomb calorimeter. Hydrogen and oxygen collected over water were introduced into the bomb in the theoretical proportions for combustion. The gas mixture , under a total pressure of one atmosphere, was ig- generated nited by an electric spark, ^the heat/being absorbed by water surroiuidine: the bomb. Andrev/s found as the average of four (0°C. 760mm.) experiments the higher heating value of one standard litre/of dry hydrogen at 20 degrees G. and constant volume to be3036 calories. (20 degree calorie) Favre and Silbermann in 1852 burned hydrogen v;ith oxygen in a closed vessel at a constant pressure of 16 centimet- ers of water above atmospheric. This burning was accomplished by leading two metal tubes into a small metal chamber, one for hydrogen and one for oxygen. By regulating the flow of the ^ases a steady flame was maintained. The heat of combustion was absorbed by water which completely surrounded the combustion chamber. Since the flame was completely enclosed the water formed by the combustion could not escape and so was condensed. / -‘i € rlluit ^ 1 1 ^ u t ■ jT. U • h Vu i' X I :. U*li { . c: ; * ) ID ..: I J-r.; ■ ’ ' * • c*~- 4 '* * ‘ V- w w‘ . X i,' XI • ' ^ ^ w *x :. .1 s , • . ■ .. .J *. V X to .S'lOV. .1 . , • ^ ^ i . ^ * . t u i ' L^< 4 « «m -t It tt'f ■ XoLiG 'iei';. - . * TTOxf|>i ai' : • • * — .. . 7 {iJ W . J GC-.-^C 'C --^i- J u 1 ^ w Xl .: . *r #». .' e X-: , io , 1 . iiVC 'j ,j. v" .’fif.- X : , . tK, - r.v.' .! x C' ■ ^:v .1 : f XfOv 1 «. '; . ; ...»' t It', * . '. . y‘i ■ 'l, . 1 i •! '. ^ 1 k« ;;i tfmOc' ft.CJ s.-i '; a ■ ■ c*’ !.••'■ * ' . ,<■. •■ eT i. JOJ -?J'‘ , ■•; • ixlL'i vi£j^ f - . * .i*xc::-fi ;^’I?rf\u - 4 *■ u c Xt ,. !.! ;f XfJ’iri ■r^v • D-.x/ l;.. . 4- . •V ^ :. i . r \L .) L/rc -;'j.i/c' . i'ii uL 9 . .'. .'.i •• X.;, jc' i4xr' *' '. iiexTyt- t •jai/Xcv V i sf . :- .:l -w ..if'-. ;3i> > i. Xij n* ■ Vi -‘N? (si toi-'^c a0%-^.s>Jj Cl;) .ijoizol/ ( r i'..c rr.: .iri oui ! L. ' 'iv:i'i" ■. 'Ik f# *s;c ' ji 1v'. I", .: rt-.aoT Li'uVit nl- -C-: V, •'■*:. -iv-J i:lrV . ' ,C'/ -oc-j t -raJ- j,7 xO ‘^*rsi o I- v -if ^ L'J't: ' aa;;iJLf OiV.;' -'o *■" “ ■'. f'lv •.!• . •; '•/••• ''.K 5ix, 1^ i-: e.'Lfj-Tv ;> 1:?' if^ifluV CiilA • -• •' t £ tJ i/ L,' -f I'i 'X.iG . w'C &CT Tw ■ '« i> ■' VioXcujo •v^r. H I:,. iieX;':7 :' ; v :j5 ■ H'T..'. ‘ . »r V# ■ . f UlS I iA. i y I ^ir | ^ii JI 1 89. At the hegimiing and end of each experiment the combustion chamber was weighed, the increase in weight being the water formed. Correction v/as made for the non-condensed water va- por within the combustion chamber by v/eighing the chamber filled with wet and then with dry gases. The difference is the v;eight non-condensed of/vapor. This weight of vapor is multiplied by the latent heat of steam at 18 degrees C. and the result added to the ex- perimental result. As the average of 6 experiments the higher heating value of 1 mol of hydrogen at 18 degrees G. and constant pressure was found to be 68,924 calories. (20 degree calories.) J. Thomsen in 1873 using the same method as Favre and Silbermann with minor changes in the apparatus found the higher heating value of one mol of hydrogen at 18 degrees C. and at constant pressure to be 68,357 calories (20 degree cal.) This isthe average of three experiments. In 1877 Schuller and V/ertha used a Bunsen ice cal- orimeter wherein the heat of combustion is determined by measur- ing the amount of ice melted at 0 degrees C. The amount of ice melted is measured by the contraction in volume of a mix- ture of ice and water. Volume of ice melted times specific weight times latent heat of fusion of ice gives the heat ab- sorbed by the ice. The closed end of a test tube projects into the mixture of ice and water. Inside of the test tube is placed a previously weighed glass combustion pipette. This com- bustion pipette consists simply of a small glass bulb into which are led two glass tubes, one for hydrogen and one for oxygen. 1 4 A . », . t. J" J ' X W k »< w 44.44, , . ;'tf 0 UM « « ’..’ :; ; 4 .1 • *.7 . 4 so • J • • ^ 4 \* ^ ' ■ Vj.^rfo -■7 7 v' ()' •■ •:. . ,•- :l i-J ■. ., f“i iC C' :.Lfi;. 7 ^;; 4 .. . '7 i ' ; ‘7’ 7 V I'.J, ijyiu&.L LI (' £ ra lii ; 4 i / %v>/' >*«. ^ ^ .if £. j \ ^ •lT- I - X ‘ 'i ^ w‘ 4 i^ < V- 1 :; . ij .'■: tuj,: -^Uj .,mx-> cu:‘* li\ i 6 w rld'iA ■ij.. , . . rtOv-i.oa '-! » j. . j.^ X..I «i lo •-'••/■ JO v' ..^ ,!i‘ . ■? ■‘.ro\'io •. i _ V - . ». t' .V • '■J . i'O'f*'' v- y OJ. v.'" . {;. ;' V o .i ‘-■' ’ ^ ' •■. >1 X. . -"a»< L ,0 .viXf&d .: e> u i;j ' > I ; • : : f • -*. 0 / C 4 * •-> 7 / e-jci/H-’c#-:.; i>': y ' W b) « f is . ' tX lu 4 ' . ' , 1 X . 4 ^ •' ■ I A i « . / i.^% . V 0 :i.r DOLL : • .: r C oc i. ' • ( » i . L ^ ■ w ./ ' ' '. } L 1 -' . f . - f ., ». ‘.y J ^ ‘-Vi.-lJu . j. ,V Xil - ■J’- I.“ 844*4 ;.Ti . v;;. w r *.:I , 4 ^ •.'»■[ vKf r.-iJi.'j; j*: ' 4 .V < 4 . • *• - - ■ !* *"• ' »'■ !>.• i r odJal '•Li .(in -.a 4 ; ..L . cofou^i. .J •• 4 .XIiJvlu»'; V?x. : rrl . ^ ’ '% - . '.a .’e. X .: 4 i i vtfi o«^. c '..0 J o:‘ .'ft' -"iViSuW’a*:fCi5rtLLiu ■:t'*::,ox) 'r. i-i j:,J r.“r Oi)i Vr J ‘ w . -•.. ./*4 ^ X J. 1 . i w O »♦' i W i- *. H. I. '. , t. .. ^ V/ •' <♦ - «-i . ... i .* . ,-1 * rf r t * v,:*.'./ rol frnc hru, nu '< V i*. 1 ? .» Kt 0 L&i! «i ■ Ooi ■ ■ ; !' . '■ . 70 * 4 - .. w .7 D. 300 i.y i: "J.O ■t^ 9 Si fi‘. Li :.C : 4 V: ii i. iow ' 4 ly * -oi CuLm ■• Of: y e Li CL 4 t:*v 44 C'illX :(.;, .: u L il av- i.'/L'l'T' ::f -X ’. r U( v> «a ^ w* IT': . oLi©cj,i ■•..x'oiieDf/ ' 'e'b C' , 1 <) i oo.E d^tii 90. Burning occurs at constant pressure inside this hulh. Since there is no outlet the water formed condenses and remains in the hulh. At the end of an experiment the glass pipette is again weighed , the increase in weight being the water formed. The experiments lasted 3 to 4 hours so that the small amount of vapor left uncondensed in the pipette introduced a negligible error. As an average of 5 experiments the higher heating value of 1 mol of hydrogen at 0 degrees C. and at constant pressure was found to be 68,250 calories (mean cal. 0 ) degrees - 100 degrees G.) In 1881 Than used the Bunsen ice calorimeter with a constant volume combustion pipette. In order to get an appre- ciable volume of gases in the pipette the calorimeter was quite large. Hydrogen and oxygen v/ere introduced into the pipette uiider a total pressure of one atmosphere (Barometer 760 mm.) and exploded by an electric spark.. The gases before combustion were saturated with water vapor so that all water vapor formed was condensed. The average result obtained from 5 experiments for the higher heating value of 1 mol of hydrogen burned at 0 degrees G. and at constant volume is 67,644 calories (15 degree cal. ) Berthelot in 1883 revived Andrew’s bomb calorimeter and much improved it. The bomb v/as first filled with dry hydro- gen under a pressure of 1 atmosphere. V/et oxygen v/as next intro- duced into the bomb from a cylinder of compressed oxygen until the total gas pressure in the bomb was about 1.7 atmospheres. The excess of oxygen was used because the compressed oxygen con- i i J L\t, 'V i., ■; .,. ©r- J*. . Jucf fAlC . ,i'. J::-'i'.uv i.! e£i.>i>iLax , v-- .j :■’» fll:, -J . . J :.; - i^itTs .1 .’la , ^V'-' - .'. '.uo: I'arr:;. t •* ..I , '■ -. C.;.:; . i'.' G iwi'ii tl §io.. . .’ j j s i sc. .[ . • -. -t idJ' ‘ o/Ic'* ji V (vA •si'.Muo - .'vo wi . •“■ '.. » vii 1' oJ K G ^rr^r^x*! vu»-'. i ofi- .i i 'ifiM ■■:; r.l £iD-,^.. . ;'.ur' J Ifil 1 '. ,xv I ;X 7 ,1J t. Tcri ?..* : . . f 5"^' 7 * 7 :?v j i. Ci-. . v^^'Xu • M- •• • ■< - • ..•• 1 .> :.. -V ^ . . r? >i> 0 * • nc^c‘rrr.;it Ic 1 }!o V . X “ n o'..'. .'‘^0 a, Sift") *i©Li<»X,?y 0 , “ oo <.•“ twol • •T* .. r J :‘ ‘ .ij o*:l *1:5 ..li/K ;• f{£ -ioav ^ - x; X-U jX '^ 1 ,,: 'v,. ;■ - ■ - '; ..7 X- . w 70 rS . .u«,£ rr'.'iua ; . n ,r.v £: / Xn .^&ri^‘d _■-■ .. .',,.7 Uw '- I' X G '•n"::f jXJc i, ifLl: a£ f'i» .' .\v Xy Oy'f'Xov oI(X/#io »*wii - w.- frl o'tcw iie- on-C^. . • { • • V I <0 ■» L’iiiC. X-.'' i *’ . *!•-' jO u ^ C ^i. *1 ij 7'i.’ ^ ' J. u ' J J3 7 (V ft*;. firi : l: 7 L c: 0 V7C .ec! otiV * ,..'.*'r.u:, .-■ iJ'; V, L'X 7 5 X ICJ <. J J. .: w * 'X 0 'jj MV r’j £ '; .i i. X riAyXrtB »107;‘ t.,: . ■' ... 'i j “T c . ^ rnc-iX - X : 'i- ^'X: ,;;u7 •>: i-;lV: , . f KJ-t-' :■ rf>"u. ro I Of X’ Xo Ci/.rcv •'-n 7 .i:-ia ©AvT' icl' Xi i'jl- ' '-X^,o » aX 'j;rui\v Jn J-rr: 0 J--’ •, • rj *i v> ** "^0 *< 0 (. ixX • i'-'. X, y j 'Co -’.v'.^riA ji>vj.vc'i hiaOj. oi ? c ,C©x*.; loft v'j'G iG J[jeiri- ii.:' t/ri' : o/iX ’ . . X .;t 0 (j \> Xo\. . ‘•■J.&.'L ■ riL 0 -icax. XX’^G '> 1 •< 0 (j -;av; ifr:C ■i V:, i -// : .1 ‘ 2 "'' &strX'- '."ff eri? 91 tained a small percentage of nitrogen. The mixture was exjiloded by an electric spark. Since all the water vapor formed is con- densed no correction is needed. Berthelot gives as the higher heating value of 1 mol of hydrogen at constant volume and at 10 degrees G. 68,000 calories. (lO degree cal.) In 1903 Mixter, at Yale University, made further improvements on the bomb calorimeter. Dry hydrogen was first introduced into the bomb at atmospheric pressure (bar. 14.743 lb. per sq. in.). The weight of hydrogen present was calculat- ed from its knov/n pressure, temperature, and volume. Dry oxygen was next introduced into the bomb until the total pressure was in excess of 1-|- atmospheres. The average of 14 experiments by Mixter gives for the higher heating value of 1 mol of hydrogen at 18 degrees C. ruid at constant volume .omitting the correction for non-condensed water vapor ich will be considered later, 66,835 calories (20 degrees cal.) The latest work done on the heating value of hydro- gen is that of G. Rwnelin in 1907. He used a bomb calorimeter of more elaborate designthan those previously used. Dry hydros gen and oxygen in the theoretical proportions for combustion were introduced into the bomb under a total pressure of 1 atmos- phere (Bar. 14.32 lb. per sq. in.) As an average of six ex- periments omitting the correction for non-condensed vapor. left in the bomb, the observed result for the higher heating vslue of 1 mol of hydrogen at 18 degrees C. rnd at constant volume -was 66,940 calories. (20 degree cal.) V. r>Pi ^rn .1 y,©*: i* j * iv yi&':o: ,. JDeAi .sv I ii b/,y!r[->^ •'^Cfi«v - _ V7 r.O J.J . Uiio . x«vu ...i. , . V ■ IT I ,^J. i.J, ,.!*■“ ** ■* 0^0.. .' -' iv '. >J \i. • tA,. Z.Z 4iv V^Xl jboci _=Jj V ixii or i.'.ov rn^jHitOi. v*^ ii» .u *x * ^iL ic X&; _ X 1: r;J^ S -J ij ♦.•» CA ^ * <« .>^. ..V .MU VJ'J •» , . ' • •. ^/JO*^C*A -»J- . rv* 'i . w iJJ X , '-j X* i.tji ^ X » 3 1U a ^tsx « -CX.-^ 'i» V , T.'i; ,1>. j v ..aVw'' „ 1 • •‘iflvJ* cx‘'0 iVi. 2)8 SijXo*I w 1 . ■ ■ - »• -• V ii K li i*,»j u Vu »* X .> nil ,qX j T ■!* iix • \ « „ " » ^ 'i * .u. — o , ii-T - -i.*’0fC3C'fl'f! «o*ii j:. ■ 4 -• ^ ^ AM.' -> v% ^ C \j , 1 L t I ») * . X w 3C6 i} Ai . ‘rf . ■ V/**: x ma A- 1‘A: . . -Xv2:. M* .4 '';;I ..l '-j^coce i\i .'>. . ".xt. XV. luM .:. .w u uu .' -\ 1 : Si1 •ii.^^iX i xiu n/Jt ,t. '.ly ‘lOJXl.' j -i - XiV/2. 4>i4 4 C^**x V ,»--wXc. / g-.i'.'w'. >c .".i •.. j’i>- • '- - ^. ■ ■ X k. i.j Cj_ 0 V n V. .*. » ., * , .0 vj,4* V '1 ■., J . , c “• .1 s'ii Tt. . ■■ . , <'di i i. •.. . / 1 ■■.• X-l^ C ^ ^ ■ i ~ y:' ^ •■’ ’■•*■* Xi.' .' ■• »x v' 81*. ?13'> ^ 'tw n - W ’JIa A V ... . . ;. : 'I'nr. .•; '.X r.i r,U£oi . ti, /: * ' .’ - .: . • - .- iClax; I;*.-', "'nj * ’'‘•or jm Xo i-.w lo t-u'vi:. . i *rC'x *>;iv.i w‘"'0c4,c\' : r, ,ci.J‘yiOi. .. r_'{- f.i. r ' fiffc ' V. r . .!■' V. 'i ^ X ^ .Z o^f .*■ tn.l: „8'ti»*.. -■ Im 'xO o"3*idv • : r. (. "X . ■* tMf .^1 . vf .*c^5) -0 ■* .jasi'a Xnc c - t).' Av c.a'.'ro-. -.:t ' '¥ •. X T - i:.. J : ?.{ ’tf„ T"'.. v^X.7s?T ■«'ft A. ; / n U- v; ; . ■ .V sao'iaoii 3i ‘j. t T'^'h ■ ' ^.' ■ ( . Li c or-J’ ■'. a ^ ?• T3 : . , D Cl' 'i . ^0 ' 92 In order to put the atove values on a coniparative basis we shall ah^mge them all from the French system to the English system of units and use the mean B.T.U. in the range 32 - 212 degrees F. Also the lower heating value will b e cal- culated in each c§.se. To convert to the mean B.T.U. we have from Callendarfe eq^uation for the specific heat of water taking the mean B.T.U# (32 to 212 degrees F.) as unity the following correction factors; Temperature Correction factor log correction Degrees C. Degrees F. tor 10 50 1.00150 0.0006499 15 59 0.99962 1.9998352 20 68 0.99842 1.9993100 V/e shall use the following notation; Hv = lower heating value per mol at constant volume , n IT IT IT If XX pressure , h; = higher XI IT II XX Tf XX Volume , h; XX It If TT IT XX pressure . The experimental methods outlined above fall into the tv;o general classes, i.e., burning at constant volume and at constant pressure. To deduce the lov/er heating value from experimental results given we shall use the folloif/ing method; As the hot gases are cooling after combustion no condensation of tlie water vapor occurs ULitil the temperature of the gases falls below the saturation temperature corresponding to the partial pressure of the v/ater vapor constituent. Condensation then occurs between the saturation tempera,ture and the final temperature of the M I 93 . gases. If the initial gases were saturated with water vapor, all the water formed by the combustion will condense if the products of combustion are brot back to the initial temperature since the amount of water vapor required to saturate a given volume of any gas is dependent on the temperature only. If the initial gases are dry, however, that portion of the water vapor formed v/hich is required to saturate the given volume of gas at the final temperature will remain as vapor. To get the higher heating value when the initial gases are dry the latent heat of the non-condensed vapor must be added to the observed results. By definition the lower heating value of a gas is the amount of heatgiven out d'oring the combustion of the gas considering the water formed to remain in the vapor state when the products of combustion are cooled down to the initial tem- perature. . The difference, then, betv/een the higher heating value and the lower heating value is the difference between the amouat of heat given out by the hot gases in cooling in the first place with condensation and in the second place cooling without condensation. The heat given up with condensation at constant vol- ume in cooling from the satiiration temperature to the final tem- perature is ,Q^ -= ■‘i," tx f*’) where u'' -^thermal energy of 1 lb. of steam at the saturation point in the cooling of the products of combustion. f ■ SI . tj * ‘ • > v« X , ' l ‘j * V* s ^■ ^ j U'l J. . 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V u J -I .. ■; (> ./ li OiijUt J ’-jrf . ^4 ^ ' j f w -J W«4V J '%’ kJ* i ■ • >' jT’ ilu (.; t» .'J-; i i-J.U 5L.-,C>i J j/'.' {!:.!. 7 -aijXocc i;-‘f -■:• »•. ,/ *' j. ■• U ; \i oZlC'O w *i .a'sJ'il'n . f.-s) j , Vx -j t*:' 'O '' ~ i- L '\J X 4 *iiw v>u A*£^,rrj /I. ;. ?■;, j r.j'i”. '.ixJ. (iQti ni oiax. .( • ' _.. EX ^^'XX/^^' i“x~ I • ,' ■ , I,- ( X L )~ .U .'■'. '' V J iX '. Sij O 'xXj J IX £? .. J . L £ to • i^'xrr-%^: .X'X; i; • L.I- ',.w c*. 7':..; ,.;Ic5- ’;u ?„riXj.tOu' ^'^r ' ■ r ■r 'r:t j-{:loq ■:,4 sr- ■,.'sr''-.t:r mr- r .gi SET 94t 11 ^= thermal energy of 1 lb. of liquid water at the final temp erature . X - fraction of water formed remaining non-condensed. ^ - intern?.! latent hert of 1 Ih. of steam at final tem- perature . The heat given up by the v/ater vapor in cooling at constant volume from the saturation temperature to the final tenii-)erature considered as a non-condensable gas is 1^ 9 . ~ j where r=. instantaneous specific heat of 1 mol of water vapor. Hepresenting specific heat by the following fuiction = a +bT +fT’" we have upon substitution i nd integration = a(T.- T^) +ib(T,’'- 2 ; - H ^ +tb(T,''-Tp+if(T,’-T’^ The temperature at v/hich saturation first occurs in the cooling process at constant volume is determined b;v the following. Knov/ing the pressure, temperature, ‘„nd composi- tion of the initial gases the total volume CcJQ be determined. This is also the volume of the resulting waiter vapor from which the volume per lb. is easily determined. The saturation tem- perature corresponding to this specific volume can be formed in the steam tables ana is the temperature desired. The heat given up with condensation at constant pressure by the gases in cooling from the temperature at which r fjrr- .1 > j: . T X '•.•/. jrii X-'. ’.r • *' *^X * * 'J 2 \l U I '^<54 'itC'. .U/ I v , . ■/* I *’ ^ X to j:: X'tvJi'l C *rt- ,,,j^ ; ^ ^k. ' . •.-v;J’.:*'xe''j' •V -.iv^ , . ' '. >.1/ ft/ . iX ■< • 7 V e(‘ ‘ 0 ••> . ■:.'»■ Jj T v arft-o 1 t \iOa dtir/ ! V ./. ■ > \ • p. / .> .>W «, 'V ^ . ’ I . ^ J uX iX t'G-j'i- *i- .' Vj ■, u’;i-.;'j >,."X - ^ fk’:a._ i.iv.Ciiv^X Ri'.J jJ J v^x.-.: / •! iw .r.c.«'‘A . •« .-. '• • • 4»v; #ti 4 Off j "' ^ c. ; / I f _ ( ■ “ (■- i« •• - 1 (. .. i/jrj J A _ - .-)J x r ( \ ~ ' )li - . - 1l / ’ ,'fj •• - • f '€ jx b" .. ^uvjc J ,‘ix X ii- 'ix/j - i'J* .,u X, -fV-i'X V. 1 -LI..M /• / ......('li J". . i-L-Olv y:l\X f.(0: « li/ iU "■ J V- i • 1. - ii » • , . I "1 I.' • , . L .'., ■/» >» V- ^•■1 *J 'xn I'-t V JxiiXJ 1 V 0-v . ^5J-XWO^X: , '.vuXioi W o/ ai>*. kW ^ . *• X V X >tx :rc % .• Xvc r;ao*! [jr » W vw y ' ru- 'CV 4::1X O X !i :,n x;Xi ' ‘ t ii/: J X . ,C Ufi / > ^ ^ • *• ov oiiX '•sc. : iiX t 4J OJ X ur.ci %, I'j . :0 0 e*; i;/ • XLCr S. . . . u '.• / r'.; « . C 'XJ. V. i / - t > ■ - I .v -•. .1X^0. , i. I I ^ L’ V :• • •■ O- . X'- ’l -' i ... ji I 'i\. ■it.. I 4, &C^4 wj ,J -' '• • Li X ' .■ '. X;-: w • xXj -a/X -Xo £ 't . ." £10 t jtr X.S "1 X tc a' ■ J” r-v V . . :..7 .. ■..'fi ur»3v(‘- £ «» *1 : ' • ^ yi.r^c ; , r:o.:..o -l i - x ;:i ' aov . ^>ri srfT ,:r I.j ,3'ia J'c.r, uiw 'uil oiuar.»'iq ■■ ' * • “>s j t W . i *1'^' V w ■;‘ •.)(<„• ^( '•-,’) ., -■( v:: -'l)- ;... t' - ;h ^ t.- :..,o>- ; ^ »)'o uii .;,nl 'io B.;‘xq b'iw*' • tr- r , ■C'jiibZ'z }o 1 >Mu i .c -^'.};>.o ijrtJ* bfiil * 'V> -V ,!a etIT . 3tnjLr,Ti; Xo/j ., ; ix. t- 'juC«:i.ix.’i: '..i-, ;i.j. 'lOcAV 'xeJ'xiw t«xU t l, ; -;., '. Ci'X a 0 0 fuf., ,' #r f* ,- < w O t . ^ V. .'. iiii/ji'C- L j’i . C 0 w* i'. yiJ'L.i'SiJ 1,'fuj 'cj 0/;/ a; ,6A;j’‘e'!x.Vv p-u. la ^ci’t yeifX •“ laH'oX onV ";.c ■ I:;v l v : :'OI,COa i.i .. l>- ;■ . 7 Jil v: ’ I'.'O e-iX ^6 Andrews. Since the initia.1 gb\ses i_re imder atmospheric pres- sure and saturated v;ith water V£ or the reaction is H^O -7(l-y) H^O From Groodenough’ s steam tables the saturation pres- sure at 68 degrees F. is 0.339 lb. per sq. in. ^ 0.339 1.5 y 14.7 Solution gives y 0.0354 mols. Volume of 1.5354 mols at 68 degrees F. = 1.5354 -^380.6x111 = 596.1 cu. ft. 380.6 cu. ft. = volume of 1 mol at 62 degrees F. and per sq. 14.7 lb. inch . ab s . Volume of 1 lb. of Hj_0 in finul mixture ^ 596.1 18a1.0354 31.715 cu. ft. The saturation temperature corresponding to this volume is E03°F. u," = 1076.2 u^ = 36.1 x=0 ,0,' = 18(1076.2-36.1) =18 . 722 B .T.U. ^Q^-^^'^dt = 5. 04(663-528 ( 6 63 *"-528^ 10~^^ (663^-528^) =791 = 18722 - 791 =17,931 Ey' = 22.412 ^036 >«1. 8 ^0.99842 =122,000 B.T.U. per mol. =^ 122,000 - 17931 = 104,069 Hp = = Hv -f T Hp =■ 104,069 -#-528 -104,597 B.T.U. per mol at 68 degrees F. Than: Method same as for Andrew's case. r T t!‘. ® ‘'S .fi r ..x . : V L .• . • ^ vr T "jt * Kt ; * oi -itaJ" n f>ffj n > ,^-lJ , U 'J£ oiJTtycrtd’esIflJ’ “£./■’ . t . j * 3| .1£ ix . j„3.« d /6 • . I • ■ ( i! i V •▼«►>• •< N/i /I i ^ i <<•» ’ 4. q ‘ r •" ' . ; •• ^3. i. M * tk J, V < I , ^ ;n rrf r. . > - r > ^ ■ r '• - • I ' r ~ <• *n •■ - •■ »» f ^ ^ 1 " • ... , . A -k. ^ W «^Uk 4 ik V • — » -f ~ • . ,if -» * fy • ■ ' . W* , . '“ Own.) .c:v r. JL'«* V4^ M ■ • .Vi'lJ V. • W • ♦ • W ' O' - J w f X «A*%> « • wu W w ■ w <#* X *. * .^ .*. ' • * u- X 4 «x •»• wwOjVwu . I OO %» >a4. ' a *-jTf * M j • , - f' . t (. . - nt 97 Initial temper' tiire =-32 degrees 5’. 3c turation pressure at 3£ degrees F, - 0.0887 y » 0.009 Volume of 1 lb. water vapor in products^ ^ 2^0 cu.ft. 18 1.009 Saturation temperature *=206.3 degrees F. u/ =-1077.2 uj = 0 X = 0 18x1077.2=19,389 ,Q,y, =1016 eJ =67644 xi.8> 0.99962 =121,713 = 19389 - 1016 =18,373 -= 121,713 - 18,373 =103,340 B.T.U. per mol. =103340 +492 = 103,832 B .T.U. per mol at 32 degrees F. To change this value to E at 62 decrees F, we have ~ 6.5 '^0.5 .10'^ T = 3.25 t 0.2778 >10~^T 3u/77 -TrTTTUTTfWTTaW^ frn,. = 7.03 -M.25 -ld^T+0.2 -IO'^T"^ P/T = 2.72- 0.4722*10-^']? - 0.2'i'd^T’' [2.72(522-492)-'0.2361*10'^(522'’-492^) - £l2.10'^( 522'’- 492*^ )]= -f- 74 3 J 0> Hp — 103,906 B.T.U. per mol. Berthelot: Initi'l partial pressure of dry hydrogen -=14.7 Ih .per.scL.in. Tot: l pressure of initial ga.ses about 1.7 atmospheres. ■T' f 3.L \ V;& .'X' • « :-iv j: . I- _ Vi . •■ , >j *’ I ’ t i-c, ... . 1 . ) ■ • . 1 ' j.i . . V r i ., -: i. i j.^ r/. i . ■■ j- I 98. Initial fnd final temperatures = 50 degrees P. Initial gases saturated with H^O Since the p^.rti^il pressure of the dry hydrogen in the initi-^1 gases is 1 atmosphere , the partial pressure of the water vapor formed in the products will he 1 atmosphere, at 50 degrees P. when considered non-condensed. Pirtial pressure of v/ater vapor used to saturate initial gases at 50 degrees P. -0.18 Ih. per sq. in. Therefore: Totfl partial pressure of H 2.0 in products at 50 de- grees P. - 14.70 i-0.18 = 14.88 Ih. per sq. in. Volume of 1 lb. of water vapor in products of combustion 18 5££ 14.68 "*20.408 cu. ft. per lb. Saturation temperature = ££7 degrees P. u/' =1083.0 u^ =18.1 x=0 = 18(1083.0-18.1) = 19,168 B^T.U. per mol. = 1037 B.T.U. per mol. hJ = 19168 - 1037 18,131 = 68,000 ^ 1.8 1.00150 »1££, 583 B.T.U. per mol. Ey = 1££,583 - 18131 =104,45£ Hp = 10445£ +510 =104, 96£ B.T.U. per mol at 50 degrees P. Mixter : Initi 1 gases dry at 64 degrees P. Initial pressure of hydiu gen =•14. 743 lb. per sq. in. Pin^l pressure of water vapor formed considered non-condensed is therefore 14.743 lb. per sq. in. 99 Volume of 1 lb. of v/rter va'oor in products of combustion ^ 580.6 ^ 524 ^ 14.700 , ^ .. " 18 522 14.743 “21.164 cu. ft. Saturation temper..-oture =-225 degrees S’, (from steam tables) u^ =1062.5 u^ s^32.1 f> = 998.4 Saturation pressure at 64 degrees P =• 0.295 lb. per sq. in. Therefore: = 0.0200 14.743 =18|l082*5 - (32.1-^0.02*998.^ ^ 18547 /Qj. = 945 -Hy =18547 - 945 =17.602 B.T.U. (observed) = 66, 835Jil. 8^0. 99642 -120,112 B.T.U. per mol. =120, 112 - 17,602 = 102,510 Hp=102, 510+524 =103034 3 .T .U. per mol. at 62 degrees F. Bumelin: Dry hydrogen and oxygen Tot;:l pressure *1 -atmosphere =14.32 lb. per sq[. in. Initi 1 temperature =64 degrees F. P- rtial pressure of water vapor as products non-condensed = 2/3x14.32 =9.55 lb. per sq^. in. Volume of 1 lb . w-. ter vapor ^ x|24 =52.673 18 ^22 9.55 Saturation temperature -202 degrees F. Saturation pressure at 64 degrees F. = 0.295 lb. per sq.. in. X = 0.295/9.55 = 0.0323 u/':^ 1075. 9 u/ =32.1 ^=998.4 =18|l075.9 - (32.1+0.0323*998.^ - 18 , 209 B . T .U. per mol. = 807 ■X o t.' ifi/l'.v JOwTt* O' Y I > a f t •' V • I 100 = 18209 - 807 =17,400 (Observed) - 66, 940 >1.8>0. 99842 - 120,300 ^ 120,300 ” 17,400 = 102,900 Hp = 102,900 f524 =103,424 B.T.U. per mol at 64 degrees F. The calculations for the lov;er heating values in the constant pressure cases are as follov/s: Favre and Silhermann . Temperature of combustion » 64 degrees F. Pressure of combustion =16 cm. of water above atmospher^ic = 14.70 -hO.23 - 14.93 lb. per sq. in. Since HjO is the only product of combustion, we have Saturation temperature at 14.93 lb. per sq. in. = 213 ®F. i/ =1152.1 =32.1 X = 0 = 18(1152.1 - 32.1) ^20,160 B.T.U. per mol +1.25 -lO^T +0.20 -lO'^T*" = 7.03 (673 - 524) f il.25-10^( 673"’ - 524^) 1o'^( 673^ - 524^) =1169 3 Hp - Hp =20,160 - 1169 = 13,991 Hp(observed) = 68,924 ^1.8 XQ. 99842 = 123,866 B .T .U./mol64°F . Hp = - /r/f / ^ -$0 rry .T. per mo / aT 'Shomsen : Temperature of combustion =64 degrees F, Pressure of combustion =14.70 lb. per sq. in. Since H^O alone is the product of combustion, the pressure of in the products = 14. 70 lb. per sq. in. Saturation temper^iture -=212 degrees F. ii t . j I ' -K.i j B l. . •i ./ ’ i 4i i » U :X^ z I f. ■'h»«r C ri r /M ^ L « - ' f < a I 1 r V: n I I 1a ' ' w > . • ^ V « f- ■ ;i . - *4 ©'i - I f " *.o .' . .. ■-. - C V. I I i ■V.Nf: r.vJf/>A .V . 101 . i/'= 1151.7 = 32.1 X i 0 ,Q/ - 18(1151.7 - 32.1) = 20,153 = 7.03 (672-524)-^-sl.25'10“^ (672^-524’") -f%2(672^-524^]*/^>'^ 3 ^ 1162 Hp -Hp = 20,153 - 1162 ’=18,991 Hp (observed) - 68,357 XL. 8^0. 99842 =122,849 Hp =122,849 - 18,991 =103,858 B.T.U./mol at 64 degrees F, Schuller r^nd Wartha : Temperature of comhustion 32 degrees F. Pressure of comhustion =rl4.7 lb. per dq. in. only as product of combustion Saturation pressure = 212 degrees F. i/' ^1151.7 i J = 0 X = 0 ,q/ =18j^1151.7 = 20,731 ,0,^ = 1408 -Hp = 20731-1408 - 19,323 B .T.U. Hp (observed) = 68250 >1.8 = 122852 Hp = 122652-19323 =-103529 B.T.U. per mol at 32 degrees F. As before (Than page 97.) Hp (at 62 degrees F.) = 103529 ■^74 =103, 603 B .T.U. per mol. Collecting results add neglecting the small correc- tion necessary to transfer the various values to the heat of com- bustion at 62 degrees F, we have the following table of values for the lower heating value of hydrogen at constant pressurd and at 62 degrees F. 102 . Date Investigator Value 1848 Andrews 104,597 1852 Favre and Silhermann 104,875 1873 Thomsen 103,858 1877 3 chillier and Wartha 103,603 1881 Than 103,906 1883 Berthelot 104,962 1903 Mixter 103,034 1907 Rumelin 103,424 We shall omit the values of Andrev/s, Favre and Silhermann, and Berthelot as being obviously high. We shall weigh the remaining five values according to the following table f and take the average as our fina,l result for the lower heating value of hydrogen burned at 62 degrees F. and at con- stant pressure. Thomsen value is given double weight be- cause of the general accuracy of his experiments and because his result is the average of seven experiments in which a total of 18 grams of water were formed, this being a much larger amount than that fomed in the experiments of any of the other investig- ators. The Mixter and Ruraelin values are given the weight of three because of the comparatively recent dates at which their work was done. Also IIixter*s value is the average of fourteen experiments all of which are within 1.^ of the average and Rum- elin’s value is the average of 7 experiments all of which are within 0.7^ of the average. Investigator. Wt. of value in taking average. Value. Thomsen £ 105,858 Schuller and Wartha 1 ;L03 603 1 103|906 Mixter 3 103,034 Rumelin 3 103,424 Average l03,459 A Siam .5 V Oi t*;i *TCU' 20 t IC. nui 1’/ u iirlJ’73 0"'0 I**' J?X w i X jti'u a . « V i’ j X itJal •- t)x*/,"- iu a JXc^ V OX' I'JMJ xxu o t) U 0 T( • a;jx ivov J, XOO fid X J1 J J xa J . o .iiafdtnxp J Xia JL J oa %iii.Li'L 00^ aJu xo ^ 3^ i ;uixax xc:o »flJ .i;^X{> / J. i. a ^ X t. u W C» u'l » .i h Si fi , O M ' 4 w J ;j -X . . . j , - • '-X J%>0 '<0 ^ i M ft s WiiXn J , . . .JJ y XA^\i\ J Vi :r k' X V M.' 1 t U i.i ^ VlAi ' 4 W « X ^ > V« t> ^4 W O ^ wt. ) 4. W * > At 1.1 w > X>^ u vxtOv, < «> W - V« V w Xi X J. !• ' A. O s » . i t .V/ i x*i ('O' i. j’ii il'x ^ ... 0 » •!■ V 4i t*x •■»-*• ^^KJ.'AIl.. -lj»* J» XV ^ Xto J

lM X V' «AI «l> A h »■ 1 u ■»« 1« J 1. tjl 0 X. iX i , vy Cllll X' '> X « .11* .JA XV X a V ' j.s« t w Uii‘i J X O t>. Ji' lix i/ cr ‘i V 1 .1 j».,i i i‘; ‘ ;'{J V ■ ST3 ?''t;jr.v rri t . 'j r .1 1 X ■» .' '• X LA y.‘ X' • . 'aZ’ 4 B 1 ill aoi ,'-.0r ' I 1ID3 As our final result we shall take the rounded nalue for hydrogen as =« 103,450 B .T.U. per mol at 62 degrees F. II. Carhon Monoxide . 7/e have the following experimental results avail- able for the heating value of carbon monoxide. Date Investigator. Value TemperatU 2 E 1848 Andrews 3057 cal/litre at cons.vol. 15^0. 1852 Favre and Silbermann 2402.7 cal/gram ” ” press. 18°C . 1873 Thomsen 67960 cal/mol " " ” 18°C. 1881 Berthelot 68200 " ” " " " 10^0. Andrews and Berthelot used the bomb calorimeter. Favre and Silbermann and Thomsen used the same apparatus as they did for hydrogen except that the products of combustion were led out of the combustion chamber through a coil of small pipe of considerable length which v;as immersed in the water of the cal- orimeter, thus insuring that the products of combustion were brought back to the initial temperature. Transferring these results into meanB.T.U. per mol at constant pressure using Callendar’s specific heat ratios cUid neglecting the correction to 62 degrees F. , we have the followirg for H^at 62 degrees F. Andrews 123,800 Favre and Silbemann 120,900 Thomsen 122,130 Berthelot 122,920 of Andrews* value cannot be considered because/the imperfection of his method. He took only one reading of the • \ J t I . I U'lii' 104. water temperature in his calorimeter after combustion and that one just thirty seconds .after combustion occurred. Due to the design of his apparatus, the thermometer hsd to be removed in order to rotate the apparatus which means was used to keep the water at a uniform temperature. To get the temperature of the water the rotation was stopped and the thermometer in- serted. It can be seen that this manipulation is subject to many errors. Z^^Cathon monoxide used by Pavre and Silbermann in their experiments contained about zfo hydrogen by weight. The correction for the heat of combustion of this hydrogen content amounted to about 50% of the heat resulting from the combustiai as observed in any one determination. The possibility of error in this correction is very great because of the methods of gas analysis in use at that time and also because it automat- ically brings in all the errors of their determination of the heat of combustion of hydrogen. Of the two remaining values we choose that of Thomsen^s in favor of Berthelots for the following two reasons. First, for apy given determination the volume of gas used by Thomsen was about six times that used by Berthelot, this tendirjg to reduce Thomsen's error. Second, Berthelot* s result is the average of five experiments where a total of about 1.3 liters of carbon monoxide v/ere burned, while Thomsen's result is the average of 10 closely accordant experiments where in a total of . .'O.C - 1 fiH m II • 5 j , . 1 . i, •» . ( \ ■ 1 t :/{••’• t :’ ‘ I.- m! . rji: ;o,t)Cc; i J'tiU^'ejsc ->. «. . _ 0 i, - V c. i \< V-. . r.'V? ' ■ ,;.i Z'^ I . 6*.i' j. 0 . t; ::;■ irw, awti.'* . . j.^- :,. , »rVc?*( • • ■ • • ~ • - *• t-”' t-' > • k- •)’ '"-1/ s :-’J [ \ozzliiiJ . . Tfiivri’'’/ V •j -- - '. w ' 'Si • w w‘ . , tvc •.•.■3,; ,snJ .0 J *.10' t* • - \f C * a i . • . i . ' J J" A i' 2 ( I >• ■ ij r> . i; I • , ' .(. J *■ ..: 1' iSj ' /XI ; i-.i . ’.V • *. :4 i-iio.T jC' t - • ' i -, A L,' I , ^ U . 1* V '!> - ^,1 » V U ‘ • ij J, . V# • li . . V C ■ i ’ j i f'3 I ci: J' .C {. <: '• ’’•‘^ 'r.i. V.'. i ..'3C a '. c, ,. J .;.ai! 0..- \ Uvik^ Dw'I'i - S trliftiiif I, t)' .' ' . : : ' .w 'jcr r.x. / JO i. j .; • . ■ a -p.. ^ ‘i'it.'V •.? * iT; i j c CTH'C-o fti '«'■ nl 'wct!i 'x-X • Oiv. . ^ cH-’ i:l i .: „X '• 2/“^. "ic . xl-:. - Xo XX_ ni. • ^ V' i ’ ' J U'-i XiijC £ .;’ 0 i! f„' {JlJ ‘♦i ■ ^ w iio" O' no n v . 4 ‘. l ■.; ;. ; ’J “i . iJU O'- nv/J- guiv/oricx Oi J" 'u.' ;iv>v ^... w-t,'*.: lo -voyi 1 n ' .-'f::v;I':. vci ondi; t; :> i:c ©iiT:yi: . r/ : .. .-uL.j , -Xoo %4_i -iqi , ic-; i ^U.\c: c,i:V ,,T - r^rfj-'roa jci.J * rrotr'ionl' li.y \zl J’Xi;C0T: ' . cloiij'icl , '..••O';'- , 'XO . ' mo O.--'? OUi/fcOl Oi.' -. ■ .;x: ’to £jt.c . '■ j'.'j ' ijj’xi'fyni”£>q;v-L> >vi.. lo L';;,-r:oYa ■ w.j'' ' i. . 'ir ' . tu.' X ; i;. , orix*;*! omcv. e...jLy^( rar-i Uw-viio xo io k 1.1 :‘jo: ■ rJiicnixoqxo o.v ^XtaoXu Cl '^.o »^y5ev.• II I . ii i' . t( w »^ £ > • ^ *V • • 5- .A V 1 » i 105 alDOut 16 litres of carbon monoxide were burned. The first six oi the experiments were performed in one calorimeter v/hile the last four were performed in another larger calorimeter. The aver- age result of the first group of experiments is exactly eq.ua! to the average of the last two. vYe have, therefore, as the heating value of 1 mol of carbon monoxide at constant pressure at 62 degrees F. in terras of the mean B.T.U. the following: / =122,130 III. Methane. 011^ Y/e have the following data available on the heating value of methane: Date Investigator Temp degrees G. Higher heating value cal. per mol. 1848 Andrews 15 209,728 constant vol. 1852 Favre and Silbermann 18 209,000 " press 1880 Thomsen 20 213,530 ” 1881 Berthelot 18 212,400 " vol. The methane used by Andrews was obtained from a a stagnant pool end contained a large percentage of nitrogen which invalidates his result. It is also very probable that the Favre and Silbermann value is low because of impurities in their gas. Thomsen generated his methane from zinc methyl and hydrochloric acid, and purified it by bubbling thru cuprous /afcsT chloride solution. The above result is from Thomsen&^work on 'i f) :: K. J t ! ; k . 1 > _.J,lJ*J. y. i) i.'. W i - ^C X t J : j. M ' ••’;•■ >.■ 'j' -: •■^. i- ♦ ,;'--r^-w avi'^y.::>'- e »ri ' L Ls-^ : : • ':a X r • : ;i J ..^ v, J > -i o > ■ ■ 'f ^'A* tj/ r.' t ;.: ■ 1-: j ‘is !!c' - .:w-x ii,.£l . XviXi' J ..0 0^' L * j- ^ . ; , i 10/iilL.^r ' , . *"• •■ . n*> '.h.*! . •• ; r. ; : • '' iXCi. .1 • • . ■- ' ■ ‘ L .; -■ X.U6ft*f 0 . • ' ,C i}._;: OJ ' A *ji(’ - i Bi \Vj(c. < or.; to ftri.-'v*' o?: ^ ^ f,> f ^ , H ni V.. C._,f .Ill f.o uj' ..iil:.iv.. lii- otlo . Li'J ov* : 'L 1? : A?' eirXi-v ■.■ ; L .: ♦ li' ■ iPl'T :.'0 - '•rf' <* ^ • 'j o . . G • ^ '••'*•. '• • 0 , T* tl ** u - _0--.C-. ax bX 0: i;nj...... .1.1^ ,.YV3\ .r v-rt'i: C'vJl M.:J t£-J ' fe{-X oeox e r;fTj-.': jt.c ajw r-YO” .r^ ? b..,, c; j e^lX ■J-A fiv^ -•,.*. J i . -Ci L'M.ioHwU'Aw \ , " . ; i. ^i.;'j:'-.^ :Cr -r lui-ti v i‘. • C.‘ \ '. ; 4 -Jl . X ' i .i I IX^;: OY til.i i.U’i -'rili'yr.-il Y I A ■ ; '1j Oi , 00' ;C £ oL c^iTii v''-XI- 6;r ■' tYV.j*'; orf. f. Xr; c6'S''.i, cn-.'iU O! ■ Y'- '.C'rj y.^Cv' vii?. ;. CL -:.*: ;,): . -xftX I i^uX;'.XiiJ.*; , ji'.< ... U.yC I no.:'ii^rf CO# uv ioiYCV:;^:: _oi.;vXiV :... c !: si ’-yvofj y/'t ..1;,;^ 6.YX*io-j^r 106 methane I and is the average of nine experiments which show a maximum variation of 1.1^. The calorimeter used was of the constant pressure type, the products of combustion being led out thru a long tube winding around the combustion ch‘-mber as described before. Correction was made for the non-condensed vapor in the products of combustion, this correction being very- small. The Berthelot result is the average c£ four determ- inations made with his bomb calorimeter. These four ex]^ri- ments show a variation of 1.6^. In order to compare Thomsen’s and Berthelot ’ s values we shall reduce them both to the locker heating v^ue in metn B.T.U. per mol at 62 degrees P. Thomsen: lie thane was burned withUie theoretical required oxygen at constant pressure of 1 atmosphere ^nd temper- ature at 62 degrees P. Reaction is GH^ t 20^ Partial pressure of H^jO vapor in products is 0 ~ 2/2^14.7 = 9.8 lb. per sq. in. Saturation temperature at this pressure is 19E degrees P. i/' ^1143.9 li =30.1 X =■ 0 ^ 36(1143.90 - 30.1) = 40,097 = 2037 -Hp = 40,097-2037 » 38,060 B.T.U. per mol CH^ Kp - 213,530 xl. 8 >-0.99842 = 383,7S0 mean B.T.U. per mol. Ep i 383,750-38,060 345 , 690 B .T .U. per mol . *. » ‘I I, Ij I i f I. » ■ . . i. ^ ip A* V ‘ i V j" ! . ^ *.i . T t I I I I •I <•' . "1 1 . V I'll. I iK ‘;,i tf 1 • J-. I • i. .* JU-V< J. •> ■* f' , j , ; i I (■; O'l j! Lj- . / ( I cf .U A./ I r V / .1 i: J. . )U a. 107 Berthelot: Methane was hurned. with excess oxyg'en at constant voliome and. temperature of 62 cLegrees S’. Pressure of dry CH^ in initial mixture -1 atm. -14.7 Ih. per sq^. in. Total initial pressure = 3.4 atm. (approx) Heaction is GH^ i- 2.40^ ->G0^^ 2H^0 +0.40^ Partial pressure of water vapor formed in products = 2 xi 4,7 =.£9.4 lb. per sq. in. Partial pressure of water vapor required to saturate initial gases at 62 degrees P. — 0.276 lb. per sq. in. Py^^^ = 29. 4-f 0.275 = 29.675 lb. per sq. in. Volume of H^O per pound in products at 62 degrees P. 29. 672 ^ 0^0 —10.475 cu. ft. per lb. Saturation temperature - 267 degrees P. u/'= 1093.4 uj -30.1 x-0 =36(1093.4 - 30.1) = 38279 ,0,^ =2415 H' = 38279 - 2415 =35864 E’ =212400^1. 8>0. 99842 =381710 H^^H;,=381710 - 35864 = 345846 B .T .U. per mol. Thomsen H 345690 Berthelot H 345846 average 345768 Lower heating value of methane at 62 degrees P. -345770 meanB.T.U. per mol. I I • .. • rU !tfi •! t.v . : . c 'I . •d 'v ■It.- 1 * 1 ’ ■ ' Uj c - ■ .', lU i.,mtTr-r j-fi- fi t, f- . j . r* -j' j '»• ? ; v' ' ■ : •' » . L J. : ( C'*:a‘ *lu V - e^Tc v i i . ; , c« ^ . - t- V.* V i) . '« , •i J J j;n. . ' *S' ',KV 'icJ’.-.r ^ , - ..." . ■ '••{*£’ r;* J't; I Li. . *i *. ^ . ~iZ Ij. ' lA'.'lj fo ■ r IV . Acetylene ( J We have the following experimental data on the 108 . heating value of acetylene: Date Ij^vestigator Temp.de- Higher heating value grees G. cal. per mol 1880 Thomsen 19 310050 const, press. 1881 Berthelot 18 314900 " vol. 1906 Mixter 20 311400 " ” { observed heat not corrected) The methods used by the above investigators are the same as described previously for other gs;ses. For the lower heating values v/e have the following calculations: Thomsen: Acejsylene burned with the theoreticsl req.uired oxygen at constant pressure of one atmosphere and temi:® rature of 66 degrees F. = 526 degrees F. (abs.) The reaction is -/- 2 i- 03 _ 200^^ +Ha.O The partial pressure of H^O vapor in products is = 1/3 ->^14. 7 =4.9 lb. per sq.. in. The saturation temperature at this pressure is 161 degrees F. i/' =1131.2 i/ =34.08 x = 0 , 0.1 = 18(1131.2 - 34.1) = 19748 B.T.U. per mol of C^H ^ , 0 ^ = 742 = 19748 - 742 =19006 B.T.U. per mol. = 310050^1.8^0.99842 =557200 B.T.U. per mol = 557200 - 19000 = 538200 B.T.U. per mol. I r«. 0^ ■ ^ /*w^ .-*» *. ♦»- f * t *\ .-*^ ♦ L L *u«:. U. .. >>. ■. :'■ V • i. ipto -t. . ' I . .t f\ f I- L'C :/ ’.If,) I H' ' ■ . "i ^.v; r; j, u/' - 1075.5 u^' = 50.1 x:^ e = 18(1075.5-50.1) = 18781 - V71 =18781 - 771 = 18010 514900> 0.99842^1.8 = 565920 B.T.U. per mol. - 565920-18010 = 547910 Hp ~ 547910 -*-522 =548452 B.T.U. per inol. Mixter: Initial pressure of acetylene =14.65 lb. per sq. in. Initial gases dry at 20degrees C . = 68 degrees F. Therefore, final pressure of wtter vapor considered non-condensed = 14.65 lb. per sq. in. Volume of 1 lb. of water vapor in products of combustion . 580.6 .528 ..14.70 IS" 21.46 no. Saturation temperature = 224 degrees F (from steam tables) u/' a 1082.2 u' =56.1 ^= 890.2 Saturation pressure at T =68 degrees P. “ 0.539 lb. per sq.iru X ^ 0.339/14.65 = 0.0231 -f- = 18459 ,Q;.=915 hJ 18459-915 = 17544 (observed) = 311400 XI. 8X). 9 9842 - 559630 - 559630-17544 - 542086 Hp = 542086 +528 = 542614 B.T. U /mof Collecting results we have for the lower heating value of acetylene at constant pressure and 62 degrees P.: Thomsen 538,200 Berthelot 548,432 Mixter 542 , 614 Weighing Thomsen's value 2, Berthelot' s 1, and Mixter' s 3, we have as the average = 542,110 B.T.U. per mol. at constant pressure and 62° P. Y. Pthylene (C,Hy) Experimental data on the heating value of ethylene: Date Investigator Temp, de- Higher heating gfees C. value Cal. per mol. 1880 1881 1901 Thomsen 17.9 Berthelot-llatignon 16.8 Mixter 18.8 (Obs.) 333350 const, press. 340000 " vol. 345080 Por the lower heating values we have the folloMng calculations : -It f :i i; Hn$% -O . -.Cl .- ncijo-ri/viie » . • r* • ^ iF.VI .- ^ -.: ;v'.»; . . - .-M. , .' n x: :;; (t.v..cUoc> ) aeoHKif’^- k ’IdV ■ \ .‘Cl J‘i: ,,.- .( ^v/ t -., t > ' \ ■- . i .-i j ■>-.;'. V-> • •i‘J-.ct£ ©O -J i’fU’S^i SlXO j v' .V ■-•^ /.if- 'I *' f ■ •* • ^,**rwix -4’ •* '-J . - 0 ■' ■ -■yn r - ' * TfriJ !: 'nee: c,‘- J.ilr 4 Xl. c-’^>,.; 'pv . c ' :: evn'i fii! ?•* i;BtiC't' ‘ (' Cc 0 0 101 • ■ * ^ r, 5 ^ i * , ' ■'■-•?' Sffi ;w* ' 'T • • :oro '■ ../tV I-ja 0/; i \i s .'v X J. »# - u .. ^ ■ ■'i*" ^ • 4. A ^ i.-i ^--ii l.;/r''':iH — C . rUe '. ',0'. .;T • OJu . . : . A) r -r vAv v r • • *' . . * ^.fT C ■* ‘ ■ *> -/-A* ,v.' C80X -• f .-j^y ;.^X r-or:.'.^’ :.' Ibex . ':r,ix: . C lis'iSfxr xoex • . >' ‘ '■'.A' f*. '-X ** r i t ' 9r :fv 'j m^ujLMy ■Afll.OSOi! 1€S»C'i7 : inX.. .'' riitc, Ill Thomsen: Ethylene burned vath the theoretical amountof oxygen at a pressure of one atmosphere =14.7 lb. per sq.. in^ and temperature of 64 degreeB E. Reaction is 1 30^ 2C 0 ^ 2H ^0 Partial pressure of H»i) vapor in products considered j^on- condensed is ‘i'-^l^.V =7.35 lb. per sq.. in. Saturation temp» at 7.35 lb. per sc[. in. = 179 degrees E. i," = 1138.7 =32.1 X - 0 -36(1138.7-32.1) = 39838 = 1800 = 39838 - 1800 = 38038 B.T.U. per mol C^H ^ =333350^1.8x0.99842 =599070 Ep = 599070 - 38038 = 561030 B.T.U. per mol Berthelot: Ethylene burned at constant volume with excess of oxygen T = 62 degrees E. Pressure of dry C^Hy.in initial mixture -1 atm. -^14.7 lb .per sq. in. 3^^ 200^-f- 2Ej:>-hiO^ Partial pressure of vapor in products of combustion considered non-condensed = 2 >14.7 =29.4 lb. per sq. in. P:rtial pressure of water vapor required to saturate initial gases at 62 degrees E. = 0.275 lb. per sq. in. P^ ^ = 29.4 +0.275 = 29.675 lb. per sq. in. Volume of H^O per pound in products at 62 degrees E. 14 .7 ^ 380 .6 A tn r- O j_ -1 29 672 q0 ~ 10.475 cu. ft. per lb. Saturation temperature »• 267 degrees E. u; - 1093.4 u» =30.1 x=0 iQa^ = 36(1093.4-30.1) = 38279 B.T.U. per mol T ce’-(- J- • *. j ■ ir. i[ 4 io J !.i mi ^ » . •/' 0 -s X uiir- o • t \ 9 ^ ,£i .1 CK'OX - ir% r ^ •• ■ CO ■~ u. , .1 : A lL 'J.r fTi..:, j; ..V * . • '> 018 *' '■' '* - ■ > .-. / ' i ' j .,j ^ . , T I, . .;.. , * C ‘ -r. £ ]:•:..'7 ,.» * , » • »n VI ^ . V w* . « • 0 > .'C l ^ ' ' L> ; • * r* ^ , 4 . . V ^ u • X n *^^ ToJ". tiolvi *11/448 /.J . /;. X ** ;xy i:-f'' *; '.J . < *’ C 7 ■ * ' 112 . = 2416 hJ ^38279 - 2415 « 35864 Ey ^ 340000’^!. 8*0. 99962 =- 611760 Ey ^ 611760 - 35864 - 576896 = H ^ = 575896 Mixter; Initial pressure of ethylene *14.7 Ih. per scl- in. at 18.8 degrees C. - 66 degrees I’. Initial gases dry. Fin>.l pressure of water vapor considered non-condensed » 2*14.7 =• 29.4 Ih . per sq.. in. Volume of 1 Ih. of v/ater vapor in rroduots of coiibustion oonsi 'dBred non-condensed III ^ -10.653 cu. ft. Saturation temperature » 266 degrees P. (from steam t ahles) u/ =1093.1 u/ ^34.1 858.8 Saturation pressure at T - 66 degrees P =0.316 To. per sq.in. X = 0.316/29.4 = 0.0011 ,Q'=36 0.093.1 - ( 34.1 to. 0011*858. 8)J - 38092S.T.U.per mol ,Q ^ = 2360 h' -Ey c 28092 - 2360 =35732 hJ = 345080*1.8*0.99842 = 620160 Hv =Hp =620160 - 35732 =584430 Collecting results we have for the lower heating vd.ue of ethylene (GjH^) per mol: Thomsen 561,030 B.T.U. per mol Berthelot 575,900 Mixter 584,430 .Veighing Thomsen’s value 2, Berthelot’s 1, and Mixter’ s 3, we h<-ve the following value for the lov/er heating value of 113 ethylene at 6E degrees F.at. constant pressure: H^z:.575,210 B.T.U. per mol. VI. Ethane Esp er imen tal value s : Date Investigator 1893 1905 Berthelot Thomsen Temp. de- grees C . IS 18 Heating value (higher) Gal. per mol. 370,900 const, volume 370.440 pressure Heduction to lower heating value: Berthelot: Ethane Burned at constant volume with excess oxygen at temperature of 55 degrees E. Pressure of dry in original mixture -s-l atm. -14.7 lb. per sc[. inch. Reaction is ECO^ 3H^0 y- - g-O^, Partial pressure of water vapor formed in products considered non-condansed is 3 a 14.7 =44.1 lb. per sq. in. Partial pressure of water vspor required to saturate initial gases at 55 degrees P. = 0.E14 lb. per sq. in. P^^ = 44.1 +0.E14 =44.314 lb. per sq. in. Volume of H^O per pound in products at 55 degrees F. 380.6.515 ,14.7 X." = 6.9S0 cu. ft. 18 5EE ^44.314 Saturation temperature = E95 degrees F. (steam tables) u,"' =1099.8 u^' = E3.1 X = 0 = 54(1099.8 - E3.1) = 58.14E , 0 ,^ = 4E60 ' I I . I' 'j / t •r ' V r r w • r ■ t »v#r»rr f • : J. I i ^ ' I J .i r -I. / cj r 114 hJ - 58142 - 4260 - 53,882 H; =370,900^1.8^0.99962 = 667,360 hJ -667,360 - 53,882 = 613,478 1-T = 613,478 1 515 = 613,993 Thomsen: 3thane hurned at constant pressure of 1 atm. -14. 7 Ih. per sq. in, with the theoretical amount of oxygen at 18 de- grees G . = 64 degrees P. Reaction is f 3-|0^ 2C0,.'H 2H^0 Partial pressure of water vapor in products considered non-con- densed is = 3/5-'14.7 - 8.81 Ih. per sq. in. Saturation temperature at 8.81 Ih. per sq. in. ' 187 degrees F i/' = 1141.9 = 32.1 X - 0 -54(1141.9-32.1) = 59,929 B.T.U. per mol = 3 [7.03(647-524) i-k 1.25 -lO'^ ( 647*’ -524^) l/S- 0.2( 647^ = 2892 -Hp = 59,929 - 2892 - 57,037 Hp 370,440^1.8x0.99842 - 665,730 ^665,730 - 57,037 - 608,693 Results for the lov/er heating value of ethane (C^H^) at constant pressure and 62 degrees F Weighing Thomsen’s value 2, and Berthalot’ s 1, we get for the average lower heating value = 610,460 B.T.U. per molat 62 degrees P. and const. press. Thomsen 608,693 Berthelot 613,993 N, •♦t V ii, >rU ■ 1 ’ -‘■ a j I , w • . I .f -'*>i -J' : : J ■/ u , 1 CJ; C‘: '‘.i j I J 115 * VII. Benzene vapor: (O^H^) For the heat of oomhustion of Benzene vapor the ex- perimental value of Stohman, Rodatz and Herzherger v/hioh is 10,096 cal. per gram at 17 degrees G, is chosen as the Best available. It is the average of 12 experiments. The method used was to pass a current of air over a wad of cotten saturated with Benzene liquid and Burning the resulting mixture of v^or and air in a constant pressure calorimeter. The products of combustion v/ere ledd through a long spiral tube and then thru absorbers to remove the moisture in the usual way. Calculation of the lower heating value: We shall assume that the oxygen and benzene in the benzene -air mixture are present in the theoretical proportions for combustion. The reaction equation is C^ -/-7.5^^ -h S8.6H^ 600^ -t 3 EJ )^80 5M^ The partial pressure of the benzene vapor in the original mixture is 1/37 X14.7 0.40 lb. per sq. in. According to Young* the saturation pressure of benzene vapor at 17 degrees C. is 65 mm. Hg, or 1.25 lb. per sq. in. Since the assumed partial pressure of the benzene vapor in the initial mixture is only about one third of the saturation pressure of benzene, at 17 de- grees C., the assumed partial pressure can be easily attained and is reasonable* The partial pressure of the water vapor in the products of combustion considered non-condensed is = 3/37.5^14.7 = 1.176 lb. per sq. in. *Young. Scientific Prodeedings Royal Dublin Society. Series 2. v.l2. p.422. (1910) .1 • I l' f‘ j r '•/ 1 ‘ k. , ‘ - - j' . ... 'b. '•. i^O'i -■ .. .1. ■C' U *1 fj / »J Jl A ' - y. i. '• 116 Saturation temperature at this pressure is 107 degrees P. i/' *1107.7 =-30.1 (at 17 degrees C. 62 degrees ,Q, ? 54(1107.7 - 30.1) ® 58190 B.T.U. per mol benzene. *1,050 -Hp = 58,190 - 1050 = 57140 Ep = 78.06*10,096*1.8^0.99842 = 1,416,460 Ep « 1,416,460 - 57,140 1,359,320 B.T.U. per mol at 62^ P. VIII. Amorphous Carbon vVe have the following experimental datasvailable for the heating value of amorphous carbon: Date Investigator. Value, cal. per gram. 1848 Andrews 7,678 1852 Pavre and Silbermann 8,080 1883 Gottlieb 8,033 1889 Berthelot 8,137 Andrews states in his discussion of the value given above, which is the average of eight determinations with highly pureified wood charcoal in the bomb calorimeter, that in spite of the presence of excess oisygen, carbon monoxide was found in the products of combustion. This fact, of course, renders his value too low. Pavre and Silbermann also found carbon monoxide in the products of combustion from their experiments. After de- termining the amount of carbon monoxide present in any one nase they added to the observed result the heat of combustion oJl this given amoujit of carbon monoxide so that their final results give the heat of combustion of carbon to carbon dioxide. This I, ♦ I .( ( e t i ( '! I 1 I j :•) i I { t - i 'j =1 i s 117 correction in their case amoimts to only about three percent, so that errors introduced by using an incorrect value for the heat of combustion of carbon monoxide are insignif icant. Eighteen experiments in three series were run using highly purified vnod charcoal. The values of the first series consisting of five ex- periments showed a maximum variation of 89 calories in the values given for the heat of combustion per gram. The average value from the first series is 8,086 calories per gram. The next seven experiments constituting the second series showed a maximum variation of 31 calories. The average of the second series is 8,081 calories per grrrnn. In the last six experiments wood char- coal purified in different ways was used in different determina- tions to note if the method of purification had any effect on the results. In this last series the maximum variation between any tv/o results v/as 19 calories and the average of these six was 8,080 calories per gram. This is the result q^uoted above. Gottlieb used a calorimeter very similar to tin one used by Eavre and Silbermann. The carbon used b^ Gottlieb was prepared by heating a five -gram ball of cotton in a loosely cov- ered dish alov/ly at first and then more intensely after all the combustible gases had been driven off. Later the cotton char- coal was transferred to a tightly covered platinum dish and neated to about 950 degrees C. for some hours and then cooled in a des- sicator. This carbon absorbed moisture freely. Upon analysis the sample showed 1.5^ moisture. It is safe to assume that only a portion of this moisture was absorbed Iby the time the sample for combustion was weighed end the rest was absorbed during the • r -J r^j‘nr?-.-.v.'5 V * ' 1. ; yn ■V.f t .» . 1 v» ,•■ ': ' ' t 1. "i, ■iT'.:' aa ■■<*# :>T ^ ' 1 7 j J'Od'J’' ; / 7u.: . ikii 7 V :;w ♦ 7 \c^ .7; or.’ -..w . : .>':]■ C :w i A.- *u.A-CX. .! r*- :' / 1 '*■* , ^ r.X'iTvO 1- .10^X4 .XWCI; '. X , X ur.'Xr* ■ ■ rv...- ..j; ' X 1 *J' ■ i.f. r.-n^r X ts^'; , ;. -:l 3l». • » X : e*fi'rZ / " '. V oi'i • ' r ■'*’*'''■ ' ‘ , . : vf. ’ ..J. r • - 'fc Xr; 3ii:SriT. ‘ r-:. o.:' • . .. . ' j * CtTT 1 •ii '.. ■ w.tfiifi j •xpr' g 7'. . V.. . . ! '* 1 »■ "r - - - • ( X',; P; <.vX A* ..:• 'C.: . ... -. I n. : v> 0 -Xsi K w V t m. 70y -V- ..sTO!.- if /.I * ,1 , r'v.-'i.* Y*' . ■/ .C . ll 0 .' C . ^ i . i- V - itO ■V.- 'I'!’ :*iCl ;i, X ■ ' a- ^fU;' ; ;i- ■ ' X v' - .! ' . 7 I ;:;£ 1 , •:» : f J .C- ut- / . . • . . V •J Xi '/■ jXjiai/*: e.:j .- {• • J X^V'O - • *• *> x‘ I • .' c\ k }, r j . < LiCiK-si>i 0-*L vu liv. ». .'j,?;'.'^’ ri • -J ••..•’.t'i.' LV:. '.I r,: .;/ .-... .u, ♦;■-:•< OVJ- - ' ■ir.-’- . •' v: ; ' 1 ^. . 1 .’ {> ‘wU. J « V ^ ijtjC’i' (j Li.'i r '•. j. ,>'■.' \'d'' fi'Cif'M/ j. r’ .'tX ;fvJu <, .0 i C'. ( .• ”Sj ; ■ ■- ;.i ■'; i iio,'r.-:;r< 0 '. ^ ; ftvii; Lxjf X „-;:X7 j- . -I.; ,: . .fov.:;';x' rt o>t ' f.C' >■;...!•;> o.*' J •. ;I :> 7 V 7 ^ V'^ c::.. wL -- f:.!: ^ r,X..'r. ,■... «-'r7 u*“:r^' :. .. ( '1? t cj I W •* C • ■''-1 - viAS V- i>OCf-^i&€ti:s -rr’ a; iJ j:o .O'TC'jutJ^ »sfiT vtX/ Sr: n'.XXi.-; ' 'iO' * * »*> «► -if . 118 timethe calorimeter was being prepared for operation* With a slight amount of moisture present in the sample as weighed, of course, the final result oalcu-lated on the basis of this weight % will be slightly low. Therefore, Gottlieb’s result ^ich is the average of six experiments which have a maximum variation of 7 calories per gram points to the accuracy of the Pavre and Silber- mann value* Berthelot’s value was obtained by burning wood char- coal, very carefully purified and dried. Oxygen under 25 atmos- pheres pressure was used in1he bomb calorimeter to insure com- plete combustion. The value given above is the average of six experiments which show a maximum variation of 10 calories per gram- Of the above values quoted we shall choose the Pavre and Silbemann value which is substantiated by a total of E4 ex- periments in preference to that of Berthelot vii ich is the result of only six experiments. Also, it is very possible that Berthelot’ £ method of purification was at fault. Seducing the Pavre and Silbermann value, which is in terms of the 20 degree calorie, to meanB.T.Ui per mol, we have for the heating value of amorphous carbon at 62 degrees P: H - 174,250 B.T. U* per mol at 62 degrees Pahrenheit* 119 * Talile of Heats of OomlDUStion No* Reaction Lower heat of comhustion at constant pressure and 62 de- terees in mean B«T.U. per mol. per Ih. per cu.ft. 1. 103,450 51,725 271.8 2. G0-+i0,.-f co^ 122,130 4,361.8 320.9 3. H^O+GO -18,680 — 4. G ( arnorpjf GQ 2 _ -f 2G0 -70,010 — 5* C " +0^->CQ^ 174,250 14,521 — 6* C " +2H^-^GHy 35,380 — 7. GH^ -t 20,,-^G0^i-2H^0 345,770 21,568 908.5 8. Gj,H^ -t 2-|0 200^ + E^O 542,110 20,838 1,424.4 9. t 30,, ~^2G0^ 1- EH^O 575,210 20,520 1,511.4 10. G^Ht -f3iO^-f 2G0^t3H^0 610,460 20,316 1,604.0 11. { vapor ) +7-JO^->6GO^ -fSE^O 1,359,320 17,415 3;571.5 ' ■ vTri • m , . > ♦ i « A. .k % V. •; . '■ ‘O' • .:r ^^.'. cer. 1-’^ ■; -.c ,r <■* ■^ ■ • ■ - ' '.' ' . * ► < r » . -* V p«. » f- ■ ■ , ' 1 1 ' .-% >-. 1 . .. . / . .' U . Cl. rii;‘ , ^;V- ' 'l'*v A >gmnB9 " 'fH • - r.v. ■- -..• ■ ’ : 5 -.fesp;s 5 rTr -~-r‘ Table of Heats of Combustion - continued 120 * Ho.* Lower heat of combustion at Heat of combustion constant volume and 62 de- at absolute zero in grees F. in mean B.T.U. mean B.T.U. per mol. Per mol Per lb. Per cu.ft. 1. 102,930 51,564 270.4 102,100 2. 121,610 4’343.2 319.5 121,250 3. -18,680 -19,150 4. -68,970 -68,430 5. 174,250 14,521 174,060 6. 34,340 31,250 7. 345,770 21,568 908.5 347,020 8. 541,590 20,838 1,423.0 541,600 9. 575,210 20,520 1,511.4 576,730 10. 610,980 20,333 1,605.3 613,520 11. 1,359,840 17,423 3,572.9 1,364,370 * For reactions corresponding to these numbers see table on p.ll9 i 1 1 : e / r e t f L. t ■ ' " ' •* ’--•'//I hi fiCHrt* .»«*« * 4, 121 6. Berthelot. References on Heats of Comtustion. 1* Andrews. Phil Mag (S) 32, 321 (1848) 2. Pavre & Silhermann.Ann de Chem et de Phys (3) 34, 349 (1852) 3. Thomsen. (H^) Pogg Ann 148, 368 (1873) (CO) Thermochem Unters,Vol II, p284 (CHyi )Berichte d.d. Chem Gesell 13, 1523(1880 (C,_H^) and (C^H^) Thaermo Unters.vIV,p65. (Cj_H^) Zeit Physical Chem. v.51, p657 (1905) 4* Schuller & Wartha. Wied Ann 2, 359 (1877) 5. Than. Wied Ann 13, 84 (1861) " " 14, 422 (1881) (Hj Compt Rendus 116, 1333 (1893) (C) Ann de Chem et de Phys (6)18, 89 (1889) (CHy) " " " ” " " (5) 23, 176 (1881 (C^H^)and (C^H^) ” " ” (6) V.30,p556(l893 Ann de Chem et Phys (6) v30,p547(l893 (HiP) Am Jour Sci (4) 16, 214 (190») (C^H,.) " " " (4) 22, pl7 (1906) (C,_Hy) " " " (4) 12, 347 (1901) Zeit Phys Chem 58, 456 (1907) Jour Praht Chem 28, 420 (1883) 10. Stohman Rodatz Herzherger. Jour Praht Chem (2) 33, 257 (1886) 11. Callendar (Specific Heat of Water) Phil Trans, V.212A, ppl-3^ (1913) 7. Mixter. 8. Rumelin. 9. Gottlieb. Appendix C Chemical Eq^uilihriiim 122 A hrief outline of the methods used in determining the eq.uilihrium composition resulting from gaseous reactions at high temperature is given in the follov/ing. The experimental data used in determining the thermodynamically indeterminate con- stant of integration in the equilibrium equation is given for each of the reactions studied. Eor detailed descriptions and discussions of the e^q^erimental methods see Haber’s "Thermody- namics of Teahnical Gas Reactions" and Hernst’s "Theoretical ChemistryV I. Streaming Method. The gases involved in the re- action are passed through a tube a section of which is heated to the desired temperature and the following section kept at a low temperature. The gases are assumed to attain equilibrium in the hot portion of the tube and to be cooled so rapidly in the cold portion of the tube that the reaction immediately stops. The equilibrium composition of the gases at the high tenrperature thus exists in the cooled gases which can then be easily analyzed. II. Semipermeable Membrane Method. A vessel which is pemeable to one constituent only of the reaction is evacu- ated and the reacting mixture of gases at the desired temperature caused to circulate around the outside of the vessel. The par- tial pressure of the one constituent to which the vessel is permeable will soon exist inside the vessel and can be measured with a manometer. This method is applicable only to a study of r .■J ' ? .1^ • ' iafcyiaC*^i w r*’.^ *j- c ’ • C -rIC V / .Jp >. *. . ,,.-*';.gv f‘ j. ijiit.if ;. oilJ t>: ! i'^J’ '.I oriiX?' O' n*:-- J/ / ’ . ."; 'T ' « '»i*vi ^ V.' N , 1 » * . J <* ' i. - 0 0 ' ' .r I. -jl : . ■ X irJ^ ,. Lei.;;*,; ' ,rJ., .:.“jo^^;!'vo, !. i/.' • :rfi ,:.. . , 1.0'. cr. i- :, o-, .v" u..;.:.i ,’>or 'r.: (. r.'sdxiiu r. .'f'a ,i “’/ ia;' , oi’ . '. "iv J'^-cJ‘31 ^ ^ A'.j.vt ..x* 0 Au t>- ' t! ’, C’• JO 0-0 ot\T iicl. Oil -I'l :' * ■ :ii. : •.» h •• . f j k'l ' • - “ ■ .i,> O'.. . .. ■’ , -V ' li" OO'I.'' i.oix'i i 1,'L.O Uij.-jC . -.Llj o Ci.oP. Of J’ JT" r.V ,' J’ '0 .’ o;iv *> . •' l i.' «. JA*. i.'.irXl i.; 0 '' '■ o'!.: .cD..i :■.•.■ OfiV V* • ' .... y.r.'xoXJrJ?’^’ * , •^ X .; ^ . . , j /'X CO ^ s .ftj' t, 0 <: O' Xo -0 ocf:;.r oX' ,’;0 'rc'i''j W.0 . vroM.v;.0-': X- L' v>*A l,* ‘ . ».) j . -' • £ 0 ' I ' > J L w aC' ..Oio'X^O' r.:Ou o-'i.,; uiiX ' -.t’ aO j .u’w‘J.fioo'j;:‘: 0 •' .• '• ■ •; , . ' '' ,.;. .1. ' & 0.. ■* f. \C 1'..: C* ‘ kj -I M S G ! « . u'X rX; 'V .JaaIL' t!i O.tlu* ■ay' ,'' O'" ••'u » S . oxX-ii..; / ’ ;',v. '*■’ ' ,.;'j ^ i t < J. f ♦ / 0";: • - .o':; cf.u or"X?>i 1. 00 4 I t ' :> '■i' '•- • j- .'■''' 0,'x oi:x 00 .."no )n6j; j,r , ij .'. u 0 f'. 0 fi jiv' v*" £; X';’.9G;- '.i-o , EX 'V ’ .1 . 1. ^ ' • ;-/•, . . ■ , Jl ' ' \ ^ -X » % «. 'Wi... .*, r w Jj\ 4t.k, u;tX x.. Oj'-'.l.'C' u"' ;w'- .i:: .■ '<.■' f)nn' btJ-£ r« ■ ■ ■.*■'■ 1 "/’ '• 1 , - '.w.j tifiv .o:'.X’aO o:'X 0 . o.rf/o'o;.;. V q£ ■ Da"b,cji 64 ). j v-j; -.LoCwoc'^v 'e/Jw ' ^ Oa jj’ a. 'Oic- artV- w*; 'ic ro. . .,::.'iY'-Ci»i.'t, «> v'j.::r)"- O' ; i,.'! r. c i'i'fir £oi\ucr/ X t:.r':f: a 'io*r oX '’:;;X.t‘. oIV oXIr/;.-* i;.r '^.tf '•: ;i." , ./O > . ... 123 the dissociation of H^O since semipermeahle substances are known for hydrogen only and are palladium, platinum, and iridiiira. III. Maximum Explosion Pressure Method. The origi- nal mixture of gases is exploded in a closed vessel and the maxi- mum pressure of e2qplosion measured. Since the maximum pressure is dependant on the heat of reaction and the heat of reaction on the ecjuilibrium composition the equilibrium composition lends it- self to calculation from the maximum pressure. Also in those reactions which incur a change in the number of mols the maxi- mum pressure is directly influenced by the equilibrium composition. IV. Method of the Heated Catalyst, (a) If a catalyst such as a platinum wire is heated electrically in an atmosphere of gas the equilibrium composition of the gas, at the temperature of the wire, will exist in the gas immediately surrounding the wire. Due to the circulation of the gas set up by the heated wire the gas in contact with the wire will be swept iiito the cooler re- 'gions and the reaction thereby "frozen”. This process is allowed to continue until the composition of the whole gas volume becomes constant. This condition is determined by analyzing samples of gas from time to time. Temperatures are determined by the change in the electrical resistance of the wire. (b) A variation of this method is to heat a vessel containing the catalyst to the desired temperature and then to lead the gases through the vessel or enclose them in the vessel until equilibrium is established. Samples are drawn out from time to time and analyzed. V. Iridium Dust Method. Iridium dust is produced by heating strips of iridium electrically in various gases. The 3 I '''i> 1 i. A ’ t. ^'- ^ '.'. .. ^ y til ..‘ w f! ttijkift. V. i' 1*.., *' *> * * 1 -• . X > -'JX-i ;y.i *'3 oX' ‘.jfv’:. )voZo(.,'. :■ Li .*, unii ■•^^■it TiTii -amauam^- •■ ■ • :,j ,c/v a '.i.iv.L-^ i .- t'i-.i. • * ^ i. IJ V i- " . n J»i ^ w I k’ .1 . .1. _'J ■- ^ ' * ^ . . . 1 .. ;.! ^:.J w r-vi-; .CO ■:;,•! O. I D;;ttJi. : . ':... tr;;i _;■-»; u- ,. XC 0.1 ot* , cc,' :, .••j- I'.'-'-lI i '3 .. O r . J' L' '\X !> ) .w .' , !!icw /I'D ujw 0 C'fiJ 1 ■■_ - or(u : ♦ ' . i 0 . ..' ' ■ >. . i! \'j-^ '-• u!.t .. u' L‘ f .’ Tij ju CvT^t)** v>'3" ''.'.'.o** f.! 'j -4V iX * u £-i 0 ■ :•' ■■ ^ I *« U r.jiJ a-0 ivoi" j ■ . 4. ^ ri X ^ 1 X * I nilJ ’2^' ’. '}C.. 0.1 V.. W ■ic.ri y/3v f»i<2 i'’ olsi '2 ..'c •.:''ci‘v U..2 c. 4 vv -J- 4 S • X .J..V a:jw I ■• •••■: a^o . .. < L.i.. oI-*i: .' tJr*2 xO nui.M.t-0f.,x0y t ' - ' ij :2''c-r. ot : :. ",i ly ri' '.'‘1* /L'fir : J o.’> tiZ yl'.j o ‘ . ■» , T l< I ; 4. • * . V-' r 'j r •' i^r J J .. >.-.i -1 • ' ,J !-/ t. ^ •»* -'S' « :.X *A:Mr?*yZ' . w <• « / •( r * r V’ *-»•*. */' • ' X-.xnci*jt X. c ■' 2i.r.re . b ' t liOi'Xc;' xl , J >• X '. ' 7 . , \ (.1 ) ■ G ,■ ) ! .' . ' X C u " ■'/,;r,:.,: J ,:6 'iV af.', toxia' ‘to iOtSf'V (>• u livirc^LS * * 1 ^ • - * * ; > -\ r • *« <* * ! , I r j' 1 2 H4 iiV fl ' < ‘ ' r"- • .^4 ' ' . -.Um VA . ki ' I -r'} :\ '2 eit 1 i ; . y .'j - . X ■;■' -,, ,i)o.;^Zx»rr'5 y.r .' ,‘il) ti ^ i X Jr 'i r- • ' '. •' - •/ - ‘i} ~t ••.,*■'• --X • . Vi-x,'. ;• ,r. :-2 ■:*. oZ'.ri’tpji.Cw iCir2.oS.‘i.X :o ■ J •« J 1£4 quantity of dust produced is dependant on the nature of the gas and the temperature to which the iridium is heated. This method is especially applicable to the measurement of the dissociation of carbon dioxide. Nitrogen and pure carbon monoxide produce no appreciable amount of dust v/hile oxygen produces large quantities of dust. The amount of dust produced by carbon dioxide at a given temperature of the iridium and at atmospheric pressure is assumed to be due to the oxygen liberated by the dissociation of the car- bon dioxide. A mixture of nitrogen and oxygen is found v/hich mil produce the same amount of dust as the carbon dioxide xtnder the same conditions. Assuming that the oxygen content of the tvjo gases is the same the equilibrium composition of the carbon di- oxide reaction is then known. VI. Measurement of Equilibrium in the Bunsen Flame. The inner and outer cones of the Bunsen flame are separated by fitting a glass tube as an extension on the end of the burner, the glass tube being of some what larger diameter than that of the burner. A stopper is made to fit tightly in the annular space betv/een the burner and the glass tube. The inner cone then burns on the end of the regular Bunsen burner tube which is now inside the glass tube while the outer cone burns on the end of the glass tube. Samples of gas are withdrawn from the space between 1he two cones and are assumed to be in equilibrium. Temperatures are measured with thermo-couples. VII. Direct Detenaination of Equilibrium, (a) Yi/hen one of the constituents in the reaction is a solid such as carbon this can be placed in a porcelain tube and the whole heated in an i=;» ■TiMTiartmiri u^- *.:U^ •■ b J 1 O r.t. • ' ^ u ' j 1 / j ^ l>jjLViT I » J.I :J ■, r..': f< J .jy. S,- • 0 • Oi.J « i-X‘3v;^X ':I.C . ‘ t. ^ . f'. ‘‘tiJ.j ■*. . :• ’.. -:f it'.'( .‘i. w* 4 :t:q: j.:-: ^£>:;CiM . ; . .iv.vX:: 2 o uci-iil -* . t; : ■; -C , : i 'i tio^;,y.v sC.LTv; X 'i.j "lo ■ ■ ,i o TXaloo'i' t. 7 . 1 , •j ‘ t? . 1 . C; :f'jcf-. c '.:! i>v::7 ,r-:- X '.;.o w-:.. .v:-?,o '. 0 -• . « ri* ■ . 1 . • * *1 .. ■-' -•» J ■ ^ !■■'.' ' : v;..V .IcOv' ilJ: DifJ' \]ii /"j £>;;■. .\ .:*rfi X r?i ,..Ci cjf - .■^ OJjt VI- cX t 1 ; < jL .7. • J.x r ■ ' !•' n*!:. - .j- -J rS , 7 ;t ^ . 'S'li.i-Xij i:c ., ; u •• v‘ . .. i: jfX-Oflf 8 .'Qa>»r-. x v;...;;;./*r I * > * I ^ -Hi. i^r - iK- I^a£u • ^ Oil-'*-.* 'A i .‘:c: 4. } i.< tr. i • .' L. ■ s." , . . - - u '. ' - V. " 1 . . *-'» •> ■" . .4 . . .• u -- ti ' j ' .» j Cl .'•.‘j o . 'lOff. k'l, .. *I U 4 *,) 0 I i4 .7'^ i &0 .' noiiJLf' ojV »•; 4 -o: . V , i ^ L*ii » « «r . f).V. ■ •(■ jrr.l. oii.’ 1 y. - « S> ^ ,i< , ■-.i.w iv Ini ;u ;},■;' -li Xh c rr - t-ci vc . 'i "x J 'i -i v.‘-iiv» nn ou 'iJ , f! ■ tv. o< c;:'. * .r %. 7^1 a--: i' i-- -- w' i it. . .4 ^ c : 1 .; v^s:J Cm 0 iJ ■• f' ^ K / f*. ’ • > ^ ^ w • V • ., ^ ^ * r ■'■ ’■ *' ' •*’ ! 3 :.r-,. .:, •' ;• e.t xt:..!; -. ,-f ■ ‘• IJ « u i--^:^:uj'[ -i. .Cr-i: ]■ '::o hiV' o:';l 40 •5. " t r- i .*v /yin 7 -j.' i.L rii;, -ii; - tJ.l. a.; A &I ooo'j: i AZ iiX v j’. u *-r ,v , . ' ^ . ia f..,l i/JO*;'- J:i VX’..I.I I’aX ’ r-X 6i;c.'.Iq &d ni.'C OiW ,' Ai** * ' ' 'f *- * «!?»S b 3 ^- T^eqi a ri - »■ • *•• .• . . . , ■> X 125 electric furnace. The gas constituents are then passed thru the porcelain tube at a rate sufficiently slov/ to give time for equi- librium to be established. The products are then analyzed. (b) Carbon in the form of rods is heated by an elec- tric current in an atmosphere of the gas. Reaction occurs at the surface of the rod and is "frozen” when the reacting gases diffuse into the colder regions. In either method YII (a) or (b) a catalytic agent such as platinum, nickle or cobalt may or may not be used. (c) A study of the water gas equilibrium is made by passing water vapor over glov/ing coals and analyzing the result- ing gases. VIII. Equilibrium from Density Measurement. The dis- sociation of carbon dioxide can be measured by electrically heat- ing a platinum bulb filled with carbon dioxide to a desired tem- perature and then dropping into the bulb a small piece of alumi- num. Changes of volume are measured by the movement of a short thread of mercury in a horizontal capillary outlet tube 'fitted to the platinum bulb. The following reaction occurs: 2A1 + AljOy t SCO According to this reaction no change in volume will occur if the carbon dioxide is undissociated and if the assumption is made t^at equal v/eights of carbon monoxide and carbon dioxide have the same volumes under similar conditions of pressure and temperature. If the carbon dioxide is dissociated, a change in the number of mols v/ill occur with the above reaction which is proportional to the amount of dissociation and which can be measured by the change of volume. t;. . , £ '-i., V - V’ ^ -‘ » I W J< *- w . - A.. V w tj .^. J-. w . ,1 j u i . O .» " J , « •< ; , "It w :. ntj, .. 1 » -* » V ^ V ,, L M 1 > V Osi • -xiiX Qj/Jo': r ‘i. w i s' «. As' — k M « k • J . U -X' 1 -. • J.AxS» 0 ’:' 0 '' »J ! 0 ,' . \ - .-’ 0 * * *- s# e.vX''. l.t. - '■ ■ • '*t ' ir ' i: -.'’ Ttr / V (./) < u W •>.C . k i vj v> X ^ V . ^ '• --• .. ‘ .0 J 'J X C" ‘ w 1 f • ‘• S' WJ» * ■ ’- ■ . 0 u 0 OjY CXiit i ') ■ 1 • ■ .» X •* .’K'.'Y ■ • - ■ * . * . ’ f* '. w lo I'.l *-0 XJ A » * ,f » . 4 « > V« . r- L i 1 t ' J. >■ to * - T:i<£ . £1 i * w*. V C> -r . « » • * .0 "».t • •* v^*'* • »£ :r: -.£ ut. £.vo.C._, .;v 'i.oi.iJpV v/^‘. . 7 ' I - u - ; u:i ; . '- .XStf n. :;•. 0 V.- -i?' r'C':;-, L.I’.wMi.' .*■ o.r tc t, L'i £;0 irbUnivf'.i. t -j J '. w O-’— • . j -I wl'j c-'j/ij] a jv'i ' ^ . f* f/J.. \/ A)’ M '- i . i, ‘ ' 0 ** .' ) , u ij .' &' 2 xfv' rX ■C, '■ '•r^ S ■'■'• uo I, : , V n.£ t;j>: ■ ;( Yr Ij :;:• <,wi.. - • cY :x.' > V r ■■ rt ' , ■ J _ilU f yf J *0 t ^ r* W . Y.. <■ 7 >*••*>) **^*,0“ X C \ w' K* *m iL^ I •:. ■). «• jv’d ii.-Ci’-.AO i>ii £ dj J. x.c'iicrr. iioJTjffO Jinir? o a/'YaY ?n-v( ?'■:■,( 'to . 'i •:Y.0r>7 oc^.}‘.r-'Y > . ' ' ■ V’ „.'i ,Xo:.:‘.-. 'ijucY':'. -o ;-u 'x^: c 4 o Y tx ruY'.. p ooifY • ' - ■ 1 •j 1V:Q0-,,X * ■ X 'w 1/ ,C ■;. , li C X 'AW roIXu 'A- v.v.c;Y otT r'oiXW •X».' .- 1*U X'.YOr . in'l! rc '/ Jg J ' s " iij.; — Au '« . B »xj * y;v ; ^j »a a g ‘ A » l t r'^.i Tl ; »'• K-'' 1 . It \26 The general expression representing the eq.uilihri'um state in any reaction is as follows: 4.571 log,^Kp=*^ ~£.3026q^lOg^^ T-i ^T-I/S^'t'^C i V«here T"is equal to the sum of the constant terms in the instan- taneous specific heat equations for constant pressure of the con- stituents of the original mixture minus the sum of the constant terms of the instantaneous specific heat equations for constant pressure of the constituents of the products of the reaction. _ II Likewise ^ is the summation of the coefficients of T in the in- stantaneous specific heat equations while ^is the summation of the coefficients of T’" in the instantaneous specific heat equa- tions. The general expression for the heat of reaction at absolute zero is = Hp- Tj^'T + i-r T / J Vi/here T is the absolute temperature at which is determined. Reaction CO CO^ Inserting the proper constants in the above general equilibrium equation we have 4.571 Iog,/^:=: - 5.3881 log,^Ti-0.001335T-0.08'10'^ T+C Z - (_x) (3 -x)'^.il)^ 100 ( 1-x) - percent dissociation of CO^ Papressure in lbs. per sq. ft. abs. T = temperature Pahr deg^’ abs. A 1 27 Experimental Data Pressure atmosphere -2116.7 lb. per sq.. ft. Temperature Do. C atbs E abs 100 (1-x) 4.571 log,^^ Method Investigator 1 1300 2340 0.00414 23.1374 I Dernst and 2 1395 2511 0.0142 19.4673 IV von Wart enb erg Langmuir 3 1400 2520 0.01-0.02 19.3040 I llernst and 4 1443 2597 0.025 17.7830 IV von Yv art enb erg Langmuir 5 1478 2660 0.029-0.035 17.0478 I Dernst and 6 1481 2666 0.0281 17.4361 IV von Wartenberg Langmuir 7 1498 2696 0.0471 15.9030 IV Langmuir 8 1565 2817 0.064 14.9835 IV Langmuir 9 1818 3272 0.45 9.1254 VIII Lowenstein 10 2243 4037 4.50 2.2520 V Bmich 11 2423 4361 10.50 -0.3710 V Emich 12 2640 4752 21.00 -2.6343 III B jerrum 13 2879 5182 51.70 6.1644 III B jerrum 14 2900 5220 49.20 -5.9265 III B jerrum 15 2945 5301 64.70 -7.4047 III B jerrum 16 3116 5609 76.10 -8.6202 III B jerrum Taking 0 = -13.1 in the above equation for equi- librium we have the following calculated values. The agreement betv/een calculated and exp)erimental results can be seen from fig. (20) page 128. Temp Eahr abs 4.571 log,^Kp 2300 24.146 2500 19.925 3000 11.861 3500 6.134 Temp Eahr abs 4000 4500 5000 5500 4.571 log,, Xp 1.855 -1.462 -4.116 -6.297 o ,-

o _^\ •y ■ji '3 <£ o' £? > 0 ,J i tf . _j. t CP !>• •$ i O J t 3 ■-J O 0 0 -0 V \ Ci ifi o < 0. o '> P 0 > <2 3 o % 0 i1 O ^ Vi- 0> ii? (0 o O' n A iD tp o u> J. ^ > f 0 » 1 i 1 ; ! Ill / / / / ,_ r i 1 ■':.:. ' .1 -.!...■.. 1 I.M..P ; ^ 1 . = ■ i i ! 1 ■ i i,:'; ,-.i. . .,; ■V'i.W ^ ' 4 -v' fi N. K . T» #x ( 129 Equilibri'um eq.uation 4.571 K: Reaction + i 0^ 102100 H^O - 6.2631 log„T+0. 0002361T+0. 033310'* o!+C - _ y (g-y)'* ' / 1 • p;: ' (i-yV 100 (l-y) ^percent of dissociation of H^JD P^pressure in lbs. per sq,. ft. abs. T temperature Pabr. deg. abs. Experimental Data Pressure =1 atm = 2116.7 lb. per sq. ft. abs. Wo. Temperature C abs P abs 100 (l-y) 4.571 log,^Z^ Method Investigator 1 1325 2385 0.0033 23.2917 IV Langmuir 2 1355 2439 0.0049 22.6355 IV IT 3 1393 2507 0.0068 21.6458 IV ” (Yifartenberg 4 1397 2515 0.0078 20.8400 I Wernst and voh 5 1434 2581 0.0103 20.4235 IV Langmuir 6 1452 2614 0.0137 19.5740 IV tt 7 1458 2624 0.0147 19.3647 IV Tl 8 1474 2653 0.0140 19.5096 IV " (Wartenberg 9 1480 2664 0.0189 18.6160 I Wernst and von 10 1531 2756 0.0255 17.7240 IV Langmuir 11 1550 2790 0.0287 17.3276 IV " (V/artenberg 12 1561 2810 0.034 16.8670 I Wernst and von 12 1705 3069 0.102 15.5950 II L Owens te in 14 1783 3209 0.182 11.8700 II TT 15 1863 3353 0.354 9.9320 II TI 16 1968 3542 0.518 8.7505 II TT 17 2155 3879 1.180 6.2900 II von Y/artenberg 18 2257 4063 1.770 5.0271 II IT IT 19 2300 4140 2.600 3.9608 III Wernst 20 2642 4756 4.30 2.3904 III Bjerrum 21 2698 4856 7.50 0.6820 III IT 22 2761 4970 6. 60 1.0776 III Tl 23 2834 5101 9.80 -0.1534 III TT 24 2929 5272 11.1 -0.5471 III IT 130 Taking C = 1.1 in the equilibrixim equation we have the following calculated values. The agreement between calcu- lated and eiqjerimental results is seen from Fig (21) page 131. Temp Fahr abs. 4.571 log,. 2500 21.457 3000 14.365 3500 9.309 4000 5.542 4500 2.646 5000 0.366 5500 -1.455 Heaction + 00^5? H^O 0 By subtracting the equilibrium equation for the reaction GO-*-^ CO,, from the equilibrium equation for the re- action O^-tH^O we get the equilibrium equation for the above reaction which is 4.571 log^, -0.8750 log,^-1.0970'10'’T 0.1133 loVtl4 . 2 ^ P.. • Pco. “ xTi^T Experimental Data Pressure •= 1 atm -2116.7 lb. per sq. ft. No. Temperature C abs P abs Log,.K^ 4. 571 log,,E:^ 1 1453 2617 2.39 0.3784 1.7276 2 1507 2715 2.46 0.3909 1.7868 3 1519 2735 2.62 0.4183 1.9121 4 1547 2787 2.31 0.3636 1.6620 5 1553 2795 2.25 0.3522 1.6099 6 1579 2842 2.69 0.4299 1.9651 7 1619 2916 3.31 0.5198 2.3760 8 1635 2944 3.10 0.4914 2.2462 9 1659 2987 3.59 0.5551 2.5374 10 1703 3065 3.13 0.4955 2.2649 Method VI Investigator Aline r i I ! V V. I , .. • ;j ‘i ■ ■f - ( ■ f / a I \ '• . ! I 1 I j ! t. t i I I t 1 a 0 : i' ■.•. J ,r ■.. .: {• • .'J 0 ' ' J. ■< ' V ' . • ' 'Tift'*.: ij I ' . n . .. j , ; . ; % I I I A sv>v» !, t j . f,“. A> o*‘f; I 4 1 J us’i^ v-yj*' o iv •\ a j' i«: \ <9 c; (V t ((■ (>■ it- ft- cT •r - .V ^ > ; > V* O r -9- 0 ^ g cP j \ > 1 ; k : 1 X ‘ \ : "<^ \ c u C'’ 0 o :? CJ u? i'’ ■■■ '^L. ,-^ ii} D- ■> iP ^ u> ^2

<^ U/ C 5 ’ J f,> C? <0 U X-; P o o> ) ( ^SCk . — ^ o. *Ti 'i: C. \\ V'* ‘ i ■ i • ^ ^ .L- ip^j 5/5 132 Bx^)erimental Data (cont.) Pressure -1 atm =2116.7 lb. per sq.. ft. Temperature Ho. C abs P abs Log,.K;^ 4.571 log,,X^ Me thod 11 1706 3071 3.26 0.5132 2.3458 ^ VI 12 1747 3145 3.31 0.5198 2.3760 13 1798 3238 4.00 0.6021 2.7522 14 1503 2705 3.04 0.4829 2.2073 VI 15 1528 2752 2.66 0.4250 1.9422 16 1538 2770 2.85 0.4548 2.0789 17 1578 2840 2.80 0.4472 2.0441 18 1586 2856 2.63 0.4200 1.9198 19 1597 2875 2.93 0.4669 2.1342 20 1643 2959 3.26 0.5132 2.3458 21 1763 3174 3.39 0.5302 2.4235 22 1773 3192 4.27 0.6304 2.8816 23 1783 3210 3.65 0.5629 2.5730 24 1795 3231 3.68 0.5658 2.5862 25 1798 3237 4.04 0.6064 2.7718 26 1824 3282 3.64 0.5515 2.5209 959 1726 0.534 -a2727 -1.2465 IV (■ 28 1059 1906 0.840 -00757 -0.3460 29 1159 2086 1.197 0.0781 0.3570 30 1259 2266 1.570 0.1959 0.8954 31 1278 2300 1.620 0.2095 0.9576 32 1359 2446 1.956 0.2914 1.3320 33 1478 2660 2.126 0.3276 1.4974 34 1678 3020 2.490 0.3962 1.8110 35 1031 1856 0.850 -a0706 -0.3227 VII ( 36 1111 1920 0.975 -00110 -0.0503 37 1134 2041 0.890 -O.C506 -0.2313 38 1227 2209 2.250 0.3522 1.6100 39 1283 2309 2.120 0.3263 1.4915 40 1333 2399 2.780 0.4440 2.0295 Investigator Aline r Haber & Hicbardt Halm Harries By using the constant of integration in the water gas reaction obtained from the H^O and C 0^eq[uilibrium equations we get the agreement shown in fig. (22) page 133 which can be considered as fairly reasonable. We have therefore a double ex- perimental basis for the determination of the constants of inte- gration in our equilibrium equations for C 0^ and H^O dissociation. The agreement shown between the calculated and ex- Fig22 Fquf hbrn 4 m of the Reaction H;^0 + C0 Showi ng agreement between ca/cu lated 134 perimental restilts for the equilibrium constants may be con- sidered also to increase the probability of the accuracy of the specific heat equations used. I?e action 0 -h Z E, 51,850 C H. 4.571 log/^ - 19.7333 log T^l. 21 -10’'^T-K).0293 '10 '‘t7g r p*- P=pressure lbs. per sq. ft. abs. T = temperature degrees Fahr. abs. Experimental Data Investigators - Pring and Pairlie. Method YII ( b ) us ing amorphous carbon Temperature Ho. C abs. F abs 4.571 log,, 1 1373 2471 -26.2129 2 1493 2687 -26.2855 3 1548 2786 -26.3774 4 1623 2921 -27.3137 5 1673 3011 -27.1358 6 1823 3281 -27.6615 7 1893 3407 -29.9960 8 1973 3551 -28.5527 Method YII ( b ) using graphite rod. Temperature Ho. C abs. F abs 4.571 log„E:^ 9 1473 2651 -27.1439 10 1548 2786 -28.2491 11 1573 2831 -28.3096 12 1648 2966 -28.7588 13 1673 3011 -29.1065 14 1723 3101 -29.3750 15 1773 3191 -29.3956 16 1848 3326 -29.8478 Method YII (b) using partly graphitized carbon rod. Ho. Temperature C abs. F abs. 4.571 log„K_ 17 1573 2831 -27.7700 18 1623 2921 -27.7700 135 Method VII (b) using partly graphitized oarbon rod. (cont.) No. Tenperature C abs P abs 4.571 log,^ K 19 1723 3101 -27.6827 20 1748 3146 -28.9150 21 1813 3263 -29.2140 Investigators - Mayer and Altmayer. Method VII (a) Passing hydrogen over sugar carbon deposited on nickle or cobalt as catalyser. Temperature No. C abs P abs 4.571 log,, EL 1 748 1346 -11.9020 2 780 1404 -13.5529 3 809 1456 -13.8736 4 840 1512 -14.3885 5 850 1530 -15.7218 6 880 1584 -16.3191 7 898 1616 -17.3384 Investigators - Clement and Adams. Method VII (a) Passing superheated steam over coke. No. Temperature C abs P abs 4.571 log,,K 1 1173 2110 -26.4310 2 1273 2290 -26.5390 3 1373 2470 -29.5910 4 1473 2650 -29.9150 5 1573 2830 -29.0260 Note: In cases where several values for the equilibrium constant v/ere given by the investigator for any one temperature the average has been t^en and is quoted here. Putting C=^£4.8 in the equilibrium equation we get the following calculated values: Temperature Pahr abs 1300 1500 1750 2000 2250 2500 2750 3000 3250 4.571 log,.Zp -10.9843 -15.1595 -19.1267 -22.1793 -24.5915 -26.5471 -28.1577 -29.5068 -30.6473 1 136 The constant places the calculated curve through the Mayer and Altmayer points and between the Clement and Adams and Pring and Pairlie points as shown in fig. (23) page 137. Consideiing the fact that the specific heat eqLuation used for methane is based on low temperature measurements only the agree- ment obtained with the equilibrium curve is very good. Heaction C+C 0^ 2 C 0 Equilibrium equation is ^ l % 4.571 log,JK: ,-68.430 +9.1874 log T - 1. 5844- lOT+0. 109* 10‘*T f C ^ " rn ^ Poo ^00- ( ft P= pressure lb. per sq. ft. abs. 1 atmosphere = 2116.7# per sq T = temperature degrees Pahr abs. Experimental Data Temperature llo. G abs P abs 4.571 log,^E:^ Method Investigator 1 796 1433 4.0615 VII (a) Mayer and Jacoby 2 1861 1550 8.5347 using 3 896 1613 9.8218 sugar 4 940 1692 11.9337 Cat bon. 5 1043 1877 17.7770 6 1091 1964 19.3503 7 1073 1931 14.1329 VII (a) Clement and Adams 8 1123 2021 16.6544 using 9 1173 2111 18.7188 charcoal 10 1198 2156 19.6607 11 1273 2291 20.5041 12 1373 2471 22.1132 13 1173 2111 18.7995 VII (a) Clement aid Adams 14 1273 2291 19.0320 us ing 15 1373 2471 21.9055 coke 16 1473 2651 23.7709 17 1573 2831 26.1465 18 923 1661 12.4445 VII (a) B oadouord 19 1073 1931 20.1926 20 1198 2156 21.4296 21 1073 1931 18.5127 VII (a) Rhea// and V/heeler 22 1123 2021 20.4567 23 1173 2111 22.2460 24 1223 2201 23.4972 25 1273 2291 24.9294 -• i 0 . -.'I .fiv UlO 01 a ij i.'. '' . *► iiw’’ .j»w^ ‘if, (-'■ i • ‘. .i-.t flL« «^a.' r • ' ■ '‘t'15 «• •Jt'l r .. C's^ \ y>. ; , > :■ ."*• < t> ■. :< CfiJ’ J ;>: ;■* : ■ i - , . \0 # , J- r ..U. 'fty.; a J n-^UvTUU rll. ;.> . . „ V- n'^ ■* Li &^^.■'l:,,^^)*. . . o: • :* OY'XJ/;, Sbl'I'i 'iz‘'j'‘j {>.:*' iJj ff '}€Hi is J 6(f ^j^o: ’ V ■9 ' 'i ' i' ' J Of •: ' I i r. • ' . r :i . rji i . ,i i ‘-rcf^X^ . 0 ' , 6 • L n) VO .X •rCK; • c'i’'-9'xir^i4'.f>v.; •' f*v ,vj;v‘ vuirf/rt.ij’ ■ '5 ' ; .•V *v - J ' . J ■■' • 'v'lv:-' . '. . V. • 1. \jOi X . iipiU4* '7 1 ^iQ£»”^ 7,.1C0"V /-' ■ ’.'V... X <■ ,. '( •4 1 XCM .'.ij.'r .1 ■* ' ■ • - m.z ^ ‘^0 -,j <2^ 1/’ OX ■ ^ X.' ^ 'ia., . . u • ■V •v.-x V si _ i \^y »* *J V-.-... .. ■ .OX f. -.-J;} . . .’ vx v‘ . i X U.C C-. .'.X ..>1 ' vju :•. .‘XT (v) I'V • v*o X • C' X. •■. c .;vox . •/■'J:'..-/ t' t j «,.' • ..' . . •XOO?1 r.3XX X^t u*Wri6 “?. '.C Iir: :.VXX • W J. ‘ iX.. t':;x •1.x ' ) . ■ . ■ . ■ . ; c. . . . ;. ■ ' t tk • “. J. i if-' ^'V:u ;. j o f 'j .c '. o.i ' ;.-) tin 11X2 .;xx ^ iji J . : . ;X A .;■ f" ■• •► "• • ■--■• j c . X'C; c.vei . -V' ■C '10.; •* n#* \ • « *- » , ; . i . V , 0 ' COOX :::^o ■ ■: • ' -“X •‘ Xf:$X V>VCX >. C': ". .r i\ > •y •.• ,;. ..» V '• J.X ^ ’.Co . f'u'M'.'iOfff; (,.•■ I'-V .'*X Xf.OX rlVC'X ■i; ,::.:XX ; ■ ■ <•.'0:. • .* r r r ^ «t 4 cl'k'Xl . c:V^ , . ;vi: '■••:- XkX-'O cXiX .A .' » . . C' . :•:::, x^aci £.v; c t: r. 'ii 0 %. ■or, XX 21 :,.i. kr xsi J5X . ar ^ ' I. S . ‘ ngZ3 Egud/bnum of the Reaction Cti^ 5how/ng agreement between ca/culated and expenmentat values. .. I o O V 7 ff :3i t if 5- ? r Jr I ^ ,; u > O » 4- a fi ^ ^ V' tp u fy ^ 'T 2 ip O' u? ^ t^* ^ ''•S ^ 2 ^ -j ^ 3 S 5 r'S g ° (0 % ' 3 ir' : g--^ . ::i! 1 f V. i# •# ./»vV WW • U '>c'T ' O' . ; Lv,- t. .:,j t.: w.-oaoL'"' L. . ffO a O ..u;- C • • ' ..to; , p L . ":f . , ;'i f r.>'> i {) i:> c' •.* ; y* .r. '■^1 page 139^ M ~ y ^ ■f J" 'V c c S .y s' J tf' !> a' *> 7* if ? o r' iT :3 Iff fC o ? n © • o £T ■V o Lt; r'y $. tr. / i I . I 1 i I 140 Adding the equilihrium equations for these reactions we have for the equilihriura equation for the oomhustion of methane with oxygen. 'x/17 npn -9 ■*- 4.571 log^^I£p=£^AA^ -^5. 6183 -log,^T -0.0552 *10 T-0. 0133*10 T-22.4 a- TT P • P He action + 0^ 2 il 0 Assuming that the specific heat of F 0 is the same as that of and 0^ at all temperr tures , and using Thomsen’s value for the heat of reaction we have for the equilibrium equation: 4.571 -77400 T ~h 4.06 K. ■/V^ The constant 4.86 is based on the experimentil data obtained by ITernst using the streaming method. The results are given in the following table : Temperature C abs F abs io NO 4.5V1 log„|A^ -77400 — — Const. 1811 3260 78.92 20.72 0.37 -18.592 -23.742 5.150 1877 3379 78.89 20.69 0.42 -16.130 -22.906 4.776 2033 3659 78.78 20.58 0.64 -16.406 -21.153 4.747 2195 3951 78.61 20.42 0.97 -14.738 -19.590 4.852 2580 4644 78.08 19.88 2.05 -11.736 -16.667 4.931 2675 4815 77.98 19.78 2.23 -11.389 -16.074 4.685 ave. 4.858 141 ScL'ulli'briiiin liquations 4.571 log,^ - 6.2631 log,^ T +0.2361 'lo'^fO. 033?- 10^ Ttl.l CO +10^ 00^ 4.571 log,^ IC^ = - 5.3881 log, + 1.3335 -lO^T-0. 08 -lo'S-lS.l + co^ n^o +C0 4.571 log^^K^ri^ - 0.8750 log,^ T- 1.0970 -lO^T+0. 1133 -1 o' V+14^ G + 2 ^ CH^ 4.571 log/„K^,^l|^ -19.7333 log,^ T+1. 21-10r-K).029 •10 ~^tV24. 8 C + C0^->2 CO 4.571 10 S,^K^-T-^^^*- + 9.1874 I T -1.9844 l6*^T+ 0.109 -lo'^T+26.4 C H^ + 20 -+00^+ 2-H^O 4.571 log,^ +5.6183 log,„ T-0.0552-l6^T-0.ol33 -loV-22.4 K^tO^ 2 ITO 4.571 +4.86 •V I pZ. SiLS i *. KT: 0ii s m^ A»w % imm • v^X ' .1 ■^t .'I »)j 1; j. :/t.:. '■^tcxir; r :' \ . .. oI -U.u::; . • -K r) n f Xcv.'.X itrvC '.< i. f • • - X ».< • . •.. j:;,r i' r I ; t . ..• ••.'JXX.C>"^ X c cv . . 00 - ' •*— •r^* - ■’• T" r^C'iC- .. tX .i..' . .r ' ir T & ' .. , !! .' t. r T'^ . •, • f ilil 4^ . X ^ I *4 • 5 - .r r./A r 1 L OX cX >v:;XA •f" X o£ X r. f - •^1 ■M :x 142 References for Experiment-:.! Data 1. Eernst and von Wartenberg 2. Langmuir 3. Lov/enstein 4» Bmich 5. Bjerrum on Reaction CO Zeit Phys Chem 5G-548 (1906) Jour Am Chem Soc 28-1357 (1906) Zeit Phys Chem 54-707 (1906) llonatshefte f Chem 26-1011 (1905) Zeit Phys Chem 79-357 (1906) References for Experimental Data on equilibrium in Reaction t Hj,0 1. Langmuir 2. Lowenstein 3. von Y/artenberg 4. Rernst 5. Herns t and von Wartenberg 6. Bjerrum 7. Seigel Jour Am Chem Soc Zeit Phys Chem Zeit Phys Chem Zeit AnprgChem Zeit Phys Chem Zeit Phys Chem Zeit Phys Chem 28-1357 (1906) 54- 715 (1906) 56- 513 (1906) 45- 130 (1905) 56- 534 (1906) 79- 513 (1912) 87- 641 (1914) References for Experimental Data on equilibrium in Reaction E^-h CO^^-t H^O GO 1. Allner Jour f Gasbel 48 (1905) pp 1035, 1057, 1081, 1107. 2. Haber and Richardt Zeit Anorg Chem 38- 5 (1904) 3. Hahn Zeit Phys Chem 42- 705 (1902-5) 4. Harries Jour f Gasbel 37- 82 (1894) References for Equilibrium Data on Reaction C f-2 C H^ 1. Pring and Pairlie Jour Chem Soc 101- 91 (1912) 2. Mayer and Altmeyer Berlin Ber 40-2135 (1907) 3. Clement aiidAdams U S Bureau of Bui # 7 Mines p 41 (1911) r aauM i ! • Is’' # (;. IS. ‘ ■ctti 3 '• • ' ^ ' u* * . *• . y:vi: ^ c inO-'T. .uiC' '» 0 aeht .V d r A, -“i'ijJI f.;* 1 ! ' ■ V, •■.li i„. ■ k* i :U j'lU-.ClCi;© r.'’ // .UJl'v : i !XC', • vt.* i U' . U . I •j A t . .IJti/ ,.V !. 'O.'.OV ,'•>•■ At > ■j Kl . . r » • V . V A J ■ • A c .. 4. :.ll :'i CJ;: AW i': C :j 'v i>qpf . -IL H ,fr, 1 ■ hi • I 4. -•- I \ r ,' ' S ;v . i r* \ - * • 1 ^ -w • f ■■ r» '• O- ^ i ^.■ . % . .-1-7 :i,.eATr j : ■j M t**. I 1 1 -\ t vJ 'ii;-. .OiT^ s , & I . . .J f'-L .;v J w C V-.'.' ho n J". r*'^ ti;.Vr,L: -A' '' . Xir : OOC, 'iu > \ uJ.X'i-i /v n- !-X *’5 vo^erc«>:tA , ’J ' '■ I? (Xipxi '■'■ T #• '\\‘£ ;.-7. ^,, - I ‘ ' lAi: ‘ 'TfK- 143 5eferenoes for I^eaotion 1. Mayer and Jacoby £. Clement and Adams 3. Boudourad 4. Hhead and Vi/heeler 0 i-C 0^ £ C 0 Jour f Gasbel U.S. Bureau of Mines Compt Bendus Jour Chem Soc 5£ (1909) £8£, 305 Bui # 7 (1909) 130rl3£ (1900) 97 (1910) 2176 89 (1911) 1140 References for Equilibrium Data for Reaction 0),^ -^ £ IT 0 1. Nemst Zeit f Anorg Chem 49 £13 (1906) iV X’ ‘i * i I f ; I I Q 1 I? Vi (' L .,^0 .. ii ; ‘ -U O: '; •- i: ! : 0 - c ' V . (^J:f .V •it;. ... .. •.. . ^.,0u tl * I* ^ • -.7 vt.^lK-w . i\. S* 1 : , »« •• -t. > if" ■ . ■ . . V- J. ^ , Vi **> . '1 O'” '.i-‘ •* « 1 . *10 .' . -W i. '1 .i .i. J. i. 4 ,1 » ) 2 « I t i ‘x (J 1 c i. . ■ • • ( 1 J :.’■ .4^2,' » »* I • ' * ■r- . w .1- .1 J APPENDIX D DETSmilMTION OP THE IIAXD.TUH POSSIBLE PEHCENTAGE OP IT 0 PRESENT AT THE POINT OP LIAXIMUH TEIIPERilTURE IN THE GAS ENGINE « ’ aasar naSBiTv^* sa ■ *J >\mf. .'lalMritt'' 144 Appendix D To determine the maximum percent of IT 0 present at the point of maximum temperature in the gas engine. The equilibrium equation is 4.571 log - P •77400 T (A) -y- 4. 86 In order to malLe the partial pressure of the IT 0 as large as possible the partial pressures of il^and 0^ must be as large as possible for a given value of Assuming a gaseous mixture with 50^ excess air and a dissociation of 10^ at the point of maximum temperature the IT^ and 0 ^ will be present in the ratio of 9.5 volumes of IT^ to 1 vol. of 0^ . Let V = of IT ^transformed to IT 0 Then at equilibrium point the mixture is mols IT 0 = 2 X 9.5 Y * 19 Y =» 9.5 (1-Y) = 9.5 - 9.5 Y 0;^ - 1-9.5 Y = 1 - 9.5 Y M = Total number of mols present P , iLI.p p 9.5 (1-Y) .p i\/o p 1-9.5 Y Substituting the expressions for partial pressure in equation (A) v/e have (19 Y)’' =■ 9.5 (l-Y)-(l-9.5 Y) ' Solving for Y Y -10.5 72.25 76 - 19 r“ T^ing T =5000 P (abs) a liberal maximum temperature IT ^0.00477. 145 Solving equation (B) V -0.0064 That is 0.64^ of the nitrogen present is transformed into IT 0 under the most favorable conditions. Decreasing the maximum tem- perature and the amount of excess air will both decrease the value of Y. The accuracy of the physical and chemical constants used in this discussion does not warrant the consideration of a quantity which amounts to less than 0.64$b of the total gas volume present. ITo appreciable error will be introduced into the calcu- lations of the equilibrium conditions by neglecting the reaction 11^ t 0^ 2 IT 0 .