THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLEGE OF ENGINEERING THERMODYNAMIC PROERTIES OF TEE "FREON't REFRIGERANJTS I. "FREON-12" DICHLORODIFTOROMETHANE B. J. an, Jr J. J. Martin R. C. MHarness Septiember, 1955 IP-120

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ACKNOWLEDGEMENT We wish to express our appreciation to the authors, the DuPont Corporation, and the Engineering Research Institute of The University of Michigan for permission to give this paper limited distribution through the Industry Program of the College of Engineering.

THERMODYNAMIC PROPERTIES OF THE "FREON"* REFRIGERANTS I. "FREON-12" DICHLORODIFLUOROMETHANE B.J. Eiseman, Jr., J.J. Martin, R.C. McHarnessa I. INTRODUCTION Twenty-four years have passed since the familiar tables of the "Thermodynamic Properties of'Freon-12' Dichlorodifluoromethane were published (8).** These tables have served the needs of the refrigeration industry well. In 1942 they were supplemented by a set of low temperature tables and later by a table of properties of the saturated liquid and vapor at high temperatures. Since different sets of equations were used in developing these later data, there are certain inconsistencies at their junctions with the original tables. Furthermore, some of the data at elevated pressures were based on estimations rather than on experimental data. The primary objective of the present work has been to provide a new set of tables and charts which will meet all possible needs of the refrigeration and other industries, particularly as regards range, accuracy and consistency. We believe this has been accomplished.'The steps taken to fulfill our objective were as follows: First it was necessary to review the extent and accuracy of the existing data available for "Freon-12" dichlorodifluoromethahe and to make the additional measurements required. The next step was to develop a new set of equations which would fit the expanded data with the desired accuracy over the entire range. The use of this single set of equations assured the over-all consistency of the final tables and charts. In most cases it was necessary to use more complicated equations than those used for the original tables in order to obtain the desired accuracy. This was particularly true of the equation of state, The final step was to carry out the calculations and to prepare the finished tables and charts. This paper presents the new data and equations obtained in this work. It compares the new tables with the old and describes briefly the form in which the new tables and charts are published. *"Freon" is the registered trademark of E.I. du Pont de Nemours and Co., Incorporated, for their fluorinated hydrocarbon refrigerants. **Numbers in brackets refer to the bibliography at the end of the paper. a"Kinetic" Laboratory, E.I. du Pont de Nemours and Co., Incorporated. b Engineering Research Institute, University of Michigan. 1

The work reported here represents a co-operative effort of the Engineering Research Institute of the University of Michigan and the du Pont Company's Jackson and "Kinetic" Laboratories. Data from the Cryogenic Laboratory of the Pennsylvania State University were used as an ind.ependent check on the cycle calculations. II. CALCULATION OF THE TABLES A. Method and Criteria 1. The'Cycle Calculation The method used to calculate the tables of thermodynamic properties involved the use of the following four fundamental equations: Vapor Pressure Psat = fl(T) (1) Equation of State p = f2(vT) (2) Density of the Saturated Liquid. f = f3(T) (3) Heat Capacity of the Vapor c = f4(T) (4) Exact thermodynamic relations were applied to the above empirical equations to calculate the tabular quantities. The relations in question are listed below. _Psat hf = (vg - Vf) T dT T2 rH = f cvdT +A (pv) (6) T1 V2 6- dV AT = f v (T + T( ( dv (7) T2 c ASv = T dT (8) = dv (9) A fifth empirical equation used to represent experimental data was as follows: Heat Capacity of the Liquid Cf = f5(a) (10) 2

This equation was used to check independently the over-all accuracy of the calculations made with equations (1) to (7). In these calculations the pressure-volume-temperature properties of the vapor and the saturated liquid are fully determined by equations (1), (2) and (3). Latent heats of vaporization are calculated from these same equations by means of the exact Clausius-Clapeyron equation (5). The entropy of vaporization is obtained by dividing the latent heat by the absolute temperature. The other heat quantities are calculated through use of the vapor heat capacity equation (4) either alone or in combination with equation (2). The above procedures are the same as those used by -Buffingtton'and. Gilkey [8] in calculating the earlier tables. 2. Properties Required in the Basic Equations The equations used in calculating the tables must meet four requirements. First, they must fit the experimental data accurately; that is, to the accuracy of the data themselves. Second, they must be mathematically "manageable." The calculations using them must not be unduly difficult or time-consuming. Third, the secondary or derived quantities which can be calculated from the primary data must be correct. It is possible to use an equation to represent the experimental data accurately, but which, at the same time gives unrealistic derivatives. In this connection, the fourth requirement arises. It is that the entire range of each property should be covered by a single equation. Otherwise, inconsistencies in the derived quantities will occur at the junctures of the limited-range equations. The foregoing requirements are met by the basic equations described in the next section. B. Basic Data and Equations 1. Scope and Accuracy The temperature range of the observed data is from -150 to +410~F, the pressure range from 0.16 to 1980 psia. The ranges for the individual properties are shown in Tables I-V. These tables contain the experimental data which were used in the new calculations. The data and equations are discussed in the sections which follow. The accuracy of the primary measurements varies, but is typically 1% or better. The smoothing and averaging accomplished by fitting equations to the data tends to improve the accuracy. Each equation fits the corresponding data over their entire range. This has resulted in excellent reliability of both the primary and secondary quantities calculated from the equations. While this improved reliability is the case over a range much broader than that covered in refrigeration work, it should be pointed out that the data in the critical region are less accurate than those below this point. This is due to the rapid change in the properties of any compound near the critical point. The "Freon-12" dichlorodifluoromethane used in making the experimental measurements was of the highest quality obtainable in our laboratory. It had a purity of not less than 99.95%. 5

2. Vapor Pressure Vapor pressures were measured by several methods [1,4]. All involved the use of an isoteniscope. There are 10 points from 001623 to 573.3 psia (96; of the critical pressure). The data are given in Table I. The equation below, prepared at the University of Michigan, fits these data with an average deviation of 0.22%,* log1i Psat = 39-.8581727 - 3436632228 T (11) - 12,47152228 loglo T + 0.00473044244T The constants of the various equations contain as many as 10 significant gures Fewer signifiant fiures could have been used without loss of accuracy However, it has been considered best to round off only in the final results in the tables and to carry all significant figures elsewhere for the sake of maximum consistency. Table I Vapor Pressure of "Freon-12""** Comparison of the Equation with Experimental Data Temper- 0bserved Calculated Deviation from Source ature Pressure Pressure Observed see below -.OF psia (Eq. 11) psia % -148.97 0.1622 0.16219 -0.01 A -108.74 1.0200 1.0202 +0.02 A 1.0204 1.0202 -0.02 B -58.00 5.688 5.678 -0.18 C -4.00 21.89 21.89 0.00 C +32.00 44.74 44.76 +0.04 A 86.00 107.9 108.04 +0.13 C 110.08 151.8 151.27 -0.35 B 163.18 290.4 290.08 -0.11 B 176.00 331.3 334.26 +0.89 C 228.51 573.1 568.95 -0.72 A:233.6*** 596,9*** *After the vapor pressure equation (Eq. 11) had been developed, additional vapor pressure data were received in a private communication from Professor A. Michels of the University of Amsterdam. The maximum deviation of the vapor pressure equation from these data was 0.36* and the average deviation 0.30% for five points ranging between 95 and 235 psia. This excellent agreement confirms the accuracy of the vapor pressure equation. ** "Freon-12" Dichlorodifluoromethane. ***Critical point. A. Engineering Research Institute, University of Michigan. B. Jackson Laboratory and "Kinetic" Laboratory, E.I. du Pont de Nemours and Company, Incorporated. C. Gilkey, Gerard and Bixler [10]. These points were calculated from the vapor pressure equation of reference [10] and used for comparison purposes. 4

35 Pressure-Volume-Temperature Data - Equation of State The experimental pressure-volume-temperature data are in the form of isometrics. The pressures corresponding to a series of temperatures were determined for various loadings of a constant volume system. The apparatus and procedures are described elsewhere [1,9]. Thirty isometrics were used ranging from 1.804 to 50.53 lb/cu ft in density (0.052 to 1.515 times the critical density, dc). The data are given in Table II. The Martin-Hou equation of state [11] has been used to represent the data. It is satisfactory to 1.5 times the critical density. The derivation of this equation and the methods used to fit it to experimental data are described elsewhere [11]. This equation of state for "Freon-12" dichlorodifluoromethane, fitted by the University of Michigan, is as follows: 0.088734T 3.409727134 - 1.59434848 x 10- T + 56.7627671 ekTr (v - b) (v - b) +0.06023944654 - 1.879618431 x 105 T + 1.311399084 ekTr (v - b)3 5.48737007 x 10-4 3.46883400 x 10'9T - 2.54390678 x 105 ekTr (v - b)4 (v - b)5 where k = -5.475; b = 0.0065093886; and Tr = T/69.3.3 Values calculated by this equation show an average deviation of 0.95% in pressure from all 114 points (on 23 isometrics) measured below the critical density.* Values from the equation have an average deviation of 2.2% from the 50 points (on seven isometrics) above the critical density. 4. Density of the Saturated Liquid The density of the saturated liquid was determined by one of two methods [5,6]. The data are given in Table III. Calibrated floats (Faraday's method) were used for the two lowest temperatures, the three highest temperatures and the +1.940F measurement. The other points were measured with a dilatometer and reported previously [6]. The following equation fits the 18 experimental points ranging from -187.44~F to- - 224.060~ with. aran verage devia tio of 0.15%. *After the equation of state (Eq. 12) had been developed, new pressure-volumetemperature data were received in a private communication from Professor A. Michels of the University of Amsterdam. The maximum deviation of the equation of state from these measurements was 0.6% and its average deviation 0.2% from 38 points ranging in pressure from 104 to 327 psia and in temperature from 122 to 233~F. This excellent agreement confirms the accuracy of the equation of state. 5

TABLE II "FREON- 12"* PRESSURE-VOLUME-TEMPERATURE PROPERTIES COMPARISON OF EQUATION OF STATE WITH EXPERIMENTAL DATA -^:^~ ^Caiculat'ed Deviation Vapor Temper- Observed Cal Source Pressure from Density ature Pressure se(See End of (Eq. 12) Observed lb/cu ft OF psia psia Table).. i,.,.. I. -................ _61.63** 214.09 737 A 224.46 944 234.14 1109 250.36 1424 261.46 1630 271.90 1828 279.05 1959 52.62 239.29 762 757.81 -0.6 A 254.30 948 943.21 -5 271.56 1154 1170.25 +1.4 286.38 1353 1375.64 +1-7 302.41 1551 1607.36 +3.6 317.55 1748 1834.32 +4.9 331.99 1935 2057.27 +6.3 50.53 236.52 680 672.12 -1.2 A 256.64 912 889.76 -2.4 274.28 1123 1093.47 -2.6 294.30 1357 1338.48 -1.4 312.60 1561 1570.13 +0.6 329.99 1767 1799.13 +1.8 344.30 1942 1992.51 +2.6 49.47 233.82 645 629.77 -2.4 A 244. 02 761 730.55 -4.0 266.22 1005 963.95 -4.1 283.64 1199 1158.03 -3.4 301.69 1410 1367.84 -3.0 319.93 1627 1587.68 -2.4 339.60 1861 1832.35 -1.5 45.17 259.57 847 822.20 -2.9 A 279.93 1035 1003.67 -3.0 301.14 1230 1199.42 -2.5 320.07 1425 1379.04 -3.2 340.47 1636 1577.05 -3.6 358 70 1798 1757.34 -2.3 376*39 1980 1934.88 -2 3 *Freon-12'" Dichlorod.ifluoromethane. ** The data at 61.63 lb/cu ft (1.8 times the critical density) lie beyond the range of the equation of state (Eq. 12). 6

TABLE II (cont.) Vapor Temper- Observed alculate Deviation Source. Pressure from Density ature Pressure 1) Osere (See End of (Eq. 12) Observed lb/cu ft OF psia psia. Table) 44.71 228.16 572 556.90 -2.6 A 254.64 789 775.57 -1.7 277.70 1000 975096 -2.4 299.16 1200 1169.34 -2.6 320.45 1400 1366.71 -2.4 342.54 1612 1576.41 -2.2 364~48 1828 1788.85 -2.1 43.76 225,41 546 535531 -2.0 A 250.61 745 735.72 -1,2 273.06 938 922.42 -1o6 296.47 1146 1123089 -1.9 318.58 1341 1319.50 -1.6 339.32 1535 1506.93 -1,8 361.76 1746 1713035 -1.9 381.24 1930 1895.13 -1 8 39.43 255.18 746:749.73 +0.5 A 281.91 947 942.38 -0.5 307.45 1136 1129.48 -0.6 333.39 1331 1321.99 -0.7 359.06 1532 1514.50 -1.1 385.95 1741 1717.89 -1.3 408.54 1918 1889.89 -1.5 34 72 238.38 614 626.24 +2.0 A 272.94 830 838.27 +1.0 306.60 1042 1044.67 +0.3 336.75 1226 1229.49 +0.3 360.47 1371 1374.85 +0.3 34.64 247.27 684 680.58 -0.5 B 307.43 1027 1048.47 +2.1 348.11 1284 1296.99 +1.0 375~36 1453 1463.39 +0.7 386.77 1522 1533.05 +0.7 34.38 235.19 600 606.56 +1.0 A 239.38 638 632.00 -0.9 270.70 810 821.95 +1.5 310.77 1059 1064.49 +0.5 337.99 1226 1230.23 +0.3 7

TABLE II (cont.) C~ut3a-t e d Deviation Vapor Temper- Observed Pressure frm Source Pressure from Density ature Pressure (q Oervd (See End of lb/cu ft OF psia (Eq. 12) Observed lb/cu ft OF psia Table) 32.46 210.39 467 463.81 -0.7 A 213.03 480 479.01 -0.2 217.05 500 502.11 +0.4 237.85 608 621.10 +2.2 275.10 823 832016 +1.1 310.27 1023 1029.56 +0.6 346.45 1227 1231.20 +0.3 387.40 1451 1458.12 +0.5 32.41 237-30 612 617.93 +1.0 A 250.20 685 691,17 +0.9 278.50 841 850.85 +1.2 322.20 1086 1095.23 +0.8 359.00 1289 1299.46 +0.8 392.40 1477 1483092 +0.5 31.73 235.70 817 608.49 -1.4 A 261.80 750 752.84 +0.5 276.40 829 832.97 +0.5 297 20 942 946.96 +0.5 313.00 1027 1032.29 +0.5 335.00 1147 1151.20 +0.4 359.00 1281 280.31 0 20.27 250.10 630 626 57 -0 5 A 277.50 720 711059 -1,2 298.10 781 774. 1 -0.9 315.90 ^833 827.46 -0.7 334.40 885 882 18 -0.3 14.06 217.21 470 476.37 +1.4 A 233.17 -512 508.26 -0.7 291.27 613 619.92 +1.1 319.88 681 672.93 -1.2 345.70 716 719.96 +0.6 11.94 203.76 416 421.56 +1.3 B 244.39 477 487.18 +2.1 285.75 535 551.24 +3.0 323.83 600 612.90 +2.1 368.59 657 674.12 +2.6 410.13 715 733.96 +2.7 10.75 222.73 424 428.26 +1.0 A 285.92 511 514.72 +0.7 354.42 602 604,08 +0.3 383.78 640 641.47 +0.2.... ~ ~ ~ ~

TABLE II (cont,)................ Calculated Deviation. Vapor Temper- Observed Calculated Deviation Source Density ature Pressure Pressure from (See End of lb/cu.ft.OF sia (Eq. 12) Observed Table) lb/cu pft a psia 6.537 164.52 264.1 263.76 -0.1 A 168.18 266.1 266.71 +0.2 199.44 298.2 291021 -2.3 236.95 312.4 319.64 +2.3 276.05 344.7 348 42 +1.1 5.293 149.2 219,8 218.29 -0.7 C 175.3 236.7 234.42 -1.0 200.1 251.2 249036 +0.7 220.3 262.8 261.29 +0.6 240.1 273.9 272.81 -0.4 5.187 140o44 211.6 209.78 -0.9 B 168.43 227.3 226.81 -0.2 195.30 343.2 242.68 -0O.3 233.37 256.5 258.87 -0.9 248.19 27303 272.93 -0.1 275.17 288.9 287097 -0.3 307.12 304 305053 +0.5 4.756 153.0 204,8 204.08 -0.3 C 154.9 205.7 205.12 -0.3 181.9 220.2 219.67 -0.2 210.0 2352 234.44 -0.3 229.1 245.3 244.31 -0.4 4.528 136.0 188.5 187,81 -0.4 C 165.4 203.7 203 01 -0.3 180,1 210.5 210.45 0.0 195.1 218.4 217.94 -0.2 218.3 229.5 229.35 -0.1 240.6 240.6 240.16 -0.2 259.0 249.8 248.97 -0.3 3.770 131.0 164,8 161.15 -2.2 C 212.0 197.6 194.21 -1.7 3.337 129.2 149.2 145.56 -2.4 C 212.0 177.7 174.89 -1.6 3.170 111.16 132,8 133.33 +0.4 A 1500o6 145.8 146.73 +0.6 203.79 162.8 164.57 +1.1 257.72 180.3 181.93 +0.9 304.34 195.3 196.66 +0.7 9

TABLE II (cont.) Calculated Deviation Vapor Temper- Observed Cressure Devi Source Pressure from Density ature Pressure ( 1) Oer (See End of ft 0F psia (Eq. 12) Observed lb/cu ft OF psia psia Table) 3.000 98-55 122.5 123034 +0.7 A 112.82 127.2 128 06 +0.7 162.36 142.0 143597 +1.4 213 80 158.1 159.88 +1.1 256 28 16909 172.72 +1.7 307.22 185.4 187.86 +1.3 2.891 106.75 121 8 122.32 +0.4 A 117.99 124,9 125086 +0.8 156 58 136.4 137-72 +1 0 198.50 148,5 150.24 +1.2 275050 17005 172.56 +1.2 2.821 127.4 129.2 126. 17 -2.4 C 210.2 15356 150037 -2.1 2.361 127 4 110.3 108.37 -1.7 210.2 130.2 128.16 -1.6 1.804 86.0 79.5 77.79 -2.3 C 93.2 80.9 79.13 -2.2 129.2 87 5 85 72 -2.0 210.2 102.2 100.08 -2.1 A. Engineering Research Institute, University of Michigan. B. Jackson Laboratory and "Kinetic" Laboratory, E.I. du Pont de Nemours and Company, Inc. C. Buffington and Gilkey [9] All their data are included in the above table. df = 34.84 + 0.0269600 (693.3 - T) + 0.834921 (693.3 - T)1/2 (13) + 6.02683 (693.3 - T)1/3 - 6.55549 x 10-6 (693.3 - T)2 Equation (13) was fitted at the University of Michigan. 5. Heat Capacity of the Vapor The heat capacity of gaseous "Freon-12" dichlorodifluoromethane at zero pressure was calculated by J. F. Masi [12] from spectroscopic data, applying an anharmonicity correction based on his experimentally determined heat capacities. The results obtained in this way are reported as accurate to better than 0o15%. Masi's values for c~ have been converted to the corresponding values of cV by subtracting 0.01642 Btu/(lb)(~F), the value of the gas constant, R. The empirical equation below,; prepared at the University of Michigan, fits Masi's converted values from -1500F to +7000~F with an average deviation of 0.06%, as shown in Table IV. 10

TABLE III DENSITY OF LIQUID "FREON-12"* COMPARISON OF THE EQUATION WITH EXPERIMENTAL DATA Calculated Deviation Observed Temp. Obsered Density from op Density (Eqo 13) Observed ~ lb/cu ft lb/cu ft O -187.44 108026 lo7332a -o086 -100.68 100.40 100.:3211" -0.19 - 36.04 9424 94.276 +0.04 - 19,12 92053 92 609 +0,09 - 11o02 91.70 91.793 +0.10 - 0.04 90.59 90,662 +0.08 + 1.94 90.45 90.458 +0.01 + 14090 88.99 89.082 +0.10 + 32.00 87.06 87.205 +0.17 + 56.84 84,41 84 324 -0.10 + 78.08 81.66 81.694 +0.04 + 95.18 79.44 79-446 +0.01 + 95.36 79.42 79.423,0 00 +116.42 76.54 760442 -0.13 +133.70 73088 73.777 -0.14 +195 98 61.09 61.162 +0.12 +210.02 56.81 56.805 -0.01 +224.06 50.82 50.452 -0.72 +233.6 34.84** 34.84 +0.'00 *TFreon-12" Dichlorodifluoromethane. * Critical density determined by extrapolating the rectilinear diameter to the critical temperature of 233.60F. Source: Jackson Laboratory and "Kinetic" Laboratory, E.Io du Pont de Nemours and Company, Incorporated. TABLE IV "FREON-12"* VAPOR HEAT CAPACITY COMPARISON OF EQUATION WITH MASI'S DATA [12] 0 Calculated Deviation Temp. c Masi Btu/(lb)(~F) co (Eq. 14) from Masi....______' Btu/(lb)(OF) % -150.0 0o0899 0.08997 +0.08 - 99.7 0 0997 0 09971 +0.01 + 32.0 0.1213 0.12129 -0.01 + 80.3 0.1279 0.12793 +0.02 +20. 3 0,1476 0.14757 -0.02 +440.3 0.1611 0.16098 -0.07 +620.3 0.1705 0.17051 +0.01 +700.0 0.1737 0.17411 +0.24 *"Freon-12" Dichlorodifluoromethane. 11

c = 00oo80993 + 3.32662 x O-4T - 2.413896 x 10-7T2 + 6.72363 x 10-'T3 (14) 6. Heat Capacity of the Saturated Liquid Heat capacity data have been published by Riedel t13]. More recently the heat capacity of the saturated liquid was determined calorimetrically at the Pennsylvania State University using methods previously described [2]. These latter data are given in Table V. The seventeen points between -155.50F and -3.50F show an average deviation of 0.20% from the following equation prepared by the Pennsylvania State University: cf = 0.195881 - 0.118739 x 10-3T + 0.361742 x 10-6T2 (15) TABLE V HEAT CAPACITY OF LIQUID "FREON-12"* COMPARISON OF THE EQUATION WITH THE DATA Observed Calculated Deviation Temp. Heat Capacity Heat Capacity from OF Btu/(lb)(OF) (Eq. 15) Observed Btu/(lb)(~F) -15 5-0 0. 1934 0. 19322 -0.09 -146 52 0,1940 0.19421 +0.11 -127.71 o01969. 19636 -0.27 -127.74 0.1966 0.19636 -0.12 -117.77 0,1974 0.19744 +0.02 -108.70 0.1993 0.19876 -0.27 - 99.61 0.2000 0.20000 0.00 - 90.52 0.2026 0.20132 -0.63 -~82,06 0.2027 0.20265 -0.03 - 69.96 0.2044 0.20455 +0.07 - 60.64 0.2065 0.20612 -0.19 52.07 0.2069 0.20761 +0.34 -42.39 0.2085 0.20935 +0.41 - 32.43 0.2106 0.21117 +0.27 - 23.18 0.2127 0.21299 +0.14 - 13.14 0.2155 0.21497 -0.25 - 3.53 0.2174 0.21696 -0.20 *"Freon-12' Dichlorodifluoromethane. Source: Cryogenic Laboratory, the Pennslyvania State University. 7. Critical Constants The critical constants were measured as follows: the critical temperature was determined to be 233.60F by observing the temperature of disappearance of the surface separating the liquid and gas. The critical pressure was determined as 596.9 psia by substituting the critical temperature in the vapor pressure equation (Eq. 11). The critical density was determined as 34.84 lb/cu ft by extrapolating the rectilinear diameter to the critical temperature. 12

C. Over-all Accuracy of the Calculated Results The heat capacity of the saturated liquid (Section B,6) provides independent data for checking the accuracy of the cycle calculation. In effect, the cycle calculation has brought us from the reference point on the saturated liquid line at -400F (419.70R) through the properties of the vapor back to another point on the saturated liquid line. As a result, any errors in the cycle calculations have been accumulated in the liquid enthalpy values. The overall accuracy of the results obtained by cycle calculations can be checked by comparing the above liquid enthalpy values with the values based on direct experimental data, calculated using the following equation: T2 P2 hf = f cfdT + f vfdpsat (16) 419.7 P1 The required values of cf* are given by equation (15). The quantity P2 Vf dPsat P1 was evaluated as [(vf2 + vf1)/2] Apsat. This procedure introduced only negligible error since the term is small and the change in vf with saturation pressure is almost linear in the range in question.** Liquid enthalpy values calculated in this way are compared with values from both the new and old tables in Table VI. TABE VI ENTHALPY OF LIQUID "FREON-12"t COMPARISON OF OLD AND NEW TABLES WITH INDEPENDENT DATA Enthalpy, hf, New Tables 1 Old Tables [38 ] Based on....Deviation. Deviation Temp. |Observed Enthal nthalpy, from Data (Eq. 15) hf Observed hf Observed |___D___ at/l15b Btu/lb Btu/lb -150 -22.098 -22.697 -2. 7 -23.50 -6.3 -120 -16.,234 -16 565 -2.0 -16 94 -4.3 - 80 - 8,238 - 8.345 -1.3 8.40 -2.0 - 40 0 0 00 0 ott + 8.519 + 8.52 o0.0 + 8.25 -3.2 t'"Freon-12" Dichlorodif luoromethane.. tt Upper temperature limit of the experimental data. *The quantity measured experimentally was: sat sat sat vsatsat sa **An exact evaluation of P2 vfdaPsat could be made by using the vapor pressure equation (Eq. 11) and the liquid density equation (Eq. 13). 13

Over the range of the experimental data, from -1500F to OO~F the deviation of the new tables from these independent data does not exceed 2.7%. The deviations are progressively smaller toward the higher temperatures. The old tables are in definitely poorer agreement with the experimental data than the new D. Comparison of the Old Tables with the New The old tables have been compared with the new over the entire range that is common to both. The results are presented in the form of a series of eight difference curves (Figures 1 to 5) which are discussed below. In Figures 1 and 2 the curves are the deviations of the values in the old tables from the corresponding values in the new tables. These latter values are represented by the zero base line. It should be noted that the deviations might be expected to be relatively large at pressures above 220 psia, since the old data in this range were based on a combination of estimated and experimental quantities. Figures 1 and 2 compare several properties at saturation. Figure 1-A shows that the old and new tables agree very well in saturation pressure, particularly in the region of the original tables [8]. (For easy reference the region of the original tables -40 to +1400F, has been set off by vertical dotted lines.) Figure 1-B shows very close agreement for the density of the liquid except near the critical point. Figure 1-C, on the other hand, indicates that deviations in the latent heat are from less than 1% to almost 3% in the refrigeration range. The reason for this is that the volumes in the old tables are too high (see Figure 3, discussed below), so that latent heats, calculated from the Clapeyron equation (Eq. 6) are also too high. The deviations in Figure 1 are given in per cent. In Figure 2, deviations in the enthalpy and the entropy of the liquid are given in absolute values. The reason for doing so is that these values are zero at -40OF so that a very small deviation leads to an enormous percentage near this temperature. However, to give the reader an understanding of the relative size of the deviation, percentage figures have been written in at high and low points on the deviation curves. It is seen that in both cases the absolute deviations are not large in the -40OF to +1400F region. The deviation plot for the enthalpy, Figure 2-A, extends the comparison already made in Table VI, to higher temperatures. Figures 3, 4 and 5 show deviations for the vapor volumes, enthalpies and entropies, both at saturation and in the superheat. The deviations are shown by means of contour lines on a pressure versus temperature graph. A contour line is drawn at each 0.5% of deviation of the values in the old tables from the corresponding values in the new tables. In Figure 3, it is seen that vapor volumes were as much as 3.5% too high at the higher pressures in the old tables. This is the major point of difference between the old and new tables. It arises from the higher pressures obtained for the low density isometrics at the University of Michigan as compared with those reported by Buffington and Gilkey (see bottom of Table II). The correctness of the more recent values has been confirmed by comparison with the independent data of Professor A. Michels, as pointed out previously. The considerable effect of these differences in volume values on the latent heats of vaporization was shown in Figure 1-C. Figure 4 shows that the old tables agree very well with the new as regards vapor enthalpies. That this is also the case for the vapor entropies is shown in Figure 514

FIGURE! DEVIATION OF THE OLD TABLES FROM THE NEW A. VAPOR PRESSURE +2 o -- _- = — - -~ —-.. -- -2B. LIQUID DENSITY +2 2 I I Z —' - - -TEMPERAT U — RE C. ENTHALPY OF VAPORIZATION +4-150 -50 +50 + 150. 230 TEMPERATURE- OF.

FIGURE'2 DEVIATION OF THE OLD TABLES FFOM THE NEW A. ENTHALPY OF THE LIQUID +45 m +2 " 3.3%-2c B. ENTROPY OF THE LIQUID +.004 noM4.4 %' at +.004 - / 3.8% +002 -150 -50 +50 +150 +230 TEMPERATURE - F.

FIGURE 3 DEVIATION OF THE OLD TABLES FROM THE NEW ~300-~ VAPOR VOLUME.. 3,0- ~ + 3.5 %/__ 200 10~+ 0.5 0% 80 + 3.0% 60" + 2.5% 0+ 1 0 % 40 200 t +2.0% 3020- / ^ ^ 0.5'%/o 0sI' G 4/ 2 -UPPER LIMIT; OF 3 y SUPERHEAT TABLES 2 e/ BELOW +0.5% 1.0 0.8 0.6 0.4 0.3 0.2 0. * -150o -10o 0. +100 +200 +300 +400 TFMPFPAT IIF -F- O

FIGURE 4 DEVIATION OF THE OLD TABLES FROM THE NEW ENTHALPY OF THE VAPOR 300 200 80-.60 40 302' / XI r~ {~\ BETWEEN < to +0.5 AND U) 8.o% 0 4- //p/ I 6 2 1 / UPPER LIMIT OF SUPERHEAT T4BLES 1.0 0.8 0.6 BELOW 0.3 0. I' I I I I. I -150 -100 0 +100 +200 + 300 +400 TEMPERATURE - o

FIGURE 5 DEVIATION OF THE OLD TABLES FROM THE NEW ENTROPY OF THE VAPOR 30C 20LOW 0.5% 10 B 60 ~- o~ r 40 204; // I% 10- BETWEEN +0.5 8 AND +1.0% % w / F 6 /-UPPER LIMIT OF SUPERHEAT TABLES 1.00.6 Q 3- l TEMPERATURESUPERHEAT F.TABLES 0.5 BELOW +0.5 %\ -150 -100 0 + I00 + 200 + 30 0 +400 TEMPERATURE ~ OF.

The standard ton characteristics given by the old and new tables are compared in Table VII. As would be expected from the differences shown in Figures 1 to 4, the largest differences occur in the vapor volumes, latent heat and net refrigerating effect. However, the compressor displacement per ton of refrigeration is not changed significantly. TABLE VII "FREON-12"* STANDARD TON CHARACTERISTICS COMPARISON OF THE OLD AND NEW TABLES Deviation New Old from New Evaporator Pressure at 5~F, psia 26.483 26.51 +0.1 Condenser Pressure at 860F, psia 108.04 107.9 -0.1 Compression Ratio (860F/50F) 4.08 4.07 -0.2 Latent Heat of Vaporization at 50F, Btu/lb 68.204 69.47 +1.0 Net Refrigerating Effect, Btu/lb 50.035 51*07 +1.0 Refrigerant Circulated per Ton of Refrigeration, lb/min 3.9972 3.916 -2.0 Saturated Liquid Volume at 860F, cu ft/lb 0.012396 0.0124 0.0 Liquid Circulated per Ton of Refrigeration, cu in./min 85.621 83.91 -2.0 Saturated Vapor Density at 50F, lb/cu ft 0.68588 0.6735 -1.9 Saturated Vapor Density at 860F, lb/cu ft 2.6556 2.569 -3.3 Compressor Displacement per Ton of Refrigeration, cu ft/min 5.8279 5.815 -0.2 Refrigeration per Cubic Foot of Compressor Displacement, Btu 34.318 34.39 +0.2 *"Freon-12" Dichlorodifluoromethane. E. The Numerical Calculation 1. Constants and Conversion Factors The molecular weight of "Freon-12" dichlorodifluoromethane was taken as 120.93. The gas constant used was 10.731 (psia)(cu ft)/(OR)(lb mole). The factor used in converting work units [(psia x cu ft)/lb] to heat units (Btu/lb) was 0,18505. One atmosphere was taken as 14.696 psia. The Rankine temperature was taken as OF + 459.7. The enthalpy and entropy of the saturated liquid at -400F were taken as zero, 20

2. The Use of an Electronic-Calculating Machine In extending the range of the tables, it was necessary to use more complex equations to obtain the desired accuracy. This would not have been feasible with a manual calculating machine. The new tables have been calculated on an electronic machine, the International Business Machines Corporation No. 701o It has allowed the use of a far more complicated equation of state than would have been practical heretofore. The calculation of some 150,000 values required only about 30 hours of machine time. The rapidity of the calculation permitted the testing of variants in some of the equations by using them to calculate sections of the tables. Choices in some instances were based on a comparative study of the tabular results. Thus, the use of the machine greatly improved the flexibility of the calculations as well as the speed, About 40,000 individual values appear in the published tables. The other numerical values were used in preparing the charts and certain unpublished tables. The IBM machine calculated ten significant figures. However, five significant figures are sufficient not only for fixing the tabular values, but also for d-etermining trends in the differences between tabular values which are frequently of interest to the refrigerating engineer. For these reasons and for the sake of compactness and ease of use, only five significant figures are included in the tables. If additional figures are required in special cases, it will be possible to supply them. This is true of both the published and unpublished values. It applies, for example, to values of Cp, cv and their ratio, which are published only in the form of small graphs. III. THE NEW TABIES* A. General Since the tables have been extended considerably and since a number of large charts are included with them, they are, for convenience, wire-bound in book form, 8-1/2" x 11" in dimensions. The new tables include the same quantities as the old tables. Values are reported to five significant figures, however, instead of to the four figures used earlier. The complete tables consist of three saturation tables (even temperature, even absolute pressure, even gage pressure) followed by two groups of superheat tables (even absolute pressure, even saturation temperature). They are described below B. The Saturation Tables All three saturation tables list values for each of the quantities reported in the old tables; namely, temperature, absolute pressure, gage pressure, volume of the liquid, volume of the vapor, density of the liquid, density of the vapor, enthalpy of the liquid, enthalpy of vaporization, enthalpy *The new tables and charts will be made available to everyone who has need of them. They will be ready for distribution about December 1, 1955. 21

of the vapor, entropy of the liquid and entropy of the vapor. The old saturation table is at 20F intervals of temperature. The new even temperature value table has a lOF interval and a range from -152 to +2320Fo The saturation values are also reported at even values of absolute pressure and even values of gage pressure There are about the same number of entries in each of these tables as in the even temperature value table. These even pressure tables have been added to eliminate the inconvenience of interpolation and to co-ordinate with the even pressure value superheat tables. C. The Superheat Tables The even pressure value tables list the volume, enthalpy and entropy of the superheated vapor at constant pressure at even 10OF temperature intervals just as in the old tables. The pressure range of the new tables is from 0.14 to 500 psia (-152 to +215~F at saturation) and the tables extend 300OF into the superheat. Of the 172 tables of this type calculated., 129 are published. These lie mainly in the refrigeration range. The second set of constant pressure tables consists of individual tables at even values of the saturation temperature. The arrangement, quantities and intervals in the individual tables are the same as in the first set. The same range is covered in 126 tables. This form of table co-ordinates directly with the even temperature value saturation table. IVo THE NEW CHARTS* A. General In general, charts serve a twofold purpose. They cover broad ranges of data compactly and they provide a convenient means for calculating cycles rapidly. The range and number of charts have been chosen with these purposes in mind so as to meet the needs of refrigerating engineers and other users of'"Freon-12" dichlorodifluoromethane as well. There is a broad-range pressure-enthalpy chart, extending beyond the limits of the printed. tables and covering all available data. A second chart gives the refrigeration range in greater detail. The refrigeration range is also covered by an eight-part sectional chart on a very large scale. There are, in addition, an entropy-enthalpy diagram and charts of the specific heats and their ratio. The charts are described below. B. Pressure-Enthalpy Diagrams The broad-range pressure-enthalpy diagram covers the range from 0.14 to 5000 psia in pressure, -150 to +700~F in temperature and extends vapor volumes to as low as 0.019 cu ft/lb (equivalent to 1.5 times the critical density). *The new tables and charts will be made available to everyone who has need of them. They will be ready for distribution about December 1, 1955. 22

This chart is about 20" x 22" in size. There is a chart of the refrigeration range which covers pressures from 9 to 500 psia (-40 to +2150F at saturation) and extends to about 4500F. It is in color and has a size of about 17" x 23". The eight-part sectional chart of the refrigeration range covers the same region as the refrigeration chart discussed above. Each section is approximately 10" x 34" and folds to fit in the 8-1/2" x 11" book of tables. The enlarged scales of these sectional charts make it possible to read them with a high degree of accuracy. For example, the smallest scale division of enthalpy is 0.05 Btu/lb so that it will be possible to estimate enthalpies to 0.01 Btu/lb. Thus, this graph should be of great utility where cycle calculations of high accuracy are required. C. Entropy-Enthalpy Diagram The entropy-enthalpy diagram covers the same range as the broad range pressure-enthalpy diagram, but with entropy as abscissa and enthalpy as ordinate. The smallest division on the enthalpy scale is 0.1 Btu/lb so that it will be possible to estimate to 0.02 Btu/lb. The size of this chart is about 20" x 45". D. Graphs of the Specific Heat Data Three graphs give respectively cp, cv and their ratio over the entire range of the data. V. ACKNOWLEDGEMENTS The tremendous amount of work involved in this whole program has necessitated the co-operation of a large number of people. The authors wish to thank all of them for their unstinting efforts which have contributed so greatly to the successful completion of the tables and charts. They wish specifically to thank the following in view of the essential importance of their contributions: Messrs. L. F. Albright, W. J. Burkett, J. D. Marks, G. E. Gryka and R. G. Reimus of the University of Michigan, for assistance with some of the experimental work and calculations. Drs. Thomas Wartik and M. J. Linevsky of the Pennsylvania State University for their precision measurements of liquid heat capacities. These measurements were made possible through the use of the experimental facilities of the Cryogenic Laboratory at the University, made available by Professor J. G. Aston. Mr. T. E. Beukelman of du Pont's Jackson Laboratory for assiduous and excellent work in planning and executing the calculations and programs for the electronic calculating machine. Dr. F. C. Chromey of du Pont's Jackson Laboratory for his advice on mathematical questions which have arisen in connection with this work. Dr. R. A. Gorski of du Pont's "Kinetic" Laboratory for assisting Mr. Beukelman in connection with the mathematics and machine programming for supervising the transcription of the numerical data. 23

Mr. R. B. Ramsey of du Pont's "Kinetic" Laboratory for his tireless efforts in laying out the plans for the various tables and charts. Mr. K. R. Weigand of South Bend, Indiana, for preliminary calculations and his exceptional craftsmanship in the drawing of the charts and diagrams. VI. CONCLUSION Data have been developed and equations derived for the purpose of calculating a new set of tables and charts of the thermodynamic properties of "Freon-12" dichlorodifluoromethane. The finished tables and charts represent the co-operative effort of several laboratories and numerous individuals. They are based both on the new data and the old data as well. Greater accuracy has been attained and a broader range has been covered than heretofore. It is expected that the requirements of refrigerating engineers and other users will be satisfied by these tables and charts for many years. VII. REFERENCES 1. L. F. Albright and J. J. Martin, Ind. Eng. Chem. 44, 188-189 (1952). 2.a.J. G.:.Adton.and G. H. Messerly, J. Am. Chem.:Soc. 58, 2354 (1936). b.Messerly and Aston, Ibid., 62, 886 (1940). 3. A. F. Benning and W. H. Markwood, "Thermodynamic Properties of'Freon-12' at Low Pressures," "Kinetic" Chemicals Division, 1942. 4. A. F. Benning and R. C. McHarness, Ind. Eng. Chem. 32, 497-99 (1940). 5. A. F. Benning and R. C. McHarness, Ibid., 32, 814-16 (1940). 6. F. R. Bichowsky and W. K. Gilkey, Ibid., 23, 366 (1931)o 7. R. M. Buffington and J. Fleischer, Ibid., 23, 1290 (1951). 8. R. M. Buffington and W. K. Gilkey, "Thermodynamic Properties of'Freon-12' Dichlorodifluoromethane," American Society of Refrigerating Engineers Circular No. 12, (1931). 9. R. M. Buffington and W. K. Gilkey, Ind. Eng. Chem. 23, 254 (1931). 10. W. K. Gilkey, F. W. Gerard and M. E. Bixler, Ibid., 23, 364 (1931). 11. J. J. Martin and Y. C. Hou, "Development of a New Equation of State for Gases," A.I.Ch.E. Journal, 1, No. 2 (1955) 12. J. F. Masi, J. Am. Chem. Soc. 74, 4738 (1952). 13. L. Riedel, Z. fur die gesamte Kalte-Industrie 46, 105-6 (1939). 24

VIII. NOMENCLATURE hfg = enthalpy of vaporization in Btu/lb, hf = enthalpy of the saturated liquid in Btu/lb, hg = enthalpy of the saturated vapor in Btu/lb, h = enthalpy of the superheated vapor in Btut/lb, H = enthalpy, v = volume in cu ft/lb, t = temperature in OF, T = absolute temperature in OR = t~F + 459.7, p = absolute pressure in psia, = gage pressure in psig, S = entropy in Btu/(lb)(OR), sfg = entropy of vaporization in.Btu/(lb)(OR), Sf = entropy of the saturated liquid in Btu/(lb)(0R), s = entropy of the saturated vapor in Btu/(lb)(~R), c~ = specific heat at constant volume at zero pressure, Btu/(lb)(OF), cv = specific heat at constant volume in Btu/(lb)(OF), cp = specific heat at constant pressure in Btu/(lb)(OF), Cf = specific heat of saturated liquid in Btu/(lb)(OF), b = equation of state constant = 0.0065093886 cu ft/lb k = equation of state constant = -5.475, Tr = reduced temperature = T/693.3, d = density in lb/cu ft, Q = heat added to the system. 25

Subscript s r = reduced. c = critical, f = liquid, sat = saturated, g = saturated vapor, T = constant temperature, v = constant volume, p = constant pressure. 26

3 9015 02841230 THE UNIVERSITY OF MICHIGAN DATE DUE 7(s 1(t 4