6250
Ind. Eng. Chem. Res. 2003, 42, 6250-6251
RESEARCH NOTES Correlations for the Enthalpy of Vaporization of Pure Substances Peter E. Liley* 3608 Mulberry Drive, Lafayette, Indiana 47905-3937
Two generalized correlations and a simple two-constant equation are evaluated for 25 pure refrigerant fluids. If two experimental data points are available, the simple equation was found to be preferable. Pitzer et al.1 showed that the enthalpy of vaporization, hfg, could be related to two entropy functions, ∆so + ω∆sl, where ω is a parameter called the acentric factor. The entropy functions were tabulated as a function of reduced temperature, Tr ) T/Tc, where Tc is the critical temperature. For the range of reduced temperature 0.6 e Tr e 1.0, Poling et al.2 state that a close approximation to the tabulated Pitzer functions is represented by
hfg/(RTc) ) 7.08(1 - Tr)0.354 + 10.95(1 - Tr)0.456 (1) Another tabulation of the saturated liquid and vapor enthalpies as a function of the reduced temperature from which hfg could be calculated was given by Sonntag and van Wylen.3 Table 1 gives hfg/(RTc) as a function of Tr from both these sources, where hfg ) A + ωB. Several earlier correlations of the enthalpy of vaporization have used the simple form
hfg ) R(1 - Tr)n
(2)
In this work, the ability of both functionals involving and independent of the acentric factor to represent hfg as a function of Tr is examined. Much work on refrigerants has been done at the National Institute of Standards and Technology in Boulder, CO, resulting in tables of thermodynamic properties by ASHRAE and others. In Table 2, values of the acentric factor from three sources4-6 are given. Xiang7 only lists the factor for the many compounds of the R10 series, so the five values applicable here are not given. In Table 2, the reduced temperatures at the melting and normal data points are given as Trm and Trb, respectively, along with the critical temperature, Tc, and the factor RTc. The average deviations, (hfg,calc - hfg,ref)/hfg,ref, usually for the range 0.5 e Tr e 0.9, from the Pitzer and the Sonntag and van Wylen formulas are listed. Values of ω used in this work were those tabulated as ω6. Values of R and n in eq 2, along with the average individual deviation, are also listed. The overall average deviation using the Sonntag and van Wylen parameters is 2.03%; using the Pitzer parameters, 1.43%; and using eq 2, 0.47%. The * Phone: (765) 447-5842. E-mail:
[email protected].
Table 1. Coefficients in the Equation hfg ) A + ωB Tr
Aa
Ba
Ab
Bc
0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
5.9088 5.7296 5.5395 5.8794 5.1187 4.8326 4.6231 4.3341 4.0050 3.6171 3.1335 2.4517
8.6746 8.3372 7.9826 7.6089 7.2103 6.7844 6.3238 5.8194 5.2563 4.6101 3.8319 2.7935
5.7620 5.6093 5.4429 5.2755 5.0870 4.8782 4.6423 4.3714 4.0527 3.6664 3.1700 2.4596
10.1186 9.5398 8.8518 8.1734 7.4878 6.8109 6.1167 5.4306 4.7351 4.0176 3.2457 2.3293
a
Calculated from eq 1.2
b
Calculated from Table A14.1, p 772.3
overall average R value is 5.832 32, and the average n value is 0.3678, close to the average, 0.377 ( 0.014, given by Srinivasan.8 If two values of the enthalpy of vaporization are known, the surprising fact is that eq 2 results in more accurate fitting than the acentric factor formulations. An independent fitting of eq 2 to 39 fluids has appeared,8 and the overall accuracy is discussed, unfortunately without any listing of average errors or ranges of fit for the individual substances. Acknowledgment The author thanks Dr. A. H. Harvey of NIST for supplying him with an extensive listing of acentric factors compiled by Dr. E. W. Lemmon of the same organization. Literature Cited (1) Pitzer, K. S.; Lippman, D. Z.; Curl, R. F.; Huggins, C. M.; Petersen, D. E.; The volumetric and thermodynamic properties of fluids. II. Compressibility factor, vapor pressure, and entropy of vaporization. J. Am. Chem. Soc. 1955, 77, 3433. (2) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001. (3) Sonntag, R. E.; van Wylen, G. J. Introduction to Thermodynamics, Classical and Statistical, 3rd ed.; John Wiley and Sons: New York, 1991.
10.1021/ie030605e CCC: $25.00 © 2003 American Chemical Society Published on Web 11/01/2003
Ind. Eng. Chem. Res., Vol. 42, No. 24, 2003 6251 Table 2. Enthalpy of Vaporization of Pure Refrigerant Substances ∆ (%) formula
R no.a
Trm
Trb
Tc (K)
RTc (kJ/kg)
ref 3
ref 2
CC14 CCl3F CCl2F2 CClF3 CF4 CHCl3 CHCl2F CHClF2 CHF3 CH4 C2Cl3F3 C2Cl2F4 C2ClF5 C2H6 C3H8 C4F8 C4H10 H2 NH3 H2O N2 O2 CO2 C2H4 C3H8
10 11 12 13 14 20 21 22 23 50 113 114 115 170 290 C318 600 702 717 718 728 732 744 1150 1270
0.4500 0.3863 0.2991 0.3052 0.3936 0.3907 0.3059 0.3133 0.3946 0.4768 0.4888 0.4277 0.4919 0.2958 0.2311 0.5998 0.2782 0.4204 0.5056 0.4221 0.5008 0.3517 0.7120 0.3684 0.2410
0.6287 0.6291 0.6322 0.6350 0.6378 0.6229 0.6246 0.6291 0.6390 0.5858 0.6582 0.6611 0.6448 0.6043 0.6249 0.6879 0.6405 0.6145 0.6211 0.5766 0.6134 0.5833 0.6401 0.6002 0.6208
556.4 471.2 385.0 301.9 337.5 536.6 451.5 369.3 299.0 190.6 487.3 419.8 353.1 305.4 369.8 388.4 425.1 33.2 406.8 647.1 126.1 154.6 304.2 282.4 364.8
29.1278 28.5148 26.4681 24.0258 21.4933 37.3703 36.4732 35.5180 35.5062 98.5799 21.6192 20.3730 19.0047 84.4249 69.8331 16.1426 60.8132 136.925 198.598 298.646 37.4234 40.3125 57.4702 83.7701 72.3026
5.79 1.13 1.97 1.68 2.23 5.56 1.51 1.21 1.57 1.01 3.12 2.38 1.64 0.46 1.09 4.85 1.76 8.42 1.75 3.28 0.63 1.01 2.57 0.51 1.00
5.19 1.59 1.77 1.61 0.76 2.24 1.13 1.21 1.19 0.74 2.33 2.22 0.94 0.59 0.72 3.25 1.00 4.77 2.38 2.10 0.86 1.15 1.55 0.59 1.03
this work
R
n
ref 4
0.73 0.17 0.13 0.32 0.31 1.55 0.30 0.17 0.62 0.93 0.41 0.28 0.17 0.63 0.20 0.29 0.27
5.616 52 5.574 10 5.479 46 5.375 45 5.255 74 5.845 26 5.847 55 5.840 91 5.860 89 6.512 62 5.381 96 5.320 84 5.324 67 6.547 52 6.412 45 5.196 12 6.333 45
0.3568 0.3794 0.3695 0.3692 0.3512 0.3340 0.3818 0.3875 0.3779 0.3239 0.3809 0.3783 0.3795 0.3747 0.3669 0.3783 0.3695
0.66 19.2 0.92 1.33 0.17 0.47 0.33
5.615 00 8.190 88 5.638 61 5.647 73 6.357 00 6.513 50 6.439 21
0.3872 0.3496 0.3563 0.3371 0.4009 0.3665 0.3704
0.193 0.184 0.180 0.180 0.186 0.213 0.207 0.219 0.267 0.011 0.255 0.252 0.251 0.099 0.152 0.356 0.198 -0.22 0.252 0.345 0.040 0.022 0.228 0.085 0.142
ω ref 5 0.194 0.176 0.180 0.216 0.202 0.215 0.008 0.098 0.152 0.198 0.250 0.344 0.040 0.021 0.225 0.085 0.148
ref 6 0.1888 0.1795 0.1723 0.1785 0.2061 0.2208 0.2628 0.0114 0.2525 0.2523 0.252 0.0993 0.1524 0.3553 0.2 -0.21 0.2550 0.3443 0.0372 0.0222 0.2239 0.0866 0.1408
a The R no. is the ASHRAE standard designation of refrigerants (ANSI/ASHRAE standard 34-1992). For a list of corresponding CAS numbers, see, e.g., McLinden, M. O.; Klein, S. A.; Lemmon, E. W.; Peskin, A. P. NIST Standard Reference Database 23; NIST: Gaithersburg, MD, 1998.
(4) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill: New York, 1999. (5) Rowley, R. L. Statistical Mechanics for Thermophysical Property Calculation; PTR Prentice Hall: Englewood Cliffs, NJ, 1994. (6) Harvey, A. H. National Institute of Standards and Technology, Boulder, CO. Unpublished results, 2003. (7) Xiang, H. W. Vapor pressures, critical parameters, boiling points, and triple points of halomethane molecular substances. J. Phys. Chem. Ref. Data 2002, 30, 1161.
(8) Srinivasan, K. A generalised correlation for heat of vaporisation of cryogenic liquids and refrigerants. Instn. Eng. Aust. Conf. 1988, 88, 79.
Received for review July 17, 2003 Revised manuscript received October 8, 2003 Accepted October 13, 2003 IE030605E
