TJ 265 VJ ^0< A 9 s \> %4 c * "oV* *b K t . : Sapors for heat engines INCLUDING CONSIDERATIONS RELATING TO THE USE OF FLUIDS OTHER THAN STEAM FOR POWER GENERATION: A STUDY OF DESIRABLE VAC- UUM LIMITS IN SIMPLE CONDENSING EN- GINES: METHODS FOR COMPUTING EFFI- CIENCIES OF VAPOR CYCLES WITH LIMITED EXPANSION AND SUPERHEAT: A VOLUME- TEMPERATURE EQUATION FOR DRY STEAM: AND NEW TEMPERATURE-ENTROPY DIA- GRAMS FOR VARIOUS ENGINEERING VAPORS BY WILLIAM DUANE ENNIS, M.E., Mem. Am. Soc. M.E. Professor of Mechanical Engineering in the Polytechnic Institute of Brooklyn Author of "Applied Thermodynamics for Engineers," etc. WITH 21 TABLES AND 17 ILLUSTRATIONS NEW YORK D. VAN NOSTRAND COMPANY 23 MURRAY AND 27 WARREN STREETS 1912 • A Copyright, 1912, BY D. VAN NOSTRAND COMPANY /£.-%{/ THE SCIENTIFIC PRESS ROBERT DRUMMOND AND COMPANY BROOKLYN, N Y. CCU312197 LIST OF ILLUSTRATIONS FIG. PAGE 1. The Clausius Vapor Cycle 4 2. Pressure-Temperature Relations of Engineering Vapors 9 3. The Binary Vapor Principle 26 3'. Turbine Characteristics 29 4. Comparative Proportions of Power Plants, Complete Expan- sion Cycle 32 5. Rankine Cycle for Dry Vapor 35 (5. Effect of Change in Back Pressure 40 7. Comparative Proportions of Power Plants, Rankine Cycle ... 56 8. Rankine Cycle with Superheat 59 9. Temperature- Volume Curves for Dry Steam 73 10. Temperature-entropy Chart for Alcohol 44 11. Temperature-entropy Chart for Chloroform 46 12. Temperature-entropy Chart for Acetone 48 13. Temperature-entropy Chart for Carbon Chloride and Carbon Bisulphide 51 11. ( 1 yclic Efficiencies and Criterion 53 If). Temperature-entropy Diagram for Ether 37 16. Temperature-entropy Diagram for Ammonia 71 17. Temperature-entropy Diagram for Carbon Dioxide 74 v VAPORS FOR HEAT ENGINES i General Considerations as to the Choice of a Working Fluid Water is the working substance in the great majority of external-combustion heat engines. It so far surpasses all other vapors in cheapness that it alone can be considered for use in a non-condensing cylinder. With condensing operation, the fluid may be mostly saved, to be used over and over again in a closed cycle; and if the loss by leakage is not too great, some other vapor may replace steam. To get a rough idea of the amount of leakage permissible, suppose a pound of coal, containing 14,000 B.T.U., to generate steam at 70 per cent efficiency, so that 14,000X0.70 = 9800 B.T.U., are contained in the steam. Let this heat perform work in a steam engine at 10 per cent efficiency, 9800X0.10 = 980 B.T.U., being converted into useful work per pound of coal burned. Suppose also that some other fluid were i 1 ,, more efficient 2 VAPORS FOR HEAT ENGINES than steam, i.e., that it could drive a heat engine at 11 per cent efficiency. In obtaining 980 B.T.U. of useful work we should then consume 9804-0.11 =8909 B.T.U. of heat in the vapor of the assumed fluid. If this fluid could be generated at the same boiler efficiency as steam, the heat necessary in the coal would be 8909^-0.70 = 12,727 B.T.U., a saving of 14,000-12,727 = 1273 B.T.U. or 9.1 per cent, in fuel cost, which might offset the expense due to leakage of fluid in operation. Suppose this new fluid to cost, pound for pound, the same as coal: leakage amounting to 9.1 per cent would be per- missible; if it costs twice as much as coal, the alloAvable limit of leakage would be 4.55 per cent; if it costs ten times as much as coal, the leakage limit is tVo of one per cent, and so on. There are volatile vapors which might be used in heat engines, costing not more than ten times as much as coal; and there are vapors permitting, under certain con- ditions, of an efficiency exceeding by T V that attainable with steam. With a leakage loss below 1 per cent, an investigation of the possibilities in applying these vapors to power production should be not without interest. Engines have actually been built using ether, sulphur dioxide, gasoline, alcohol and ammonia, among other vapors besides steam. Ammonia, not steam, is the fluid commonly used in the cylinders of refrigerating compressors; steam would of course not answer; but the expense due to leakage of ammonia is not ordinarily a matter of vital importance. II Data for the Analysis In what follows, it will be assumed that the Carnot formula, V- {A) is recognized as an expression in terms of the absolute temperatures for the ideal limiting efficiency of any heat engine whatever, working between the temperatures specified. For a vapor engine, however, there is an equally definite and lower limit of efficiency. Some acquaintance with the temperature-entropy diagram must now be assumed. In Fig. 1, ordinates are absolute temperatures, abscissas are entropies, horizontal lines are isothermals (and also, for saturated vapors, lines of constant pressure), vertical lines are acliabatics. The area under any line, down to the ON axis, represents the heat absorbed or emitted in working the substance along the corresponding path. The ideal cycle for a vapor initially dry is abed, ab being the path of constant pressure and nearly constant specific heat followed in heating the liquid, be the path of vaporization, cd that of adiabatic expansion, and da that of condensation at con- stant pressure. The cycle Ibcd is that of Carnot, bounded by isothermals and adiabatics alone. It is an impracticable cycle for a vapor. 3 4 VAPORS FOR HEAT ENGINES The efficiency of the cycle abed is, Heat converted into work abed Gross amount of heat expended eahef _ eabk + kb cf—eadf eabk-\-kbcf ■ (B) 32 °F. Fig. 1. — The Clausius Vapor Cycl< If the upper and low r absolute temperature limits of the cycle be T and t respectively, L and I being the corresponding heats of vaporization, then I . L I bc = y, aq = -; -t and if the specific heat of the liquid be constant and equal to c, I 7 fdH CedT f T dT . T al= J T=J~T~ = c J i T- =clogc T' the H and T in the first integral denoting heat and temper- ature; respectively, in general- If h and h a denote the DATA FOR THE ANALYSIS 5 respective heats of the liquid corresponding with the absolute temperatures T and t, we have as a definite expression for the efficiency l of the cycle abed, ho — ha+L 1 aq . h b -ha+L ' C log e y+y, = 1 ~*' h-ha+L (C) Eq. (C) is, however, inapplicable for the purpose in hand, because c is in general quite variable. We may use successive values of c for computing changes of entropy for short temperature ranges and thus obtain a close approx- imation to the change for any finite range. The values of c over the short temperature ranges chosen in the exemplifying table on. page 6, are, of course, obtained by dividing the differences of " heats of liquid " by those T temperature ranges. The expression — denotes the quotient t of absolute temperatures expressing the range. If now we sum up the figures in the last column, we shall have a series of figures representing the entropies of liquid (abscissas of the path yb in Fig. 1) at various temperatures, these entropies being tabulated above 32° F. as an arbitrary 1 This statement of efficiency has been preferred by the writer, although some authorities compute efficiencies on the basis of heat absorbed above 32°, making the denominator in Eq. (C) simply H c (total heat in dry steam) = the area oybcf, Fig. 1. But even in bad practice water is fed to the boiler at a higher temperature than 32°; so that it seems reasonable, in establishing ideal standards, to assume it to be delivered thereto at the temperature at which it is rejected by the engine. VAPORS FOR HEAT ENGINES Table I COMPUTATION OF ENTROPY OF LIQUID OF ALCOHOL Heal of the Liquid Differences, Corre- sponding Value of c T t Tempera- ture, ° F. Tempera- ture Heat of Liquid clo SeJ 32 — — — — — 50 10.06 18 10.06 0.559 510 492 = 1.036 0.0198 08 20.56 18 10.50 . 583 528 510 = 1.035 0.0204 86 31.48 18 10.92 0.607 546 528 = 1.033 0.0198 104 42.68 18 11.20 0.622 564 546 = 1.032 0.0200 122 54.38 18 11.70 0.650 582 564 = 1.031 0.0206 140 67.27 18 12.89 0.716 600 582 = 1.031 0.0227 158 80 . 24 18 12.97 0.721 618 600 = 1.030 0.0214 176 93.80 18 13.56 . 753 636 618 = 1.029 0.0211 194 107.95 18 14.15 0.786 654 636 = 1.028 0.0217 212 122.72 18 14.77 0.821 672 654 = 1.027 0.0223 230 138 . 13 18 15.41 0.856 690 672 = 1.027 0.0232 248 154.21 18 16.08 0.894 708 690 = 1.026 0.0230 266 170.96 18 16.75 0.931 726 708 = 1.025 0.0225 284 188.46 18 17.50 0.972 744 726 = 1.024 0.0230 302 206.68 18 18.22 1.012 762 744 = 1.023 0.0235 DATA FOB THE ANALYSIS 7 starting point. The distance al on the diagram may then be written, al = yz—yx = n b — n a , where n b and n a denote, respectively, these tabulated entro- pies of the liquid for the two points specified. The symbol n tc will be employed for entropy of liquid in general, measured a 1 ove32 F. Again, widths like be, from the liquid to the saturation curve, are always equal to the quotient of latent heat of vaporization by absolute temperature; that is, to L I T or T These quantities may also be tabulated for various tem- peratures, the general symbol being n e ; or, referring to Fig. 1, ribc, n aQ , etc. Finally, by adding the values of n w and n e , for any temperature, we have that of n s , the total entropy of the dry vapor at the same temperature. These three properties 1 have been tabulated for all of the vapors to be considered (except steam) in Table XXI. We may now write Eq. (B) in the form, ■nrc • h b —ha-\-L — t(n b — n a +n hc ) n Efficiency = J^+Z • • (O which is the exact expression for the cycle with complete adiabatic expansion. 1 The vapor properties employed in this discussion have been taken from the appendices to Vol. II of Zeuner's Technical Thermodynamics, Klein Edition (D. Van Nostrand Co.). The tables of entropies were, however, compiled by the writer from data given by Zeuner, especially for the present work. » VAPORS FOR HEAT ENGINES The Pressure-temperature Relation. This must be clearly understood: that a fluid boils at a definite tempera- ture for every pressure to which it may be subjected; the greater the pressure, the higher is this temperature; a vapor cannot exist, as such, at a temperature below that which thus " corresponds " with its pressure; but, by superheating, it may be brought to any higher temperature desired. The lower the pressure at which a non-superheated vapor is formed, the greater is the space which it occupies; and (an important fact in the subsequent discussion) this even holds in a rough, approximate way for vapors generally, so that if for any boiling-point we should tabulate the cor- responding pressures of a number of vapors, and afterward the spaces occupied by unit weight (the specific volumes) of the same vapors, we should find that they ranked, in order of pressures, somewhat inversely as they ranked in order of specific volumes. In Fig. 2, we have plotted the pressure-temperature curves of various vapors from the figures given in Table II. The curve for steam occupies the extreme right-hand posi- tion; i.e., its pressure, at a given temperature, is less than that of any other vapor considered. DATA KOI! TIIK ANALYSIS UOOr _j 1 n 2 I m f h j T . T T n . 33 si oi t T 2;/ „- n Q: . ^ 7 „ T r j _ □ i £ ^ / / i ^ 1 t -1 t 1 r i 1 ; t > r - 7/7 r >iV / T V#? 2 S-- ^«a _/ «y 120 - d^ - 3>W z T^ j£ - / #T,W/ / £" ^fe - _V OW/' • / w' £ / #4zz ~M-2~ml / t - ' AAA/ -SW A T -/ V ,&#k&r 5>T 1/'$' Z ite ' j: ^4Xp^<^fe ^ ^!z T&X oy ^3>|^^p^ ^ -V - C'l , z , ^5 7 - -'' -£> 3>i 1^ ^P'^ 20- -,** - m = = -,^^^f^, ^f ]— ? =-* s — A-T-MGSPHERK3-PRESS-UAE n . - c 5 = * s ffp^f— * ■F- — H+T H -20 20 40 60 '80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380400 TEMPERATURE IN FAHRENHEIT DEGREES Fig. 2. — Pressure-Temperature Relations of Engineering Vapors Ill The Limit of Efficiency with Steam The maximum pressure at which steam is commonly worked on a commercial scale is 250 lbs., corresponding to a temperature of, very nearly, 400° F. With superheat, temperatures up to 600°, or even higher, are employed. These limits of temperature may be easily accounted for on mechanical and commercial grounds. They are not necessarily permanent. There are equally definite (and far more permanent) limits of lower temperature. A vapor cannot exist at a temperature lower than that corresponding with its pres- sure. If an engine exhausts into the atmosphere, the tem- perature of heat rejection cannot be less than that cor- responding with a pressure of 14.696 lbs. per square inch — 212° F. If it exhausts into a vacuum of 28 inches of mer- cury, the corresponding temperature is 100° F. Lower than these temperatures we cannot go. The best average vacuum that can be commercially maintained is not over 28 ins. The pressure of steam is then only 0.946 lb. per square inch. It has been brought to its condition of greatest attenuation outside the laboratory. By applying Eq. (A), taking the Fahrenheit zero as 460° above the zero absolute, 10 THE LIMIT OF EFFICIENCY WITH STEAM 11 coa>OiTt<»OrH^coo^cooo i I i I i i i i i i i I i I i i i i ri^OOCOOO^Ot^iOeoCNOOo* C5"tfOcOiOC500»0'-ia}OcOOCl>l> (OrtNcCHOHTfOLOiOOONN i-h00OCNIt^I>0}CN HHnririM I I I I II I I I I I I I I I I ■SI £5 TfXNOHjHOMCOHHCOlOO IO l> 00 iO ■* 05'-i'^00COait^cOcOl>0 i-*rHr-ICNCNIG0C0' COOOiCiO _ CO (N iO iO M irj © M M O W CX) I TtJoO'*GOiO'20C5 I r-l l-HCM00TtC5 iJ> i HOOOnN^iOWOQOON i I© 'i-i ' i-l ' QOO COiOOCNCOrH oocooot>xooooooco>oio»ot^. OOOJN^miO-HrtOOOOOrHONONOcOOMM O-HHiMMTjfOaOONOCiOOOiHNNOOTHTttOcOO^ro^ OOOOOOOOhhin^cOO^OOOONOJCS^UJhio ^-li-iCNCNCOiOOOO--i-^00OOG30CN|Tt<»Ot^05^HCO-*cOXO^COiOt^OS CNCNCNCMCNCOCOOOOOOOOO 12 VAPORS FOR HEAT ENGINES we have the following as the ideal limits of efficiency in steam engines according to present practice: Non-condensing, saturated steam, — =0.22; Condensing, saturated steam, inruudRin = ^' 35, ^ , . i_ 600-100 n „_ Condensing, superheated steam, fin h-Mfif) = 0,47 - The best actual (cylinder) thermal efficiency ever recorded for a vapor engine was about 0.25. IV The Line of Attack Suppose we assume a pressure of 250 lbs. or a tem- perature of 600° (with superheat) to determine the upper limit of the cycle, and a vacuum of 28 inches to fix the lower limit. The use of a vapor other than steam might then, apparently, be justified on one of three grounds: 1. A higher temperature might be attained at 250 lbs. pressure, without superheat. 2. A temperature of 600° might be attained by super- heating, with an efficiency higher than is possible from steam at that temperature. 3. A lower temperature might be attained at 28 ins. of vacuum. If, as in Fig. 2, we plot curves with temperatures as abscissas and corresponding pressures as ordinates, con- ditions 1 and 3 taken together require a vapor giving a curve which crosses that for steam. At a very low pressure, we wish the boiling-point to be lower than that of steam; and at higher pressures, its boiling-point should be the greater. No such vapor is known to the writer. It is not impossible that one may exist, for similar crossings of the pressure-temperature curves occur with other pairs of fluids. For example, the carbon chloride and ethyl alcohol curves, in Fig. 2, show a crossing point near 190° F.; our hypothetical vapor should give a curve related to that of steam in much 13 14 VAPORS FOR HEAT ENGINES the same way as the carbon chloride curve is related to that of alcohol. Its properties would have to be somewhat as indicated by the dotted line. Condition 1 is easy to meet. There are many known vapors giving curves lying wholly to the right of the steam curve in Fig. 2; but these vapors have the general dis- advantage of giving a higher temperature than steam at 28 ins. of vacuum, so that condition 3 is violated. Condition 3 would lead to a lower temperature of heat- rejection, and thus increase the potential efficiency of the cycle; but in any case this temperature cannot be below that of the average available supply of cooling water; or, say, in our latitude, about 60° F. The limit of efficiency with superheat, for any vapor, would then be, from Eq. (A), 60 °- C0 0.51, 600+460 an increase of about 8 per cent over the present limit with steam. If we disregard the possible existence of such a vapor as is designated by the dotted line of Fig. 2, and for the present restrict the discussion to saturated (non-superheated) vapors, we must obviously dwell upon Condition 3. The vapor to be preferred is one which boils at about 60° F. (any lower temperature is needless, on account of the cool- ing water limit, and likely to lead to excessive maximum pressures) at an absolute pressure of from 1 to 4 lbs. per square inch. Carbon bisulphide, chloroform, acetone and carbon chloride (with possibly alcohol) are the only fluids to be considered (see Appendix I) . The last (carbon chloride) requires the best vacuum — a moderate one, however — but is most desirable from the standpoint of maximum pressure, as indicated on page 15. THE LINE OF ATTACK 15 Table III MAXIMUM PRESSURES WITH VARIOUS VAPORS Vapor Pressure in^bs.^per Sq.in., Alcohol 142 Chloroform 140 Acetone 163* Carbon bisulphide 176 Carbon chloride 88 Steam 69 * Extrapolated. The pressure with carbon chloride is only 28 per cent greater than that with steam. The indication is that at higher temperatures the excess percentage will be less, the two curves in Fig. 2 perhaps crossing near 400° F., our assumed upper limit with saturated steam. It may then be that the " suggested ideal vapor " of Fig. 2 really exists, as carbon chloride, the curve for which resembles the dotted curve shown, excepting that it occupies a position further toward the left. In such case, the objection to the use of carton chloride as a substitute for steam ? with an accom- panying 8 per cent increase in potential efficiency, is the probable expense due to leakage. Efficiencies of Dry Vapors in the Complete Expansion Cycle Considering now the diagram abed of Fig. 1, to which Eqs. (B), (C) and (Z>) apply, we may examine the efficiencies shown by these equations as representing more nearly the limits of practice. It is first proposed to establish a criterion for estimating relative efficiencies in advance. The cycle abed is less efficient than the Carnot cycle ahed drawn through the same extreme limits. The work areas are: Carnot, ahed: Clausius 1 i abed; and the amounts of heat chargeable are; Carnot, ehef; Clausius, eabef. The excess of heat chargeable in the case of the Carnot cycle 1 It is a current, but (the writer believes) unjustifiable, habit to refer to the complete expansion cycle abed, Fig. 1, as Rankine's. It does not appear that Rankine ever described such a cycle, although Clausius did, in his Fifth Memoir on the Application of the Mechanical Theory of Heat to the Steam Engine. Rankine shows the adiabatic expansion cycle with terminal drop (incomplete expansion) in The Steam Engine, 1897 Ed., Art. 278; and this is the cycle which should properly be associated with his name. The Clausius (complete expan- sion) cycle is perfectly definite for a given dry vapor. The temperature limits fully determine the efficiency, just as in the Carnot cycle. It is the ideal cycle of a vapor engine. The terminal drop Cycle, on the other hand, is indefinite and establishes no standard for comparison with results obtained in actual engines. Any number of such cycles, of various degrees of efficiency, is possible between two given temper- ature limits. 16 COMPLETE EXPANSION CYCLE 17 is ahb; but the excess of work obtained is also ahb, so that this work is obtained at 100 per cent efficiency. Whatever makes the Clausius cycle more nearly like that of Carnot increases the efficiency of the former. The ideal work area should be rectangular, not trapezoidal. Departure of the area abed from rectangular form is due wholly to the slope of the line ab. This slope varies with the specific heat of the liquid, since the entropy or abscissa of the path ab, {at), has been shown to be equal to c log e —, where c is la that specific heat. When c = 0, ab is vertical and abed is a rectangle. Further, slope of the line ab becomes less important in producing deviation of the area abed from rectangular form when the width be is relatively great. This width is — , the quotient of the latent heat of vaporization by the absolute temperature. At any temperature, then, it is desirable that the latent heat should have a high value. Considering both factors, the most efficient fluid is likely to be that for which there is obtained at a given temperature, the maximum value of L _ Latent heat of vaporization c Specific heat of the liquid The following table applies this (not new) principle to Fig. 1. 18 VAPOKS FOR HEAT ENGINES > O ° *» *■« T 1 o ^ cc Tj- CC o o o c CC 1— 1 CO r- J] ~ O tO C\ co d d +> cc c T— CO 00 oo cc T— CN r-i OS *> i^i "* rJH O Tt< t^ o c rH T* lO -* w I—? CO rH CO cc H TP »0 OS lO Tt T— c\ t-H o * CO Tp" rH O CM s u 00 OS H OS O 4 CO (M 00 1^- d oo O OS b- i— 1 CO o CO r-i rH OS /— \ O t-h »o o TjH o a o ^ t^ »o 0) 00 1 II OS _u II CO 1 II CO ^ CO C^ ^ <# <^ CO OS TT" • CO OS CM lO ^ CO ^ to CM T*H c3 °° CM »o CO * O 00 CO ^ lO "CH ' CO - N 1 CO 1-1 ,-( CM 1 cc > r- H CV 1 CO 00 b- q ir > ^ < If 5 lO o rfS C > a i ) OC 5 00 t^ d CO * cx ) a ) CC > r> l> 00 rH CO -S2 CC > ^ H C- i d l> ,_j c > cc ) If 5 CO »o w Cv 1 2 O e C t > c j 3 ! I 5 S3 < C > < : c ) O QQ I COMPLETE EXPANSION CYCLE 19 Steam appears likely to give the most efficient cycle, carbon chloride nearly the least efficient. If we now apply Eq. (D), taking additional values from the entropy tables, page 78, we obtain: Definitive Vapor Efficiencies Alcohol, 186.12+306.86-52 8(0.325 0-0.0402+0.40 3) 492.98 ' Chloroform, 56.37+92.94-528(0.1077-0.0172+0.1219) _ 149.31 -U.^4J; Acetone, 134.24*+178.11*-528(0.2465*-0.0368+0.236*) 312.35 • '" ' Carbon bisulphide, 58.29+117.90-528(0.1099-0.0172+0.154) 176.19 -0.250; Carbon chloride, 49.93+69.02 - 528(0.0953 - 0.0145+0.0905) 118.95 -0.238; Steam, 235.53+908.00-528(0.4398-0.0707+1.1921) 1143.53 = 0.279: the order of efficiencies being substantially as predicted. The efficiency of the Carnot cycle between the same tem- perature limits is 302-68 .... 302+460 = a30b - * Extrapolated. 20 VAPORS FOR HEAT ENGINES But while four of the six vapors could in practice be worked down to a temperature of 68° F. without difficulty, this would be impossible with steam or with alcohol. Steam, for example, would at this temperature exert a pressure of only 0.34 lb. per square inch, equivalent to a vacuum of 29.2 ins. With a more practicable lower temperature limit — say 110° F. — the efficiency of the Clausius cycle, using steam, would be (from Eq. (D)) only 271.60-77.94+908.00-570(0.4398-0.1471 + 1.1921) 271.60-77.94+908.00 ' slightly lower than that obtainable with the better temper- ature range possible with the other vapors. A reduction in lower temperature limit is thus shown likely to be prof- itable (though only slightly so) when the matter is viewed under conditions more closely corresponding to practice than those of the Carnot cycle. It appears, then, that an engine using the vapors of chloroform, acetone, carbon bisulphide or carbon chloride would, with a less perfect vacuum than is now common in steam plants, permit of an efficiency somewhat exceeding that attainable with steam. Expansion is assumed to be complete, and (in some cases at least) the maximum pressure would be increased. VI Superheat This conclusion is unsatisfactory in that some excess of initial pressure is involved. It is true that with carbon chloride the excess is not great, and might at the upper limit of 400° become nil; but with this vapor the gain in efficiency is also small and might disappear if 400° F. were fixed as the upper temperature. We might avoid excessive pressures by superheating, while at the same time increasing efficiency; but steam can be superheated as well as the other vapors. We have assumed that it is virtually a pressure condition, rather than a temperature condition, which establishes the lower limit of our cycle; the vacuum necessary must not exceed about 28 ins. of mercury. Let us now accept a pressure condition as also establishing the upper limit and examine a superheated cycle in which a maximum ten>jierature of 600° is attained at a pressure not exceeding 100 lbs. per square inch. Is there in this case any criterion from which we may hazard an advance guess, as with the saturated vapor cycles, regarding the probable order of efficiencies? The area abcig, Fig. 1, represents the operation to be considered. Com- paring it with the former cycle abed, we find the added* work area, dcig, to consist of the two parts dejg and cij. The increased expenditure of heat may similarly be divided into the two parts ; fcjm, giving the work area dejg (a Carnot 21 22 VAPORS FOR HEAT ENGINES cycle), and cij, giving a work area equivalent to itself. The first work area is necessarily obtained at slightly greater efficiency than the original Clausius cycle abed between the same temperature limits. The latter work area is equal to the heat which it costs. It is gained at 100 per cent efficiency, and is the potent factor in making the cycle abcig more efficient than abed. The extent to which superheating will increase cyclic efficiency is thus c'osely related to the ratio of the areas cy, abed. The former area will be large when T~T C is large and when the width cj is large. The former condition is approached as T c decreases, for Ti has been fixed at 600° F. We have also established the pressure at c as 100 lbs. We wish, then, for a vapor in which the saturation temperature at 100 lbs. pressure is relatively low; that is, a vapor lying to the left of the steam curve in Fig. 2. Again, the width cj is directly proportional to the specific heat of the superheated vapor. The slope of the constant pressure path of superheat, ci, is related to this constant, just as the slope of the liquid line, ab, is related to the specific heat of the liquid. Considering both conditions, then, the most desirable vapor will be that in which (a) The specific heat during superheating is large, and (6) The temperature at 100 lbs. pressure is small. Superheated steam has, undoubtedly, the highest specific heat of any of the vapors under discussion. That of alcohol (0.4534) approaches it, while that of chloroform, for example, is only 0.1567. Whether the better pressure-temperature relations of these two vapors may offset their less desirable specific heat values can be determined only by computing the efficiencies in detail. The advance criterion of efficiency is in this type of cycle indefinite; but we may at least pre- sume that alcohol will give a more favorable result than chloroform, on account of its much higher specific heat. SUPERHEAT 23 We will then examine the cycle in which 7 7 i = 600° F., the maximum pressure is 100 lbs., and the lower pressure is not less than 1 lb. For steam, at 1 lb. absolute pressure, the lower temperature limit will be 101.83°; for alcohol, it will be 72°; while for chloroform, since it would be only 28°, we will regard the cooling water as establishing a lower limit at 60° F. The following thermal properties are tabular: Table V " VAPOR PROPERTIES FOR CYCLES WITH SUPERHEAT Vapor. Tc h ta fl n Lie Tic k* n n Steam .... Alcohol . . . Chloroform 327.8 277.0 270.3 298.3 181.8 57.0 101.83 72.00 60.00 69.8 23.0 6.54 888.0 320.0 96.37 1.602 0.728 0.229 0.52 0.4534 0.1567 0.1327 0.0446 0.0134 * Specific heat of the superheated vapor. The expression for efficiency is, if the expansion line crosses the saturation curve, abcig abke + kbcf+fcim — agme eabcim abke + kbcf+fcim = 1 (ni—n a )t a h-ha+Ltc+klTt-Tc) . . (E) Where n is the symbol for entropy above 32° F. In order to find rii, we write, T n ( -n c = &log e ^, (F) ric being tabular and T t always 600+460 = 1060. Then, For steam, n t = 1.602+ (o.52x2.3 log ~^\ =1.7558; 24 VAPORS FOR HEAT ENGINES For alcohol, n, = 0.728+ ^0.4534X2.3 log I^q) =0.8925; and For chloroform, w,= 0.229+ ^0.1567X2.3 log ^\) = 0.2874. But in the general case the vapor may remain superheated at the end of expansion, giving such a cycle as pbcino, Fig. 1. To determine whether this is the case for our conditions, we have only to compare values of nt and n 0f the latter being the total entropy of the dry vapor at the lower temperature, and having the following values: for steam, 1.9754; for alcohol, 0.857; and for chloroform, 0.2416. Since n exceeds nt for steam, the cycle is like abcig, and Eq. (E) is applicable, yielding, „ , , (1.7558-0.1327)561.83 Forsteam > 1 -228.5+888.0+0.52(272.2) = °' 272 ' But for alcohol and chloroform another equation must be found, applicable to such a cycle as pbcino. This equation is pbcino Efficiency = h-hp+LK+HTt-Tc) 1 _ J^po\K{l n 1 ) , ~x h h -h p -\-L ic +k{T t -T c y ' ' w in which T n is to be found from the relation T n i —n P =n vo +n on = n vo +k\og e -~ l - . . . (H) 1 o The values of L p0 are respectively 433.01 and 117.91; those of n p0 are 0.814 and 0.2278. Applying Eq. (H), T„ = 571° absolute or 111° F .; For alcohol, 0.8925-0.0446 = 0.814+1 and SUPERHEAT 25 while for chloroform, 0.2874-0.0134 = 0.2278+ (o.1567X2.3 log ^Y \ 520/ and T» = 706° absolute or 246° F. The corresponding efficiencies, from Eq. (G), are 1 433.01+0.4534(111-72) Q7C ... *~ 478.8+ (0.4534X323) =°' 278 f ° r alcoho1 ' and - 117.91+0.1567(246-60) n oro , ,. . 1 - 146.83 + (0.1567X329.7) = °- 259 f ° r chloroform > confirming the prediction made, in spite of the greater tem- perature range with chloroform. Alcohol and steam are about equally efficient, while chloroform is decidedly less desirable under these superheated conditions. The values of k taken are somewhat uncertain, and this property is too variable to warrant our drawing any closer conclusions; but it seeems safe to say that there is no inherent advantage on the part of either of the proposed vapors in a complete expansion condensing engine using superheated steam; the three efficiencies seem to have no relation to the con- denser temperature. We cannot by superheating, con- sequently, evade the high initial pressures to which excep- tion has been taken, without at the same time losing the efficiency advantage shown under certain circumstances to be possible. VII The Binary Vapor Principle High initial pressure may, however, be eliminated by the vapor engine of Du Tremblay, in which steam, discharged from a cylinder at, say 110° F., may be condensed by the Fig. 3. — The Binary Vapor Principle abcd= primary tfgh= binary Ideally, idcj = khefl circulation of a more volatile fluid in the condenser coils. This second fluid is thus vaporized and may be used to perform work in a second cylinder. We may thereby work down to the cooling water limit of temperature — about 60° F. — and so obtain the slight increase in efficiency that our calculations have shown to be possible, without any increase in maximum pressure. Commercially, this 26 THE BINARY VAPOE PRINCIPLE 27 gain is insufficient to offset the added complications. The principle has been applied, intermittently, in actual engines for at least sixty years, with the expected economical thermal result, if not with commercial success. Fig. 3 shows the combined ideal indicator and entropy diagrams. The initial and back pressures on the two cylinders will usually differ, though not always in the way here indicated. There might be a mechanical advantage in having them equal. VIII Application to the Turbine The Clausius cycle analyzed is that of the steam turbine rather than that of the reciprocating engine; in -which latter, cylinder condensation makes anything like complete expan- sion undesirable. The nozzle velocities obtained from a frictionless adiabatic flow, adopting the usual approximate formula, V = 224:Vh, where H is the cyclic area in B.T.U., may be computed as follows : these cyclic areas are the numer- ators of the efficiency expressions given in sections V and VI, so that if the efficiencies be each multiplied by their respective denominators we have at once the required numerators. Table VI CYCLIC AREAS AND NOZZLE VELOCITIES Vapor E_ V (a) 302° to 68°, Vapors Initially Dry Alcohol 0.264X 492.98 = 130.0 2550 Chloroform 0.249X 149.31= 37.1 1360 Acetone 0.246X 312.35= 77.0 1960 Carbon bisulphide . . 0.260X 176.19= 45.9 1520 Carbon chloride . 238 X 1 18 . 95 = 28 . 3 1 190 Steam 0.279X1143.53 = 319.0 4000 (b) Initially Dry Vapor, 302° to 110° Steam... 0.231X1101.66= 255.0 3570 (c) Vapors with Superheat at 600° F. Steam 0.272X1257.5 =342 4150 Alcohol 0.278X 625.0 =174 2960 Chloroform 0.259X 198.48= 51.3 1600 28 APPLICATION TO THE TURBINE 29 The variation in velocities is notable. These velocities are of course proportional to the square roots of the quan- Fig. 3'. — Turbine Characteristics with Frictionless Buckets (a) (6) Jet velocity ab, ab' ab Peripheral velocity ac, ed ac, ac', ed, e'd' Absolute exit velocity ec, e'c e'c', ec Rotative components of ] . .. . ... , ,.. , . absolute exit velocities} cf > cf (negatlve) <*''/' (negative) tities of heat converted into work in the various cycles con- sidered; and in the actual working out of a turbine design, the question of absolute emerging velocity is fundamentally related both to mechanical limitations and to the obtained 30 VAPORS FOR HEAT ENGINES efficiency. Our efficiency equations have been applicable to ideal conditions only. The velocity of flow will be an important factor in determining how nearly the actual turbine will approach the ideal efficiency. To consider this subject in all of its bearings would require a somewhat extended discussion. We may briefly point out three facts: (1) With a given nozzle angl and peripheral speed, and with buckets of usua form a relative y low nozzle velocity is apt to lead to a retarding reaction at exit. (See Fig. 3', a.) (2) With a given nozzle angle and nozz'e velocity, positive exit reactions are associated with the lower periph- eral speeds. (See Fig. 3', b). (3) With a given nozzle ang e the per pheral speeds of impulse turbines using various vapors will with usual bucket angles vary about as the nozzle velocities of those vapors. An efficient velocity turbine would therefore be possible at low peripheral speeds, with these special vapors, without excessive compounding into pressure stages. IX Some Commercial Considerations Boiler Capacity. The argument is sometimes advanced, in connection with a'cohol vapor launch engines, that the low value of the latent heat of vaporization of this fluid is an advantage in that less time and less boiler surface are required to " get up steam." The size or capacity of a steam boiler is measured by its heating surface. Under the conditions which normally exist a heat transmission of about 33,000 B.T.U., per square foot of surface per hour, is considered reasonable. Very nearly the same conditions hold, regardless of the particular fluid contained in the boiler. With boilers of a given type, the quantity (volume) of fluid contained will bear a fairly constant ratio to the heating surface and therefore to the heat transmission. In a power p ant, the efficiency of the engine determines the quantity of heat to be supplied by the vapor leaving the boiler, per horse-power-hour. This efficiency, therefore, determines also the heating surface of the boiler, and, from the conc'usion already reached, it determines the volume of liquid in the boiler. The " time to get up steam " for a given volume of liquid in the boiler will depend also upon the specific volume of that liquid. Finally, therefore, boiler capacities neces- sary with various fluids may be expected to vary inversely as the cyclic efficiencies; the times consumed in starting 31 32 VAPORS FOR HEAT ENGINES up the boilers will vary inversely as the products of efficiency by specific volume of liquid. The data for comparison are given in Table VII, volumes being taken at 212° F. The " quick steaming " boiler will, however, lack steadiness, and the comparison really means very little, for quickness 100 98 i 89 93 94 88 Steam Carbon Chloride Carbon Chloroform Acetone lisulphide Relative Boiler Capacities Necessary Alcohol Steam Carbon Chloride Carbon Bisulphid* Chloroform Acetone Alcohol Relativ b Times Rec nil •ed to "C jet Up Steam ' ' in a Given Boiler 102 99 88 93 95 87 Steam Chloroform Acetone Alcohol Carbon Carbon Chloride Bisulphide Relative Amounts of Condenser Surface and Cooling Water Fig. 4. — Comparative Proportions of Power Plants Using Various Fluids in the Complete Expansion Cycle, All Initially Dry Vapors and All Developing the Same Horse-power of steaming might be attained in any case by using a type of boiler having a low ratio of liquid contents to heating surface. Cooling Water. In Fig. 1, the area abed represents work done and the area eadf represents heat which must be removed by the condenser. The ratio of the latter area to the for- SOME COMMERCIAL CONSIDERATIONS 33 Table VII BOILER CAPACITY AND STEAMING RATE Clausius Cycles with Vapor Initially Dry Vapor Efficiency Relative Boiler Capacity Volume of Liquid Volume X Efficiency Relative Time to "Get up Steam " Alcohol Chloroform Acetone ,••••• Carbon bisulphide. . . Carbon chloride Steam 0.204 0.249 0.246 . 2G0 0.238 0.231 88 93 94 89 98 100 0,0208 0.009G 0.0192 0.0130 0.0069 0.0160 0.00549 . 00238 . 00472 0.00339 0.00104 0.00370 68 15G 78 109 225 100 Temperature limits: for steam, 302° and 110°; for the other vapors, 302° and 08°. mer therefore varies directly as the cooling water consump- tion per horse-power, and as the amount of condenser sur- face necessary. The values of this ratio show no great variation; what difference exists is unfavorable to steam. The following is the comparison for the conditions adopted in Table VII: Table VIII CONDENSER SURFACE AND COOLING WATER CONSUMPTION Vapor. Area, abed Area, cadf Alcohol 130.0 Chloroform 37.1 Acetone 77.0 Carbon bisulphide. . . . 45.9 Carbon chloride ...... 28 . 3 Steam 255.0 362.98 112.21 235.35 130.29 90.65 846.66 cadf ■r-abed 2 80 3 02 3 06 2 84 3 20 3 31 Relative Condenser Surface and Coolinf.' Water Consumption per Horse-power 87 93 95 88 99 102 These commercial factors are represented graphically in Fig. -1. X The Rankine Cycle This is shown in Fig. 5. Expansion terminates before the pressure has been reduced to that of the exhaust, and the pressure falls at constant volume (line rs in both diagrams) at the outer end of the stroke. The heat converted into work is abcrs: the gross amount of heat expended is, as in the Clausius cycle, eabcf=h b — h a -{-Lc. The efficiency of the former cycle is obviously less than that of the latter. The area of this cycle may be regarded as the algebraic sum of the quantities of external work done along the three paths be, cr and sa, which quantities may be denoted by the symbol W with appropriate subscripts. Now Wb C = PV Cl Wsa = pV s ; and by the common formula for adiabatic expansion, Wcr = h+r c — hu — Xrr h ....(/) in which expressions V denotes the vapor volume at the subscript state and r the " internal latent heat of vaporiza- tion." Then abcrs = PV c — pV s -\-hi,-{-rc—hu—Xrrt. . . (J) The conditions of the problem give all quantities except- ing x r , n and V s . If we assume a limiting temperature at r, these also may be readily computed, for n is tabular for a given value of t r , and X T li h 34 THE RANKINE CYCLE 35 Fig. 5. — Rankine Cycle for Dry Vapor 36 VAPORS FOR HEAT ENGINES from which x T may be obtained when l t is tabular, and V s =Vr = X T V h very nearly, V t being also tabular. Such a comparison would be of little value. Expansion is in practice limited, not by an assigned temperature t r , but by a "ratio of expansion," V r +V c , which in simple engines has been established at about the value 4:1, as a compromise between technical cyclic efficiency and the detrimental effect of extreme cylinder condensation at more complete expansions. This makes the problem more difficult of direct analytic solution, in the absence of knowledge of properties other than the volume and entropy of the wet vapor at the state r. Such a formula between temperature and volume as is given in Appendix II does not aid us, because it is applicable only to dry steam. Both dryness and temperature are unknown at r, if the ratio of expansion V r + V c be alone assigned. A carefully plotted entropy diagram, on which the lines of constant volume were drawn at close intervals, 1 would permit of an easy solution; or we might employ simultaneous equations in the forms clog^+^ = clog 6 i- 6 +,-. Vr = XrV t = Xr(f)t r , latent heats of vaporization and volumes being expressed as functions of temperatures and c (the specific heat of the liquid) being not too rapidly variable. The method to be adopted is that suggested by the entropy chart, on which lines of constant volume and constant dry- 1 See the author's Applied Thermodynamics (D.Van Nostrand Co.), 1910, pp. 212, 223. THE RANKINE CYCLE 37 ness may be drawn. There is no lack of such charts for steam, and it is needless to reproduce one here. Those for other vapors considered have been plotted (Figs. 10 to 13) for this work. The one for ether (Fig. 15) is reproduced, as PRE8SURE. LBS. PER.EQ. IN. en o c o o> o O. / I / J / // /, /} 7 / j I i / / / '/ / / 1 ' J I / / A ' J 1 1 t j 1 J :' h -- — - --— 7 '/ / t /jj M. y2^- c T > &4 I ' / j 71 / / / / c / c / / ~7 / / 1 1 A / / / / 1 / / i 0.1 0.2 A r Vr DRYM 07 ESS | o's W c. D6 0. 10 0. 15 0. 20 ENTR 0. OPY 25 30 0. 35 10 1.0 2.0 3.0 4.0 6.ol o 6.0 o JL O 7.0 g 8.0 9.0 100 11.0 12.0 130 110 Fig. 15. — Temperature-entropy Diagram for Ether showing the peculiar behavior of that vapor — evaporation during adiabatic expansion from any initial condition, an evaporation which merges into superheating if expansion from a fairly dry initial condition be sufficiently long continued. Most common vapors condense with adiabatic expansion from an initially dry condition Carbon chloride (Fig. 13) appears to remain practically in the " just dry" state for even an extreme range of expansion. XI Efficiencies in the Rankine Cycle; Economical Condenser Temperature The cycles compared will be those with initially dry vapor and a ratio of expansion of about 4 to 1. The tem- perature limits should be, as in the Clausius cycles considered, 302° and 68° for the special vapors and 302° and 110° for steam. For steam, then, F c = 6.28 and V r should be 6.28X4 = 25.12. The entropy diagram gives for n c = 1.6319 and V r = 25.12, £, = 210°. At this temperature, n u = 0.3087, nvi = 1.4510. Since n b = 0.4398 and n bc = 1.1921, 0.4398-0.3087+1.1921=^X1.4510, and Xr = 0.912. The steam table gives V t = 27.80, so that the actual value of V r is close to 0.912X27.80 = 25.4, the departure from the assumed value being due to inaccuracy in plotting and reading the entropy chart. We wil use the value F r = 25.4, so that the ratio of expansion will in this case be 25.4^6.28 = 4.04, instead of 4.0, as assumed. Taking the necessary tabular values for substitution in Eq. (J), we have 144 abcrs = ^ j (69.03 X 6.28) - (1 .271 X 25.4) | +271.6+828.1 -177.99- (0.912X899.0) 144 = =^(434-32.2)+271.6+828.1- 177 .99-820 / to = 74.5+ 1099.7 - 997.99 = 176.21 B.T.U. 38 EFFICIENCIES IN THE RANKINE CYCLE 39 The boat expended is, as in the Clausius cycle, 1101.66 B.T.U., so that the efficiency is 176.21 -^ 1101.66 =0.16. If we should proceed in this way with the other vapors we should find a total lack of correspondence in the order of efficiencies for the Rankine cycles with that of efficiencies for the Clausius cycles. A rather curious fact, which we are now to consider, will suggest a fairer comparison than that proposed. Suppose we take the case of steam, working between 302° and 68° F. Values of V r and x T will be as for the cycle already considered. Then 144 abcrs = -^ { (69.03 X 6.28) - (0.3386 X 25.4) | +271.6+828.1 -177.99- (0.912X899) 144 = ~(434-8.6)+101.71 = 78.9+101.71 = 180.61 B.T.U., 77o eabcf= 1143.53, as for the Clausius cycle, and Efficiency = abcrs + eabcf= 180.61 -r- 1 143.53 = 0.158. An increase in temperature range has thus, contrary to expectation, decreased the efficiency of the cycle. No such result would be possible with the complete-expansion Clau- sius cycle. Too good a vacuum, with limited expansion, appears to be undesirable. Fig. 6 suggests an explanation. Let abcde represent the steam cycle between 302° and 68° F., gbcdf that between 302° and 110° F. The additional work, agfe, of the former cycle, is gained at an expenditure for heat of mnga. Now, mnga = c(t g —t a ), or, very : nearly, 42 B.T.U.: while agfe = (P -P a ) F e =~X 25.4 (1.271 -0.3386) = 4.4 B.T.U. The 77o 40 VAPORS FOR HEAT ENGINES ratio of , additional work obtained to additional heat con- sumed, when the low temperature limit is changed from 110° to 68°, is 4.4^-42 = 0.105; which is less than the efficiency of the 110° cycle, so that the change must neces- sarily be unprofitable. Analytically, if t —t a be small, so that the temperature along the path ag may be represented by the single symbol mn Fig. 6. — Effect of Change in Back Pressure t (absolute temperature), and I be the corresponding value of the latent heat of vaporization, the area agfe is t (t-ta). EFFICIENCIES IN THE RANKINE CYCLE 41 When this is small in relation to the area tnnga — c(t ff — t a ), or when the quotient tc has a lower value than the efficiency of the cycle under consideration; then we may expect to find a lowering of the condenser temperature undesirable, and vice versa. The value of x e is, of course, very nearly 4F C XII Rankine Cycle of Maximum Efficiency A new problem is thus suggested: given the upper temperature, t Cj and the ratio of expansion Vd + V c , at what lower temperature should the vapor be discharged in order that the efficiency may be a maximum? Let us take the value -— as a criterion of the desirable tc discharge temperature. For steam, with 4F C =25.4., c = 1.0. Table IX DESIRABLE CONDENSER TEMPERATURE WITH STEAM Four Expansions, from 302° F. Assumed Lower Temperature I v x ) • Xe Xel 68 86 104 107 1053.4 1043.4 1033.4 1031.7 928 529.5 313.3 288.3 0.0274 0.0480 0.0811 0.0879 0.0548 0.0919 0.1480 0.1600 We may infer, therefore, that as the discharge tem- perature is reduced from 110° to 107°, the efficiency first increases and afterward decreases, passing a maximum at some temperature between these two, and being 0.16 at the two temperatures stated, or practically that at its maximum. 42 RANKINE CYCLE OF MAXIMUM EFFICIENCY 43 Alcohol. This vapor gives V c , Fig. 6, as 1.139, so that F d = 7/=7 e = 4X1.139 = 4.556. Fig. 10 gives fc=210°; at which, by interpolation, 7 = 4.73. This is the V t of Fig. 5, in which, also by interpolation, n u = 0.2073, n u t = 0.537. Since n & = 0.325, n bc = 0.403, we have 0.325 - 0.2073+0.403 = x T X 0.537, x T = 0.971, and the check value of V T is 0.971X4.73 = 4.60, as against 4.556 intended. Using this in Eq. («/), with 68° as the discharge temperature, 144 abcrs = ~ { (142.0X 1 . 139) - (0.86X4.60) 11 o +206.68+277.36- 121.08- (0.971X331.77) 144, = ^(160.4-3.90)+484.04-443.08 = 69.98. The heat expended being 492.98, the efficiency is 0.142. The following approximation is now necessary, as in Table IX. Table X DESIRABLE DISCHARGE TEMPERATURE WITH ALCOHOL Four Expansions, from 302° F. Assumed Lower Temperature I v x Xe X e l tc 86 122 140 432.92 420.82 409.73 91.82 34.20 21.69 0.0501 0.1342 0.2120 0.065 0.135 0.201 44 VAPORS FOR HEAT ENGINES 300 ' i I ^ 290 / 1 / |.y 280 - ' / f / Y ^ 270 , ' n --,'- /' v Pi {y 200 / / fl, »/ / /j 7 X 250 / / /S *p / 1 A X 240 / / / ^ ' \>y y / / \ ,''? y / / / k'h y 230 / / / / r ■'. J V?' 220 / / / ,/ ; s i / o Jpd *' 210 y / im / ' / ' y >t 200 ' / y / y / / ' / / y K L_ 1-190 / /, ' V y""T_ / / /' y 1 \ Ul X180 o / \ *>'/ / ^ I #170 fl / L £ if 160 V* I V !*150 / \ ^ j O £140 / \ I* \ \ 2 130 / i 1 \ / \ ' \ 1 1 *~ 120 / I \ no / \ / 100 ' 90 / / 80 1 70 / / 60 / / 50 / \ 40 / ko so_ JZQ , .9 J / | 1 r 30 Ice NST/> kit df YNES 3 - P ER C IE NT 1 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 ENTROPY Fig. 10. — Temperature-entropy Chart for Alcohol 0.90 RANKINE CYCLE OF MAXIMUM EFFICIENCY 45 For this last lower temperature of 140°, we have 144 abcrs = ---{(U2.0X 1.139) -(0.78X4.60) | +484.04-443.08 I to = ~(160.4 -30.8) +40.96 = 64.91; 77o while the difference between the heats of the liquid at 140° and 08° being 67.27-20.50 = 46.71, the heat expended is 492.98-46.71=446.27, and the efficiency is 64.91-^-446.27 = 0.145. Again, the presumption is that maximum efficiency occurs at some discharge temperature between the two con- sidered, viz., 140° and 68°. To shorten the matter, let us note that 144 abcrs = ^(160.4 - 4.60P a ) +40.96. For t a = 122°, 104°, 86°, respectively, P a = 4.25, 2.59, 1.52, and abcrs = 67.06, 68.56, 69.36. Also for h a = 54.38, 42.68, 31.48, as compared with 20.56 for a 68° discharge temperature, the reductions in heat expenditure are 33.82, 22.12, 10.92, and the respective heat expenditures are 459.16, 470.86, 482.06, giving efficiencies of 0.146, 0.145, 0.144. The discharge temperature had better be 122° than 140°; a lower temperature than 122° is undesirable. Maximum efficiency will be attained when it is between 122° and 140,° probably nearer the former than the latter, and this max- imum efficiency will be not far from 0.146. Chloroform. We have, in Fig. 5, V c = 0.457, V r = 4 X 0.457 = 1.828 (desired value). From the chart, Fig. 11, U = 181° F. Applying the principle n b — n u +n b c = x r nut J 0.1077-0.0647+0.1219 = 0.1651 x T , x r = 0.998. 46 VAPORS FOll HEAT ENGINES 320 T£73 T ll it - Q / / /l /// H ^1% § t li^a _n_ i i 190 52 r In ZZ/jr_4_ | a 180 zii: , trtA'± 4> * X 170 4-4 1 Li I 4J&4 h wo -+-j fit "#t J £160 lit 1 X 7 4 3,, fi I rnh, f f/ :j- £ 150 ^ t t t/ A ^140 ., H -j i ^fc _ .4- ± S h 1 II ^zr _. __4- siso lift z± _ _.n_ ^130 + £ f--f- -J- -f H 190 t J 3 J _ .. ..4- 120 _, H _j j 7 1 _. j_ _ 1in 1 1 1 1 t I .. 4_4_ 110 7 11111... -4- - inn t t 1 h t I 4- t 100 ^ £ t - 4- I qn -4 -i L I ._.._[- I 90 7 J , k ._ 4. 1 80 £ 2 4 -I - --4- 4 80 t t t i - --4- j 70 -j J f j _ ..4- 4 LET _„4 co I 4 CI. ..it tJn t - -in 50 4 I 1 t 44 t 50 1 h i h i . ± t at Jl t j I .± I 40 f- h i i t ± i qq L Jio 20 J3o Uq_i£o 6( '70 _aoj_'90 ' wu : QJs SX^NlT D B_Y N fes S,-P EJB G E M±_ T [ i r i r i 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 ENTROPY Fig. 11. — Temperature-entropy Chart for Chloroform RANKINE CYCLE OF MAXIMUM EFFICIENCY 47 From the table, F* = 1.85, whence V r (value employed) checks as 0.998X1.85 = 1.85. By Eq. (J), with a discharge temperature of 104°, 144 abcrs = ~~{ (141. 4X0.457) -(7.14 XI. 85) / to +64.78+81.23 -35.24- (0.998X95.42) 144 = ~(64.4- 13.2) + 15.67 = 25.17. The heat expended is 140.85, and the efficiency is 25.17 -r- 140.85 = 0.179. Table XI DESIRABLE DISCHARGE TEMPERATURE WITH CHLOROFORM Four Expansions, from 302° F Assumed Lower Temperature. I v x x e Xgt tc 86 104 115.38 113.63 10.275 7.1 0.1798 0.261 0.158 0.218 The best condenser temperature is between 86° and 104° and somewhat exceeds 0.179. For acetone, tabular values above 284° F., are extrapolated merely, and the results to be obtained must be regarded with some reserve. The initial volume is about 0.706; that at the end of expansion must then be approximately 0.706X4 = 2.824; at which, from the chart (Fig. 12), the 48 VAPORS FOR HEAT ENGINES 300 1 t 290 1 h ' / 280 J 7 J 1 ^ ?.70 / / ^ 260 1 Tlpf / / ~T7 250 / I h I. 210 i h / I / ^/ J 230 / If / / i^_ -7- 220 / j "V .L ' / c| i 210 _J 1 'V / 200 / / \ / M/ 190 f 1 ; L/ v ' 7 m ft 180 m j ~- 4>l } j "> 170 3 */ Dm fels a. i i/y 1 1 W > 160 1 L a: 150 / /__£/ , pU4I, Vrffl 1 - h / r l v - / H - 95 160 f- / / i riVvAXi 4 H L 1.^, 1 1 ^4$u7 ^ 1 tit tZ y ^M i 4 /[iz®> g t i j y Pr 1 1 4i;aSr: / / z ^$_ 110 l 1 1/ If ' -4j3&_ _,_A / ^_t/ Jim a \^ 1 _/iz it 130 LIZI7 „ / / /* / 10 20 30 4i 50 61) 7D 80 90 10 ^jtEin? ' .• \ CONSTANT DRYNESS, PER CENT. 120 1 'I'lfTij' ,7/-— f •y .._ r no I j ti: ti4 I j IfVI / CARBON GHlJofl DE / CARBQN BISU .PHIDE 100 g4 f : ::: 1 qn I L t £4 H t 80 -J- ti h - >- t-i i 1 __. ._ j 70 ti ±-J ::: .:: / ti ti - _.. ._ £ fi oXt-j ti - L 60 1 L2J~t - I .__ L 50 4 1-Ct - J tit- ::: t:_ 1 40 1 ti t^ t i 1 if 1- : : t :: t ± 30 -4o-20-30-4(H5(- ti i / CONSTANJ DRYNf 5S, pER CENT.' 0.05 0.10 0.15 0.20 0.05 0.10 0.15 ENTROPY 0.20 0.25 0.S Fig. 13. — Temperature-entropy Charts for Carbon Chloride and Carbon Bisulphide 52 VAPORS FOR HEAT ENGINES The best discharge temperature is then between 86° and 104°, and the corresponding efficiency is not far from 0.162. Finally, for carbon bisulphide, V c (Fig. 5) =0.502, Fr = 2.008, and Fig. 13 gives ^ = 173°, x r = 0.90. From the table, 7^ = 2.226, whence V r (actual value used) =2.226 % X 0.90 = 2.003. If we take t a at 68°, 144 abcrs = ^- 7 - i (176X0.502)- (5.76X2.003) | +66.82+101.9-34.07- (0.90X128.44) 144 = =^(88.3-1 1.56) + 19.05 = 33.25. Here ea6c/= 66.82+ 117.90 -8.53 = 176.19, and the efficiency is 33.25 -^ 176.19 = 0.189. Applying the criterion, x e l (2.003 -J- 12.879) X 158.44 tc 528X0.2385 = 0.196, so that in this case maximum efficiency (which will not much exceed 0.189) will be obtained at a discharge tem- perature possibly a little below 68° F. We now tabulate these results : Table XII MAXIMUM EFFICIENCIES WITH FOUR EXPANSIONS Initially Dry Vapors, from 302° F. Vapor Discharge . Temperature Efficiency Vacuum (Inches of Mercury) Order of Efficiencies Alcohol Chloroform Carbon bisulphide Carbon chloride. . Steam 122°-140° 86°-104° below 68° 86°-104° 107°-110° 0.146 0.179 + 0.189 + 0.162 0.16 16.13 to 21.26 15.38 to 20.17 at 68°, 18.19 21.46 to 24.32 27.33 to 27.55 RANKINE CYCLE OF MAXIMUM EFFICIENCY 53 '900 800 \ 700 \ \ 600 \ \ \ „ -- CY CLE s ri ITI- \ SUPE }HE AT 500 A \ s \ c ■100 \ | J- "25 INI TIA LLY DRY C LAUSIL 8 CYCLES 302- 68" F. \ 24 s / / s / 23 22 21 20 19 / \ RA NKI >JE 3YC LEJ FR OM 302 J 18 / \ 4 EXP ANIONS -MA> IMUM ;ff CIE NC 1 / \ 1 V 17 / \ / \ / \ 1 / \ 16 / r^ \ \ / 15 \ / / OI mo. a. -i Fig. 14. — Cyclic Efficiencies and Criterion 54 VAPORS FOR HEAT ENGINES The order of efficiencies is strikingly different from that for those cycles in which expansion is complete. It is note- worthy also that with some of the vapors the best efficiency is attained with only a moderate degree of vacuum. Alcohol is the only vapor showing a lower efficiency than steam; those with the other vapors are such as to justify the expecta- tion of saving from 1 to 18 per cent of the fuel by their substitution for steam. In compound condensing engines, with ratios of expan- sion greatly exceeding 4, the most economical discharge temperature would probably be the lowest attainable, and the efficiencies of the various vapors would rank more nearly in the order found for the Clausius cycle. T—t The use of the — =— criterion furnished by the Carnot cycle is wholly unreliable; but it is a curious fact that in Table XII the efficiencies rank very nearly in the order of the temperature ranges. Some graphical expressions for both the Clausius and Rankine cycle results are given in Fig. 14. XIII Commercial Factors with the Rankine Cycle If we apply the principles already enunciated for the cycles of complete expansion, we have, in Fig. 5, — — = efficiency, as an inverse measure of the relative boiler eabcf capacities necessary; abcrs ~~hl x v °l ume °f liquid, as an inverse measure of the relative " times to get up steam"; easrf eabcf— abcrs „ ^ , ,. „ -= — - = — — —i , as a measure of the relative amounts of abcrs abcrs condenser surface and cooling water necessary; and (a new feature) V =V S -~ -, as a measure of the relative sizes of cylinder necessary for a given output. The comparisons are shown graphically in Fig. 7. Alcohol is an unattractive vapor on account of its low efficiency. Carbon bisulphide presents the unusually desirable features 55 R HEAT ENGINES 100 99 85 StoH 110 Steam 100 Carbon Chloride Carbon bisulphide Chloroform Relative Boiler Capacities Necessary Steam Carbon Chloride Carbon Chloroform Bisulphide Alcohol 84^ Alcohol Relative Times to "Get Up Steam" in the Same Boiler 100 99 82 87 112 Steam Carbon Carbon Chloroform Alcohol Chloride Bisulphide Relative Amounts of Condenser Surface and Cooling Water 100 78 42 51 41H Steam Carbon Carbon Chloroform Chloride Bisulphide Relative Sizes of Cylinders Alcohol Fig. 7. — Comparative Proportions of Power Plants Using Various Fluids in the Rankine Cycle from 302° F., with Four Expansions. All Developing the Same Horse-power RANKINE CYCLE— COMMERCIAL FACTORS ;>< of highest efficiency, maximum cylinder capacity, minimum condenser surface and cooling water consumption, min- imum boiler capacity; and a " time to get up " pressure only 5 per cent greater than is necessary with steam. Table XIII BOILER CAPACITY AND STEAMING RATE Rankine Cycles, Four Expansions, Dry Vapor from 302° F. Vapor Efficiency Relative Boiler Capacity Necessary Volume of Liquid Volume X Efficiency Relative Time to "Get Up Steam " Alcohol Chloroform Carbon bisulphide Carbon chloride. . Steam 0.146 0.179 0.189 0.162 0.16 110 89£ 85 99 100 0.0208 0.0096 0.0130 0.0069 0.0160 0.00304 0.00172 0.00245 0.00112 0.00256 150 105 229 100 Table XIV CONDENSER SURFACE AND COOLING WATER CONSUMPTION Rankine Cycles, Four Expansions, Dry Vapor from 302° F. Vapor abcrs eabcf easrf easrf -5- abcrs Relative Conden- ser Surface and Cooling Water Consumption Alcohol 67.06 25.17 33.25 18.01 176.21 459.16 140.85 176.19 111.62 1101.66 392.10 115.68 142.94 93.61 925.45 5.85 4.58 4.30 5.20 5.25 112 Chloroform Carbon bisulphide Carbon chloride. . Steam 87 82 99 100 58 VAPORS FOR HEAT ENGINES Table XV SIZE OF CYLINDER FOR A GIVEN OUTPUT Rankine Cycles, Four Expansions, Dry Vapor from 302° F. Relative Vapor abcrs V V r + abcrs Volume of Cylinder Alcohol 67.06 4.60 0.0685 47± Chloroform 25.17 1.85 0.0735 51 Carbon bisulphide .... 33.25 2.003 0.0602 42 Carbon chloride 18.01 2.04 0.1125 78 Steam 176.21 25.4 0.1440 100 XIV Rankine Cycles with Superheat Not enough is known of the properties of these vapors when in the superheated condition to warrant the attempt to solve comparative cycles of this type. Even for steam, 5 a I" Ih d 9\^ e J A 7 J x \ n 5 e S \ \ \ 9^' f m 3 N Fig. 8. — The Rankine Cycle with Superheat the last word has probably not been said on such properties. The following method for computing the efficiency etc., of any Rankine cycle with the vapor initially superheated, is believed to be accurate and perfectly simple: requiring only exact values for the specific heats and entropies calcu- lated therefrom. The need of the method arises from the 59 60 VAPORS FOR HEAT ENGINES inaccuracy in computing the work along an even partially superheated adiabatic, either by the pv- PV 1 formula or by an expression for the loss of internal energy The present method may be considerably shortened by the employment of the Mollier or total-heat entropy diagram Case I Let expansion be wholly in the superheated region, the steam becoming saturated (dry or wet) during the terminal drop - cycle abcdef, Fig. 8. Then Efficiency Work abcdef Heat expended mabcdri Draw the line of constant pressure egh through e. Then hbcdeg-\-ahgef Efficiency mabcdn 144 (jhbcdn-jhgen) + - f7 - { (P h V e ) - (P a V e ) mabcdn H d -h h -H e +h h +~(P h -P a )V e H d —h a H i -H e +~V e {P h -P a ) Hd~h a H d and H e being the total heats above 32° F., at the states denoted by their subscripts, h a the heat of the liquid at a, and V and P pressures and volumes. The entropy and volume at e determine the total heat and pressure at that point. RANKINE CYCLES WITH SUPERHEAT 61 Case II. If the vapor remains superheated at the end of the terminal drop (i.e., at the point /), the computation is unaltered, and the fact of such superheat might even be unsuspected. Case III. If the vapor becomes saturated during expansion, its initial entropy must have been less than that of the dry vapor at the terminal pressure. This is the most probable case, and the condition is sure to be detected when the total heat is ascertained at e. The saturated steam tables will give H e , and the expression for efficiency is not changed. * XV Summary: Conclusions The use of a special vapor to replace steam might be justified on one of three grounds: (a) A reduced lower temperature limit for the cycle without the necessity for an impracticably high vacuum. The extreme limit is determined, however, by the cooling water supply, and the gain in this direction appears likely, from a rigid application of the second law of thermodynamics, to be small. (b) But the properties of the substitute vapor may be such as to cause a greater gain than is thus indicated. Examination shows that steam ranks best as to the critical ratio Latent heat of vaporization Specific heat of liquid ' between certain assumed temperature limits, at which, correspondingly, it gives the highest efficiency. These limits (302° and 68° F.) are impracticable for steam, though practicable with the other vapors. With a more practicable lower limit of 110° F. for steam, it gives with complete expansion an efficiency below that attainable by the other (saturated) vapors. This comparison is of practical impor- tance only with the turbine engine. The velocities attained \ by complete adiabatic expansion between the assumed » 62 1 SUMMARY: CONCLUSIONS 63 limits arc with the substitute vapors in all cases much less than those attained with steam. In cycles with terminal drop, at such ratios of expansion as are common in simple engines, all of the vapors except alcohol surpass steam in efficiency, but this superiority is not traceable to a reduced lower temperature limit. This limit is sometimes too low for best efficiency in the simple condensing engine. The limit at which the efficiency is a maximum may be approximated from the variation in the determining ratio xj> tc' Maximum efficiencies for the various saturated vapors in this type of cycle occur at lower temperature limits rang- ing all the way from 68° to 140° F. The total unreliability of any surmises based on the Carnot expression, T-t is evident. It may be objected that the use of a uniform expansion ratio of 4 : 1 in all cases is an improper assumption : that in a vapor showing relatively slight — or no — condensa- tion with adiabatic expansion, the influence of cylinder con- densation would be so mitigated that the ratio of expansion might be advantageously increased. But cylinder condensa- tion means virtually heat transfer; and this heat transfer would go on just the same as long as the substance re- mained a wet vapor. Further, the evils of such transfer are largely evidenced in initial condensation; that which occurs, not during expansion, but during admission of steam to the cylinder. A given loss of heat to the walls actually means a greater loss of dryness in the case of the substitute vapors, 64 VAPORS FOR HEAT ENGINES because the heat contents of given weights of such vapors are less than those of the same weight of steam. This may appear an argument in favor of the use of a lower ratio of ex- pansion in their case : but, on the other hand, the substitute vapors uniformly contain more heat and give more work, in proportion to the space which they occupy. (c) The capacity of the apparatus may be affected by the properties of the fluid chosen. It appears that there are perceptible advantages with some of the substitute vapors in respect to boiler capacity, time of getting into operation, condenser capacity and amount of cooling water necessary, as long as we limit the consideration to the complete expan- sion type of cycle. With the terminal drop cycle, the vapors maintain their advantage in all respects excepting that of " quick steaming" : and they produce from 50 to 75 per cent more power from a cylinder of given size than does steam. The objections to the use of a substitute fluid include: (a) Its cost. This need not be prohibitive, if the leakage loss is not excessive in proportion to the gain of efficiency. (b) Increased maximum pressure. This is associated with all of the fluids, with the possible exception of carbon chloride at high temperatures. This substance comes nearest to the desired pressure-temperature relation, standing to steam in much the same relation as it does to alcohol at a lower temperature. Its pressure-temperature curve is of abnormally slight slope. The binary vapor principle permits of a slight gain without excessive maximum pressure; but involves more complication than would the use of a substitute vapor. In practice, pressure conditions influence the cyclic range and superheating may be resorted to in order to increase the range. With superheat, a high specific heat of the superheated vapor and a left-hand location for the pressure- temperature curve (Fig. 2) furnish criteria of desirability. SUMMARY: CONCLUSIONS 65 The disadvantage of an increased maximum pressure may be offset by the reduction in size of cylinder probable with all of the substitute fluids. The only remaining question is, then, whether with such a fluid a sufficient increase in efficiency may be obtained to offset the expense due to leakage. With superheat and complete expansion the answer appears to be in the negative. With only saturated vapor employed, we have found at least one con- dition at which, with carbon bisulphide, for example, leakage amounting to the percentage 18 or might be tolerated, a representing the ratio of the cost of carbon bisulphide, pound for pound, to that of coal. The properties of some of the vapors are not known with great exactness, and the figures presented are in all cases approximate. Investigation of terminal drop cycles with, say, 16 expansions, both saturated and superheated, is warranted; but on the whole it seems safe to say that there is nothing inherently absurd in the proposal to use some vapor other than steam for power production. The substitution appears far more promising than the use of a binary vapor on the steam cylinder exhaust. APPENDICES APPENDIX I The Vapors Discussed The alcohol referred to (C2H6O), is the ordinary ethyl alcohol (not wood alcohol); a light colorless, inflammable, rather pleasant-smelling liquid. When free from water its specific gravity is 0.785. It boils at 172° F., and has been frequently used as a working fluid in heat engines. Chloroform (C2HO3), known from its use as an anaesthetic, is a heavy clear fluid of powerful odor, specific gravity about 1.48, boiling-point 140-144° F. The commercial product sells for about 25 cents a pound. Acetone (C3H6O), is a colorless liquid of specific gravity 0.797 and boiling-point 135° F. Carbon Bisulphide (CS2), costs (in a somewhat impure state) about 4 cents a pound. It is a poisonous pungent- smelling clear liquid, boiling at 115° F. The specific gravity is 1.27. Carbon Chloride (CCU, the tetrachloride), boils at 168- 171° F., is 1.6 times as heavy as water, and costs about 8 cents a pound. It has recently been employed as a cleansing fluid in place of gasoline. It is claimed that it can be manufactured on a large scale at a cost much below the 67 VAPORS FOR HEAT ENGINES present price. The ordinary commercial substance is a transparent fluid, with an odor suggesting garlic. It is slowly hydrolized by water, forming CO2 and HC1. These fluids, with ether, gasoline and 90 per cent benzol, are all grease solvents; most of them are inflammable, but in this respect chloroform and carbon chloride are exceptions. All seem to be non-corrosive in their action on iron pipes or plates. Reference should be made to the paper by Booth, " Commercial Extraction of Greases and Oils," Trans. Am. Inst. Chem. Engrs., II, 1909, 248: and to p. 114 of Gill's " Oil Analysis," relating to the action of oils on metals. APPENDIX II The Volume Temperature Relation of Dry Steam The sources from which a relation between the volume and temperature of saturated steam must be found are, essentially, the exponential equations of Rankine and Zeuner for the pressure-volume relation, PV n = constant, where P and V are corresponding specific pressures and volumes and n is either -}-J (Rankine) or 1.0646 (Zeuner): and the Thiesen formula for pressure-temperature, Hog y|y = 5.409(7 7 -212) -8.71 Xl0- 10 [(689-7 7 ) 4 -477 4 ], in which t is the absolute and T the Fahrenheit temperature, and P is in pounds per square inch. The pressure-volume formula is an empirical expression intended to describe the results following the application of the well-known Clapeyron differential equation from which specific volumes are usually calculated. The pressure-temperature expres- sion is also empirical, but stands on a somewhat more satis- factory footing, expressing the results of recent experimental work so closely that it has been used in computing the lately published steam tables of Marks and Davis. It is, however, too cumbersome for our purpose, which is that 69 70 VAPORS FOR HEAT ENGINES of deriving a fairly accurate and quickly available expres- sion for the relation between volume and temperature. We will adopt the Marks and Davis tables (Longmans, Green & Co., 1909) for reference. A recent magazine article (Power, March 8, 1910), gives the surprisingly accurate expression, *=200p*-101, for pressure (pounds per square inch) and temperature Fahrenheit. This gives confirmation of tabular values with an error not exceeding that involved in computation with a 10-inch slide rule. If we combine this equation with that between pressure and volume, we find P* = ^^ = 0.005^+0.505, pt;H=(0.005*+0.505) 6 t;H = a constant, 477, the approximate evaluation of which is as follows: t o lO £+ >o o o © log (7) 6 log (7) 76 All log »I5 s O bio M V 101.83 1.01415 0.00610.0366 1.089 437.5 2.6418 2.49 309 153.01 1.270 0.104 0.624 4.2 113.5 2.056 1.934 85.9 182.86 1.419 0.152 0.912 8.16 58.4 1.766 1.661 45.8 200 1.505 0.178 1.068 11.69 40.9 1.612 1.516 32.8 220 1.605 0.206 1.236 17.2 27.9 1.446 1.359 22.82 240 1.705 0.232 1.392 24.62 19.36 1.2877 1.211 16.23 260 1.805 0.2565 1 . 5390 34.58 13.8 1 . 1402 1.072 11.8 280 1.905 0.28 1.68 47.9 9.97 0.998 0.938 8.66 300 2.005 0.3023 1.8138 65.04 7.315 0.864 0.812 6.49 320 2.105 0.324 1.944 87.9 5.43 0.735 0.691 4.91 340 2.205 0.344 2.064 115.8 4.125 0.616 0.58 3.8 401.1 2.5105 0.4 2.4 251 1.9 0.28 0.264 1.835 APPENDICES 71 40 60 Pressure. LbB. per Sq. In. 100 120 140 160 180 200 220 240 16.0 Entropy above 32 °F„ B.t.u; Fig. 16. — Temperature-entropy Diagram for Ammonia 72 VAPORS FOR HEAT ENGINES The values of v closely correspond with those in the steam table adopted, excepting in the case of the lower temperatures — below 200°. A simpler formula is, however, desirable. If we assume the possibility of an expression in the form tv n = constant, then by successive trials we may find the most plausible value of n to be 0.248, and fe°- 248 = 477|. This gives the following approximate results. V log V 0.248 log v ^0.248 t 30 1.4776 0.3663 2.323 206 25 1.398 0.3465 2.22 216 20 1.3016 0.3233 2.102 227 15 1.176 0.2919 1.958 244 10 1.0 0.248 1.77 270 8 0.936 0.2315 1.701 281 5 0.6985 0.1725 1.488 321 Between the tabulated limits, this has an accuracy within one or two degrees; but it is wholly unreliable for either very low or very high temperatures. Fortunately, it is the medium temperatures (between 200° and 260°) that we are principally concerned with; and within this range the temperature varies very nearly inversely as the fourth root of the specific volume — a convenient statement in the absence of logarithms. The fact that both expressions given have about the same constant term is a curious coincidence. In Fig. 9, the tabular volume-temperature curve has been plotted along with that given by the latter of the two equa- APPENDICES 73 tions. There would be no purpose served by plotting the more accurate values from the former equation, which within the charted limits, and to the scale adopted, actually coincide 30 \ ores TABULAR OR e — 005 t ■+ 0.505) V ,6 =477; OTES > ^**> =**»» 210 220 230 240 250 260 270 280 290 300 310 320 330 340 TEMPERATURES FAHRENHEIT Fig. 9. — Temperature- volume Curves of Dry Steam with those of the tabular curve, the departure from coin- cidence being less than 1 per cent even at a temperature above 400°. The error rapidly increases, however, as the temperature is lowered below 200°, being about 3 per cent at 183°, 5 per cent at 153° and 7 per cent at 102°. 74 VAPOKS FOR HEAT ENGINES saw niOA DldlD3dS s 1 ^ 2 s 1 -4 - r x "^ V g d >ft> ^ l S CI *> \ \ d §s <| cv v ; \ \ -*"=> V >?> -< J /v *^\ ', = £ 7 ^ s>-> s H /y^ 9 \ \ 1 . „ *7 10 -V^Z \ ^ ■^ '- d 57 V" o/ \ **\ \ \ \ J y> \ \ \ \ d A / V \ \ r= /' ' \ \ \ T \ ° \ \ \ W \ 0>\ \ \ d r^ -\_ _^ o \ \ \ \ = d r o ^ '* ^\ _^_ *, \ s \ ^ % \ \ \ o ■I- I x ^ s sA \ ^ ^r \ 2 \ \ v* \ \ ^v< t-A ^~~~~- *£, i a \ \N x - \ o 0. \ \ ,>> ^ J " , _ 00 -I \ V \ \ = O V) \ \\ \ » N ' N N* " N 5 ,, Ul \ \v \ V ° V * 'v \ \ s S3 y VSJ ^ \ \ ?, % ^§s * v O" \ ., — JUO O^' \ \ N] 5 T . ^ ^ \^ .riju. '1 S ! 1 iS ; ? i , ! < < — i S H r d ™ H3HN3aHVd 3anivaadiAi3i TABLES 75 TABLE XVL— PROPERTIES OF THE DRY SATURATED VAPOR OF ALCOHOL Note. Tables XVI to XX are abstracted by permission from Klein's Translation of Zeuner's Technical Thermodynamics. (D. Van Nostrand Co.) Internal Latent Specific Volume Heat of the Latent Heat Heat of of Dry Vapor — Temperature, Fahrenheit Liquid above 32°, B.T.U. of Vaporization, B.T.U. Vaporization, B.T.U. Specific Volume of Liquid, Cu.Ft. 32 0.00 425 . 70 402 . 18 513.989 50 10.06 429.86 405.62 277.595 68 20.56 433.04 407 . 90 156.956 86 31.48 432.92 406.95 91.800 104 42.68 428.92 402.29 55 . 289 122 54.38 420.82 393.74 34.174 140 67.27 409.73 382.38 21.671 158 80.24 397.12 369 . 60 14.112 176 93.80 383.56 355 . 94 9.430 194 107.95 370.85 343.08 6.479 212 122.72 358.42 330.49 4.564 230 138.13 347.15 318.97 3.305 248 154.21 336.29 307.85 2.443 266 170.96 325.84 297 . 10 1.845 284 188.46 316.44 287.31 1.424 302 206.68 306.86 277.36 1.118 TABLE XVIL— SATURATED VAPOR OF CHLOROFORM 32 0.00 120.60 112.45 37.899 50 4.19 118.88 110.36 23.536 68 8.41 117.14 108.29 15.314 86 12.64 115.38 106.23 10.265 104 16.87 113.63 104.20 7.090 122 21.13 111.84 102.15 5.025 140 25.42 110.03 100.11 3.646 158 29.72 108.20 98.05 2.702 176 34.04 106.36 96.00 2.042 194 38.38 104.49 93.92 1.571 212 42.73 102.62 91.85 1.230 230 47.11 100.71 89.75 0.977 248 51.50 98.80 87.65 0.788 266 55.91 96.86 85.52 0.644 284 60.34 94.91 83.38 0.533 302 64.78 92.94 81.23 0.447 320 69.25 90.95 79.05 0.378 76 VAPORS FOR HEAT ENGINES TABLE XVIII.— SATURATED VAPOR OF ACETONE Temperature, Fahrenheit Heat of the Latent Heat Internal Latent Heat of Specific Volume of Dry Vapor — Liquid above 32°, B.T.U. of Vaporization, B.T.U. Vaporization, B.T.U. Specific Volume of Liquid, Cu.Ft. 32 0.00 252.90 237.34 68.206 50 9.18 250.22 233 . 19 42.851 68 18.52 247.20 228 . 96 28.043 86 27.99 243.86 224.76 18.932 104 37.60 240.19 220.38 13.111 122 47.36 236.19 215.82 9.286 140 57.26 231.87 211.06 6.707 158 67.30 227.22 206.05 4.937 176 77.49 222.23 200.77 3.696 194 87.82 216.92 195.23 2.811 212 98.30 211.26 189.38 2.171 230 108.90 205.31 183.29 1.700 248 119.66 199.01 176.90 1.347 266 130.57 192.39 170.25 1.081 284 141.61 185.43 163.29 0.876 TABLE XIX.— SATURATED VAPOR OF CHLORIDE OF CARBON 32 0.00 93.60 87.40 52.196 50 3.58 92.61 86.16 31.990 68 7.18 91.57 84.86 20.465 86 10.84 90.37 83.42 13.569 104 14.51 89.13 81.94 9.295 122 18.22 87.76 80.34 6.547 140 21.96 86.33 78.70 4.729 158 25.74 84.78 76.97 3.489 176 29.56 83.12 75.15 2.624 194 33.39 81.40 73.29 2.006 212 37.26 79.56 71.35 1.554 230 41.17 77.65 69.36 1.219 248 45.11 75.62 67.29 0.966 266 49.09 73.49 65.15 0.772 284 53.08 71.30 63.00 0.622 302 57.11 69.02 60.78 0.503 320 61.20 66.60 58.47 0.408 TABLES 77 TABLE XX —SATURATED VAPOR OF BISULPHIDE OF CARBON Internal Latent Specific Volume Heat of the Latent Heat Heat of of Dry Vapor — Temperature, Liquid above of Vaporization, Vaporization, B.T.U. Specific Volume Fahrenheit 32°, B.T.U. B.T.U. of Liquid, Cu.Ft. 32 0.00 162.00 149.02 28.172 50 4.25 160.31 146.90 18.762 68 8.53 158.44 144.62 12.866 86 12.83 156.39 142.20 9.058 104 17.17 154.15 139.63 6.526 122 21.53 151.76 136.93 4.801 140 25.94 149.16 134.06 3.599 158 30.35 146.41 131.07 2.742 176 34.81 143.46 127.91 2.123 194 39.29 140.35 124.63 1.666 212 43.81 137.05 121.19 1.323 230 48.35 133.58 117.62 1.064 248 52.92 129.92 113.: «9 0.863 266 57.53 126.09 110.03 0.708 284 62.15 122.10 106.05 0.586 302 66.82 117.90 101.90 0.489 78 VAPORS FOR HEAT ENGINES 0> 'C o o d o 03 o ©00S>OO(NOO)©«:00H(N«0000 O0000G000CC0000000000M0000G00000 ddddddddddodddddd 8 CDWtNHffiCOHOO^COOOlOfflLOiO HCOiOOOOCONO'fOOlNfflHiOOiO 05Q0NC0l0iO^C0C0(MHHOO0303(Z) ,-H,-lT-li-lrHT-li-lr-(T-Hr-lT-(i-l,-l,-lOOO ooooooooooooooooo s MiOiO^O©05HlN(N(N(N(M03MW IS m n d o .Q c3 O CO 05C0N(NNHNMOiC--i(Xli0H00'* (MMHHOO05O000000NNNO© COC0C0C0C0C0(N(M(M(N(M<6(6ci(6d>d>d><6d>d>d>d>d> •OINOMO^CONMCMCOIQOCDM CO^lNfficOINOC^OcOCOON^INO , OOOOOOOOOOOOOOOO 8 OOOOOcDCONOOiOOOOOiCLOO OiOOOOCO^»ONaifO(DOOHiO 1 H^COOON^COOOOiMiONOlN 1 1 OOOOi-H'-H'-irHT-i