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IC 8871 
 
 Bureau of Mines Information Circular/1982 
 
 A Computer Program for Calculating 
 Thermodynamic Properties 
 From Spectroscopic Data 
 
 By R. P. Beyer 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 

Information Circular 8871 
 
 A Computer Program for Calculating 
 Thermodynamic Properties 
 From Spectroscopic Data 
 
 By R. P. Beyer 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 James G. Watt, Secretary 
 
 BUREAU OF MINES 
 Robert C. Horton, Director 
 

 ^fiO- 
 
 <fl 
 
 n\ 
 
 This publication has been cataloged as follows: 
 
 Beyer, R. P. (Richard P.) 
 
 A computer program for calculating thermodynamic proper- 
 ties from spectroscopic data. 
 
 (Information circular ; 8871) 
 
 Bibliography: p. 19. 
 
 Supt. of Docs, no.: 1 28.23:8871. 
 
 1. Thermodynamics— Computer programs. 2. Gases— Thermal 
 properties— Computer programs. 3- Gases— Spectra— Computer pro* 
 grams. 4. FORTRAN (Computer program language). I. Title. II. 
 Series: Information circular (United States. Bureau of Mines) ; 8871. 
 
 TN295.U4 [TJ265] 622s [536'.25] 81-607926 AACR2 
 
CONTENTS 
 
 Page 
 
 Symbols and terminology ii 
 
 Abstract 1 
 
 Introduction 2 
 
 Calculat ional methods 2 
 
 Program operation 5 
 
 Program listing 11 
 
 Program output 18 
 
 References 19 
 
11 
 
 SYMBOLS AND TERMINOLOGY 1 
 
 e. = energy of the ith electronic level, cm - 
 g* = degeneracy of the i th electronic level 
 
 = symmetry number 
 
 a = rotational vibrational interaction constant 
 x = anharmonicity correction 
 0) = fundamental frequency, cm - 
 
 e 2 
 
 1 = moment of interia, g cm 
 
 S = entropy, cal mol~ K~ 
 
 C = heat capacity, cal mol - K - 
 
 H = enthalpy, cal mol A K 
 
 r = bond distance, A 
 
 e 
 
 T = transition point temperature, K 
 
 p -01 
 
 h = Planck's constant, 6.62617636 x 10 z/ erg-sec 
 
 k' = Boltzmann's constant, 1.38066244 x 10 erg molecule K 
 
 R = gas constant, 1.98719.7 cal K~*mol~* 
 
 R 1 = gas constant, 82.056826 atm cm 3 mol K 
 
 N. = Avogadro's constant, 6.02204531 x 10 23 mol -1 
 
 c = Speed of light, 2.9979245812 x 10 10 m sec -1 
 M = molecular weight , g mol" 
 e i = energy in ergs, (cm -1 x he) 
 
 Values for the physical constant are from (2) . Underlined numbers in 
 parentheses refer to items in the list of references at the end of this 
 paper. 
 
A COMPUTER PROGRAM FOR CALCULATING THERMODYNAMIC 
 PROPERTIES FROM SPECTROSCOPIC DATA 
 
 by 
 
 R. P. Beyer 2 
 
 ABSTRACT 
 
 A FORTRAN IV computer program has been written to calculate thermodyna- 
 mic properties over a desired temperature range from spectroscopic data. 
 This program computes heat capacities, enthalpies, and entropies for monatom- 
 ic, diatomic, linear, and nonlinear polyatomic gases. This research is part 
 of the Bureau of Mines effort to provide thermodynamic data for the advance- 
 ment of mineral technology. 
 
 2 
 
 Chemical engineer, Albany Research Center, Bureau of Mines, Albany, Oreg. 
 
INTRODUCTION 
 
 As part of a program to advance technology, reduce energy use, and abate 
 pollution, the Bureau of Mines generates thermochemical data on various min- 
 erals and metals. A computer program for calculating C~, S°(T)-S°(0), 
 and H°(T)-H°(298) was written to further this aim. The program was written 
 in FORTRAN IV Plus, Version 2.5, to run on a Digital Equipment Corp. 3 PDP 
 11/34 minicomputer with the RSX-11M, Version 3.2, operating system. 
 Although programs have been written previously for this type of calculation, 
 [e.g., McBride and Gordon (5)], the vast differences in hardware, operating 
 systems, and compilers necessitated a rewriting rather than an adaptation of 
 previous work. 
 
 The program accepts as input the electronic energy levels, degeneracies, 
 moment of inertia, number of atoms, vibrational frequencies, vibrational- 
 rotational interaction constant, symmetry number, and molecular weight. 
 The output consists of the heat capacities, entropies, and relative enthal- 
 pies over a given temperature range. The normal output consists of the ther- 
 modynamic properties calculated over the desired temperature range at 
 intervals starting at K and including 298.15 K. Any noninternal desired 
 temperature may also be included . 
 
 CALCULATIONAL METHODS 
 
 The methods to calculate the thermodynamic properties follow the adapta- 
 tion of Mayer and Mayer (4) by King and others (3) . For the definition of 
 the symbols used, refer to the symbols and terminology section. 
 (1) Monatomic gases 
 
 Translational contribution: 
 
 (C p ) tr = 5/2 R 
 
 (H - H ). Y . = 5/2 RT 
 
 tr 
 
 S tr = RCJtnR^ 5/2 AnT + 3/2 &nM + 3/2 £n±™ - 5/2 AnN + 5/2) 
 
 Reference to specific brand names does not imply endorsement by the Bureau 
 of Mines. 
 
Electronic contribution: 
 
 C e= R 
 
 0^ - (Q^ 2 1 
 . Q Q J 
 
 [f] 
 
 (H - H ) = RT H 
 
 S e = R |AnQ + 
 
 where 
 
 v _e i /kT 
 Q = I g ± e 
 
 C 1 
 
 e . 
 
 1 
 
 Q 1 = I 8i 
 
 kT 
 i l^J 
 
 Q 11 = I 8l 
 
 i L kT J 
 
 •e 1 /kT 
 
 2 -e./kT 
 
 e 
 
 (2) Diatomic gases 
 
 Translational and electronic contributions: same as for monatomic 
 
 gases. 
 
 Rotational contribution 
 
 c r = r(i + z£) 
 
 r 45 
 
 (H-H ) r = RT(l-^-^) 
 
 v 2 
 S, = R (1 - lny - lno - £-) 
 
 r 90 
 
 where y = 
 
 hcB ( 
 kT 
 
 B = B - 1/2'acm -1 
 
 B„ = *_ cm" 1 
 e 8n z cl 
 
Vibrational contribution 
 
 2 u 
 r - R u e 
 C vib " R (e u _ 1)2 
 
 (« " H 0) v ib - 
 
 RT 
 
 (e u -l) 
 
 S vib = R 
 
 -S— - *n (l-e _u ) 
 e u -l 
 
 where u = 
 
 hctoc 
 kT 
 
 u e e e' 
 Anharmonicity corrections 
 
 -1 
 
 _ R 
 
 cor 
 
 4x 
 
 u 3 e u (2ue u -2e u +u+2 ) 
 
 (e u - 1)' 
 
 + 6 
 
 u 3 e u (e u +l) 
 
 (e u -l) 3 
 
 + 16Y 
 
 < H " H o) C or " 
 
 RT 
 
 2x 
 
 u 2 (2ue u - e u + 1 ) 
 
 (e u -l) 3 
 
 + 6 
 
 2 u 
 u e 
 
 + 8Y 
 
 (e u - 1) : 
 
 cor 
 
 4xu 2 e u + 6ue u f 6 + 16Y 
 
 (e u -l)3 (e u -l) 2 (e u -l) u 
 
 where x = 
 
 l-2x. 
 
 6 = 
 
 Y = 
 
(3) Linear polyatomic gases 
 
 Electronic: Same for all atoms and molecules. 
 
 Trans lational: Same for all atoms and molecules. 
 
 Rotational plus symmetry: Same as for diatomic molecules except 
 
 for calculation of I(moraent of inertia) . 
 Vibrational: Fundamental frequencies 3n-5 in number. Follow the 
 diatomic method and sum the results. 
 
 (4) Nonlinear polyatomic 
 
 Electronic: Same as linear polyatomic. 
 Translational: Same as linear polyatomic. 
 Rotational plus symmetry: 
 
 (H(T) - H(0)) r = (3/2)RT. 
 
 C D = (3/2)R 
 F r 
 
 512u 7 k 3 , 
 S r = 3/2R + R[l/2 In I A 1 B I C + 3/2 InT - Ino + 1/2 in g J 
 
 Vibrational: Fundamental frequencies 3n-6 in number. Follow the 
 diatomic method and sum the results. 
 
 PROGRAM OPERATION 
 
 Input consists of a data file containing the pertinent information. 
 There are four different types of data input files, depending on which type 
 of gas is being studied. All data in the examples are from JANAF (1). The 
 following examples show the required format. 
 
 (1) The monatomic input file: 
 
 a) In general, 
 Name 
 
 Monatomic 
 
 Highest temperature to be calculated 
 K, the number of noninterval temperatures (Tp^, i = 1,2 K) 
 
 T Pl 
 
Number of energy levels 
 
 Electronic energy of level 1 (e.) 
 
 F(g) 
 
 
 Monatomic 
 
 
 2000. 
 
 
 
 
 
 12 
 
 
 
 
 4 
 
 404. 
 
 2 
 
 103327.14 
 
 18 
 
 115918.7 
 
 6 
 
 116597.23 
 
 14 
 
 117465.88 
 
 22 
 
 118627.73 
 
 10 
 
 123118.7 
 
 12 
 
 128346.36 
 
 80 
 
 132786.07 
 
 16 
 
 133531.81 
 
 22 
 
 134978.71 
 
 88 
 
 18.9984 
 
 
 Degeneracy of 
 level i (g ± ) 
 
 Molecular weight 
 b) Monatomic example, F(g): 
 
 (2) The Diatomic input file: 
 
 a) In general, 
 
 Name 
 
 Diatomic 
 
 Highest temperature to be calculated 
 
 Number of noninterval temperatures 
 
T Pi 
 
 Number of energy levels 
 
 Electronic energy of level i (e.) 
 
 Degeneracy of 
 level i (g i ) 
 
 Atomic weight of atom 1 
 Atomic weight of atom 2 
 Internuclear distance (r in A) 
 Fundamental frequency (u> in cm" ) 
 Anharmonicity correction (uj x ) 
 
 Rotational-vibrational interaction constant (a) 
 Symmetry number (a) 
 
 b) Diatomic example, CuF(g); 
 
 CuF(g) 
 
 Diatomic 
 
 6000 
 
 
 
 1 
 
 
 
 63.54 
 
 18.9984 
 
 1.743 
 
 621.89 
 
 3.941 
 
 0.004586 
 
 1 
 
8 
 
 (3) The linear polyatomic input file: 
 a) In general, 
 
 Name 
 
 Linear polyatomic 
 
 Highest temperature to be calculated 
 
 Number of noninterval temperatures, (Tp) 
 
 T Pi 
 
 Number of energy levels 
 
 Electronic energy of level i (e-) 
 
 Degeneracy of 
 level i (g ± ) 
 
 Molecular weight 
 Number of atoms 
 
 Fundamental frequency of level i (u>. ), enter degenerate 
 
 frequencies as many times as the degeneracy of the modes , 
 
 see examples below. 
 
 Moment of inertia (I) 
 
 Rotational vibrational interaction constant (a) 
 
 Symmetry number (a) 
 
b) Linear polyatomic example, CuF 2 (g): 
 
 CuF2(g) 
 
 Linear Polyatomic 
 
 2000 
 
 
 
 3 
 
 2 
 
 9000 4 
 
 18000 4 
 
 101.5368 
 
 3 
 
 608 
 
 205 
 
 205 
 
 768 
 
 112.4008735 (see below for units) 
 
 
 
 2 
 
 (4) The nonlinear polyatomic input file: 
 
 a) In general, 
 
 The same as the linear case except the second line should 
 read nonlinear polyatomic and I is the product of the 
 three principal moments of inertia I = I.Iglp. 
 
 b) The nonlinear polyatomic example Zrl^g): 
 
 ZrI4(g) 
 
 Nonlinear polyatomic 
 
 2000. 
 
 2 
 
 155.3 
 
 623.9 
 
 1 
 
 1 
 
 598.66 
 
 5 
 
 146. 
 
 45. 
 
 45. 
 237. 
 237. 
 237. 
 
 58. 
 
 58. 
 
 58. 
 65718000 (see below for units) 
 
 12 
 
10 
 
 The FORTRAN-IV Plus compiler used with this program limits calculations 
 to numbers between ±10 and ±10 . Therefore, values for the moment of 
 inertia for linear and nonlinear polyatomics should be entered as follows: 
 
 (1) Linear: values of I in units of g-cm should be multiplied by 
 (N A /10 -16 ) before entering in the data input file. CuF 2 (g), I = 
 
 18.7 x 10 g-cm . For the input file this number would be changed 
 to (18.7 x 10 -39 )(N A /10 -16 ) = 112. A. 
 
 (2) Polyatomic: Values for I.IgI~, which would have an exponent of 
 
 10~ 117 [from (10~ 39 ) 3 ], should be entered without this exponent. 
 For example, Zrl^Cg), I A I B Ic = 65718000 x 10" 117 . This should be 
 
 entered as just 65718000. 
 
 An example of the output file for the Zrl^Cg) example is given after the 
 program listing. The program was checked by running all the examples shown 
 and comparing the output with the accepted JANAF (1) results. Agreement 
 between the computer output and the JANAF values was exact. 
 
11 
 
 PROGRAM LISTING 
 
 C 
 
 C A PROGRAM TO CALCULATE HEAT CAPACITY, ENTHALPY, AND 
 
 C ENTROPY FROM SPECTROSCOPIC DATA 
 
 C 
 
 Real*8 HT,e(100),g(100),w(100) ,xe(100) ,wexe(100) ,MW,MW1,MW2 
 
 Real*8 re,a,sig,Be,BO,y,x,c,R,pi,k,h,kT,lny 
 
 Real*8 c trans, htrans,s trans, crot,hrot,srot,cvlb,hvib,svib 
 
 Real*8 celec , helec , selec , cr298 ,hr298 , sr298 ,ht298 , ct298 , st298 
 
 Real*8 cv298,hv298,sv298,ce298,he298,se298 
 
 Real*8 qO , ql , q2 ,MI , Rprime , Na , hout 
 
 Real*8 del,hcor,scor,eu,htotal,h298,stotal,s298,eul,T(100) ,gam 
 
 Real*8 Td,ccor,ctotal,c298,u,w0(100) 
 
 Byte lgas,gasnam(30) 
 c 
 
 c Initialize 
 c 
 
 do 500 1=1,100 
 
 e(i)=0.0 
 
 T(i)=0.0 
 
 g(i)=0.0 
 
 w(i)=0.0 
 
 wO(i)=0.0 
 
 xe(i)=0.0 
 500 wexe(i)=0.0 
 
 Na=6.02204531e23 
 
 Rprime =82. 056826 
 
 k=1.38066244e-16 
 
 h=6.62617636e-27 
 
 c=2.9979245812el0 
 
 R=l. 9871917 
 
 pi=3. 141592654 
 c 
 
 c conversational input of constants 
 c 
 
 open( unit=l, name -'dll: gas.dat* ,type='new' .dispose"' save' ) 
 
 write(5,130) 
 
 130 format(/,lx, 'Enter name of the input file') 
 read(5,131)(gasnam(i),i=5,30) 
 
 131 format (30A1) 
 
 type *, 'Output is in file gas.dat' 
 
 gasnam(30)=O 
 
 gasnam(l)='S' 
 
 gasnam(2)='Y* 
 
 gasnam(3)='0' 
 
 gasnam(4)=' : ' 
 
 open(unit=2,name=gasnam, type-' old' .dispose-'save' ) 
 
 read(2,131)(gasnam(i),i=l,20) 
 
 write(l,132)(gasnam(i),i=l,20) 
 
 132 format (lx,20Al,/) 
 
12 
 
 read(2,101)igas 
 101 format(lAl) 
 
 if(igas.eq.'M' .or.igas.eq. 'm' )go to 2 
 if(igas.eq.'D' .or.igas.eq. 'd' )go to 3 
 if (Igas.eq. 'L' .or.igas.eq. *1' )go to 4 
 if (igas.eq. 'N' .or.igas.eq. 'n')go to 5 
 type *,' INVALID GAS TYPE!' 
 stop 
 
 2 type * , ' monatomic gas * 
 iflag=7 
 
 go to 6 
 
 3 type *,' diatomic gas' 
 iflag=8 
 
 go to 6 
 
 4 type *,' linear polyatomic gas* 
 iflag=9 
 
 go to 6 
 
 5 type *,' non-linear polyatomic gas' 
 iflag=9 
 
 go to 6 
 
 6 read(2,*)HT 
 iHT=HT 
 
 ntemp=iHT/100 
 T(l)=298.15 
 
 do 43 i=l,ntemp 
 
 43 T(i+l)=100.*i 
 c 
 
 c Read tranisition temperatures 
 c 
 
 read(2,*)nTp 
 
 if(nTp.eq.0)go to 41 
 
 do 42 i-l,nTp 
 42 read(2,*)T(ntemp+l+i) 
 c 
 
 c Arrange the temperatures in ascending order 
 c 
 
 do 44 j=2,ntemp+nTp 
 
 do 44 i»2,ntemp+nTp 
 
 if(T(i).lt.T(i+l))go to 44 
 
 Ttemp=<r(i) 
 
 T(l)-T(i+1) 
 
 T(i+1)-Ttemp 
 
 44 continue 
 
 41 read(2,*)nlevel 
 
 do 50 i«l,nlevel 
 50 read(2,*)e(i),g(i) 
 
 If (igas.eq. 'M' .or. igas.eq. 'm' )go to 7 
 if (igas.eq. 'D' .or.igas.eq. 'd')go to 8 
 go to 9 
 c 
 
 c monatomic gas 
 c 
 
 read(2,*)MW 
 go to 20 
 
13 
 c 
 
 c diatomic gas 
 c 
 
 8 read(2,*)MWl 
 read(2,*)MW2 
 read(2,*)re 
 
 c 
 
 c calculate moment of inertia 
 
 c 
 
 MI =( (MW1*MW2 ) / (MW1-HW2 ) )*re*re 
 
 MW=MW14MW2 
 
 read(2,*)w(l) 
 
 read(2,*)wexe(l) 
 
 read(2,*)a 
 
 read(2,*)sig 
 
 nvib=4 
 
 go to 20 
 c 
 
 c polyatomic gas 
 c 
 
 9 read(2,*)MW 
 read(2,*)natom 
 nvib=3*natom-6 
 
 if (igas .eq. 'L' .or.igas.eq. '1' )nvib=3*natom-5 
 
 do 51 i=l,nvib 
 51 read(2,*)w(i) 
 
 read(2,*)MI 
 
 read(2,*)a 
 
 read(2,*)sig 
 
 iharm=0 
 c 
 
 20 write(5,300) 
 300 format(//,6x, , T , ,10x, , Cp , ,10x, , H-H298\llx, , S , ) 
 
 write(l,300) 
 
 write(l,302) 
 302 format(6x, 'K' ,7x»'cal/mol-K' ,6x, 'kcal/mol' ,5x, 'cal/mol-K' ,/) 
 c 
 
 c start calculations 
 c 
 
 ht298«O.0 
 
 hr298^).0 
 
 he298«O.0 
 
 hv298*).0 
 
 hc298-O.0 
 
 istart-1 
 17 do 55 i-i8tart,ntemp+nTp+l 
 
 if (igas .eq. 'M' .or.igas.eq. 'm' )go to 16 
 c 
 
 c rotational calulations 
 c 
 
 12 if(igas.eq. 'D* .or.igas.eq. 'd' )go to 13 
 
 if (igas .eq . 'L' .or .igas .eq. ' 1' )go to 13 
 c 
 c non-linear polyatomic rotational 
 
14 
 
 c 
 
 crot=1.5*R 
 
 hrot=T(i)*crot+hr298 
 
 srot=(R/2.)*(log(512.*pi**7*((k*l.el6)**3)/((h*l.e27)**6)) 
 &-3.*log(10.)+3.)+(R/2.)*(log(MI)+3.*log(T(i))-2.*log(sig)) 
 
 go to 14 
 c 
 
 c diatomic or linear polyatomic rotational 
 c 
 
 13 Be=((n*Na)/(8.*pi*pi*c*l.e-16))/MI 
 B0=$e-0.5*a 
 y=(((n*Na)*h/(k*8.*pi*pi*l.e-16))/(T(i)*Ml)) 
 
 &-((h*c)/(2.*k))*(a/T(i)) 
 
 crot=R*(l .+(y*y/45.)) 
 
 hrot=R*T(i)*(l.-y/3.-(y*y/45.))+hr298 
 
 lny=O.0 
 
 if(y.gt.O.O)lny=log(y) 
 
 srot=R*(l.-lny-log(sig)-(y*y/90.)) 
 c 
 
 c vibrational calculations 
 c 
 
 14 cvib=0.0 
 hvib=O.0 
 svib=O.0 
 ccor=O.0 
 hcor=0.0 
 scor=O.0 
 
 do 53 j=l,nvib 
 
 w0(j)=v(j)-2.*wexe(j) 
 
 u=((h*c)/k)*wO(j)/T(i) 
 
 eu=exp(u) 
 
 cvib=(R*u*u*eu/ ( (eu-1 . )*(eu-l . ) ) )+cvib 
 
 hvib=(R*T(i)*u/(eu-l . ) )+hvib 
 
 svib=(R*( (u/ (eu-1 . ) )-log(l .-exp(-u) ) ) )+svib 
 c 
 
 c anharmonicity corrections 
 c 
 
 if(nvil.eq.l)go to 15 
 
 if(iharm.ne.l)go to 53 
 
 15 xe(j)-wexe(j)/w(j) 
 del-0.0 
 
 if(a.ne.0.0)del«a/(Be-a/2.) 
 gam=Be/w(j) 
 
 eul "eu-1 . 
 
 x=xe(j)/(l.-2.*xe(j)) 
 
 ccor-(R/u)*((4.*x*u*u*u*eu*(2.*u*eu-2.*eu+u+2.)/(eul*eul*eul*eul)) 
 &+( del*u*u*u*eu*( eu+1 . ) / ( eul*eul*eul ) )+16 . *gam)+ccor 
 
 hcor-(R*T(i)/u)*(((2.*x)*u*u*(2.*u*eu-eu+l.)/(eul*eul*eul))+ 
 &( de l*u*u*eu/ ( eul*eul ) )+8 . *gam)+hcor 
 
 scor«**((4.*x*u*u*eu/(eul*eul*eul))+(del*u*eu/(eul*eul))+(del/eul) 
 &+(16.*gam/u))+scor 
 53 continue 
 
 hvib=hvib+hv298 
 
 hcor=hcor+hc298 
 
15 
 c 
 
 c Translational calculations 
 c 
 
 16 ctrans«2.5*R 
 
 htrans=ctrans*T(i)+ht298 
 
 strans=R*(2.5*log(T(i))+1.5*log(MW) 
 &+log(Rprime)+1.5*log(2.*pi*k)-3*log(h)-2.5*log(Na)+2.5) 
 c 
 
 c electronic calculations 
 c 
 
 celec=0.0 
 
 helec=O.0 
 
 selec=O.0 
 
 call Q(e,g,nlevel,T(i),qO,ql,q2) 
 
 if(q0.eq.O)go to 22 
 
 celec=R*((q2/qO)-(ql/qO)*(ql/qO)) 
 
 helec=**T(i)*ql/qO+he298 
 
 selec=R*(log(qO)+(ql/qO)) 
 c 
 
 c calculate total thermodynamic functions 
 c 
 
 22 ctotal=ctrans+celec+crot+cvib+ccor 
 
 htotal=htrans+hrot+hvib+helec+hcor 
 
 stotal=strans+srot+svib+selec+scor 
 c 
 
 c if T=298.15 then go print values 
 c 
 
 if(i.eq.l)go to 18 
 
 jflag=0 
 
 if(T(i).eq.200)jflag=l 
 
 write( 5, 122 )T(i),c trans, htrans.s trans 
 
 122 format(/,lx,F9.2,3(lx,fl2.4)) 
 vrite(5,123)celec,helec,selec 
 
 123 format(10x,3(lx,fl2.4)) 
 
 if (iga8.eq.'M' .or.igas.eq. 'm')go to 21 
 write(5,123)crot,hrot,srot 
 write(5,123)cvib,hvib,svib 
 write(5,123)ccor,hcor,scor 
 21 vrite(5,123)ctotal,htotal,stotal 
 hout-htotal/1000 . 
 
 write(l,301)T(i),ctotal,hout,stotal 
 301 format(lx,f8.2,3(3x,fll.3)) 
 if( jflag.eq.0)go to 55 
 T(i)-298.15 
 ccor«cc298 
 hcor«hc298 
 scor-8c298 
 crot-cr298 
 hrot-0.0 
 srot-sr298 
 ctrans«ct298 
 htrans«=0.0 
 8trans-st298 
 cvib«cv298 
 
16 
 
 hvib=O.0 
 svib=sv298 
 celec=ce298 
 helec=O.0 
 selec=se298 
 hcor=0.0 
 go to 22 
 55 continue 
 go to 19 
 
 18 hc2~8=>-htrans 
 hr298=-hroc 
 he298~-*-hel^ 
 hv298=-hvib 
 hc298=-hcor 
 h298=-htotal 
 cr298=crot 
 ct298=ctrans 
 cv298=cvib 
 cc298=ccor 
 ce298^celec 
 sr298=srot 
 st298=strans 
 sv298=svib 
 sc298=scor 
 se298=selec 
 c298=ctotal 
 s298=stotal 
 write(5,124)ht298 
 
 124 format(5x, '0' ,13x, '0' ,4x,f 12.4,10x, *0' ,5x, "Trans lational' ) 
 write(5,125)he298 
 
 125 format(19x, '0' ,4x,f 12.4,10x, '0' ,5x, 'Electronic' ) 
 if (igas.eq.'M' .or.igas.eq. 'm' )go to 25 
 write(5,200)hr298 
 
 200 format(19x, '0' ,4x,f 12.4,10x, '0' ,5x, 'Rotational' ) 
 write(5,201)hv298 
 
 201 format(19x, '0' ,4x,f 12.4,10x, '0' ,5x, 'Vibrational' ) 
 write(5,202)hc298 
 
 202 format(19x, '0' ,4x,f 12.4,10x, '0' ,5x, 'Anharmonic' ) 
 25 write(5,203)h298 
 
 203 format(19x, , 0•,4x,fl2.4,10x,•0•,5x,•Total , ) 
 hout«=h298/1000. 
 
 write(l,204)hout 
 
 204 format(8x,'0',13x,'0',3x,fll.3,13x,'0') 
 is tart -2 
 
 go to 17 
 
 19 continue 
 close (unit-1) 
 end 
 
 c 
 
 c subroutine to calculate partition functions 
 
 c 
 
 subroutine Q(e,g,nlevel,T,q0,ql,q2) 
 
 Real*8 e(nlevel) ,g(nlevel) ,T,q0,ql,q2,kT,ekT,ge 
 
 kT=1.438785935/T 
 
17 
 qO=-0.0 
 ql=0.0 
 q2=O.0 
 
 do 1 i=l,nlevel 
 ekT=e(i)*kT 
 ge=exp(-ekT)*g(i) 
 qO=qO+ge 
 ql=ql+ekT*ge 
 q2=q2+ekT*ekT*ge 
 return 
 end 
 
18 
 
 PROGRAM OUTPUT 
 
 Zrl4(g) 
 
 
 
 
 T 
 
 Cp 
 
 H-H298 
 
 S 
 
 K 
 
 cal/mol-K 
 
 kcal/mol 
 
 cal/mol-K 
 
 
 
 
 
 -6.330 
 
 
 
 100.00 
 
 21.258 
 
 -4.743 
 
 80.982 
 
 200.00 
 
 24.284 
 
 -2.430 
 
 96.897 
 
 298.15 
 
 25.090 
 
 0.000 
 
 106.772 
 
 300.00 
 
 25.098 
 
 0.046 
 
 106.927 
 
 400.00 
 
 25.410 
 
 2.574 
 
 114.196 
 
 500.00 
 
 25.559 
 
 5.123 
 
 119.884 
 
 600.00 
 
 25.642 
 
 7.684 
 
 124.552 
 
 700.00 
 
 25.692 
 
 10.251 
 
 128.509 
 
 800.00 
 
 25.725 
 
 12.822 
 
 131.942 
 
 900.00 
 
 25.748 
 
 15.395 
 
 134.973 
 
 1000.00 
 
 25.764 
 
 17.971 
 
 137.687 
 
 1100.00 
 
 25.776 
 
 20.548 
 
 140.143 
 
 1200.00 
 
 25.785 
 
 23.126 
 
 142.386 
 
 1300.00 
 
 25.792 
 
 25.705 
 
 144.450 
 
 1400.00 
 
 25.798 
 
 28.284 
 
 146.362 
 
 1500.00 
 
 25.802 
 
 30.864 
 
 148.142 
 
 1600.00 
 
 25.806 
 
 33.445 
 
 149.807 
 
 1700.00 
 
 25.809 
 
 36.026 
 
 151.372 
 
 1800.00 
 
 25.812 
 
 38.607 
 
 152.847 
 
 1900.00 
 
 25.814 
 
 41.188 
 
 154.243 
 
 2000.00 
 
 25.816 
 
 43.769 
 
 155.567 
 
19 
 
 REFERENCES 
 
 1. Dow Chemical Co. Thermal Research Laboratory. JANAF Thermochemical 
 
 Tables, 2d ed., NSRDS-NBS 37, S/N 03030872, U.S. Government Printing 
 Office, Washington, D.C., 1971, 1141 pp. 
 
 2. International Union of Pure and Applied Chemistry, Division of Physical 
 
 Chemistry, Commission of Physicochemical Symbols, Terminology, and 
 Units. Manual of Symbols and Terminology for Physicochemical Quantities 
 and Units. 1979, p. 35. 
 
 3. King, E. G., A. D. Mah, and L. B. Pankratz. Thermodynamic Properties of 
 
 Copper and Its Inorganic Compounds, INCRA Monograph Series II (sponsored 
 by The International Copper Research Association and the U.S. Bureau of 
 Mines), New York, 1973, pp. 5-8. 
 
 4. Mayer, J. E., and M. G. Mayer. Statistical Mechanics. John Wiley and 
 
 Sons, Inc., London, 1940, 495 pp. 
 
 5. McBride, B. J., and S. Gordon. Fortran IV Program for Calculation of 
 
 Thermodynamic Data. NASA TND-4097, 1967, 129 pp. 
 
 trU.S GOVERNMENT PRINTING OFFICE: 1981-505-002/131 int.-bu.of mines,pgh.,pa. 25902 
 
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