Calorimetric Measurements of Some Hydrocarbons Citation Vermeulen, Theodore (1937) Calorimetric Measurements of Some Hydrocarbons. Master's thesis, California Institute of Technology. doi:10.7907/bbv4-2x12. https://resolver.caltech.edu/CaltechTHESIS:11052024-220419432 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemical Engineering) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Lacey, William Noble Thesis Committee: Unknown, Unknown Defense Date: 1 January 1937 Record Number: CaltechTHESIS:11052024-220419432 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11052024-220419432 DOI: 10.7907/bbv4-2x12 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16834 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 13 Nov 2024 18:31 Last Modified: 13 Nov 2024 18:53 Thesis Files PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

CALORIMETRIC MEASUREMENTS OF SOME HYDROCARBONS Thesis by Theodore Vermeulen In Partial Fulfillment of the Re~uirements for the Degree of Master of Science California Institute of Technology Pasadena, California 1937 T.AELE OF CONTENTS I Specific Heats of Some Mixtures of Propane, n-J3utane, and n-Pentane and H. S. Backu.s) II III (With B. H. Sage Specific Heats of Liquid Hydrocarbons Heat of Vaporization of Isobutane Reprint Page 1 Page 19 ILLUSTRATIONS Figure Page 1 Bomb Calorimeter 8 2 Bomb Calorimeter (photograph) 8 3 Cv - T for Ethane OP - T for Four Hydrocarbons OP - TR for Ten Hydrocarbons Vaporization Assembly Condensation Assembly (photograph) Calorimeter, with Vapor Lines (photograph) 11 Interior of the Calorimeter (photograph) Latent Heat of Vaporization of n-Butane Latent Heat of Vaporization of Isobutane Latent Heat of Vaporization of Isobutane 25 4 5 6 7 8 9 10 11 12 13 13 22 23 25 27 29 29 Reprinledfrolll l N DUSTlUAL AND EN<:INEEHLNG CH t~\ll S'l'HY, Vu! . 28. Pauel18.9, April, ·t .9."{/j within 1.5 per cent. The directly measured values of specific heat are under con0 ~tant volume conditions in the two-phase region. These values are not as useful as are values of the specific heat at constant pressure for condensed liquid adjacent to the bubble point, although the difference between the two quantities may be rather small. The calculations which must be utilized to convert the specific heat in the two-phase region to the specific heat at constant pressure for condensed liquid adjacent to the bubble point are based upon a knowledge of the pressurevolume-temperature relations of the material. To obtain these values for all the systems involved would require a rather extended experimental program. If, however, the mixtures follow the laws of ideal solutions within the accuracy required for the evaluation of the correction terms, the experimental work is greatly reduced. In order to check the agreement of these two-component mix1 tures with the laws of ideal solutions, a study was made of the pressure-volumetemperature relations of a mixture of propane and pentane. This study was restricted to the condensed region and part of the two-phase region. The methods B. H. SAGE, H. S. BACKUS, AND T. VERMEULEN and apparatus used for this work have alCalifornia Institute of Technology, Pasadena, Calif . ready been described (2, 6). Briefly, the method consisted in isothermally changing the volume of a steel ehamber conOMPOSITION and temperature have a taining a known amount of the sample by addition or withmuch larger effect upon the specific heats drawal of mercury. The change in equilibrium pressure with of hydrocarbon mixtures of low molecular change in volume was thus determined . An agitator was weight than they do upon those with a large number of carbon provided within the chamber to insure equilibrium. atoms in the molecule. A great many more experimental Pressure-Volume-Temperature Measurements measurements have been made for hydrocarbon mixtures of high average molecular weight than for more volatile ones. In the pressure-volume-temperature measurements the Because of the lack of suitable information in this region, a following precision was attained: mass of sample, 0.1 per study was undertaken to determine the variation of specific cent; volume of sample, 0.1 per cent; pressure, 0.1 pound per heat with composition and temperature for liquid mixtures square inch from atmospheric pressure to 300 pounds per in the three two-component systems containing propane, square inch, and 1 pound per square inch from 300 to 3000 n-butane, and n-pentane. The work also includes the specific pounds per square inch; temperatures, 0.02° F. heat of n-pentane and of a series of liquid mixtures of propane The materials used in this work were used in other studies. and a highly refined water-white oil (average molecular (1, 5, 6). The Philgas Company, from which the samples of weight, 337) called "crystal oil." The specific heat measurepropane, n-butane, and n-pentane were obtained, submitted ments were made throughout the temperature .interval from the following special analyses, expressed in mole per cent: 70° to 220° F. propane, 100.0; n-butane, 99.21 with 0.18 isobutane and The specific heat measurements reported in this paper were made at constant volume in the calorimeter previously described (1). After determining experimentally the specific heat at constant volume in the two-phase region, we can then The specific heats at constant pressure calculate the specific heats at constant volume and constant pressure at any temperature within the range studied and for a number of two-component mixtures for any pressure for which the pressure-volume-temperature consisting of propane, n-butane, and relations for the substance in question are known. n-pentane are reported for the condensed In brief, the method consisted first of introducing a sample liquid adjacent to bubble point. In order of fixed composition into a light-weight steel bomb, adding to demonstrate that the behavior of such known amounts of electrical energy, and measuring the rise mixtures was sufficiently close to that of in temperature of the bomb and contents by the use of thermocouples. Heat loss from the bomb was prevented by surroundideal solutions for the purposes of the ing it with a vacuum jacket and maintaining the jacket at specific heat calculations, a study of the the same temperature as the surface of the bomb. The thermodynamic properties of a mixture specific heat measurements are considered trustworthy tu of propane and n-pentane was made, 1 Previous articles in this series appeared dur in g 1934 and 1935 , and in and the results are reported. January and February, 1936. Phase Equilibria 1n Hydrocarbon Systell'ls XII. Specific Heats of Some Mixtures of Propane, n-Butane, and n-Pentane 11 C 489 INDUSTRIAL AND ENGINEERING CHEMISTRY '190 ai -' 0.050 a: w a. >--' "- 0.045 :j u w 2 :::, 0.040 .J 0 > s! ': u 0.03 w a. V) 200 400 300 PRESSURE LB S. 600 500 PE R SQ. 700 IN. FIGURFJ 1. SPECIFIC VOLUMES FOR A MIXTURE CONTAINING 79.41 MASS PER CE N'l' PROP ANE AND 20.59 MASS PER CENT n-PENTANE ai .J a: w a. f-C l._ ::; u w 2 :::, .J 0 > 75 100 125 TEMPERATURE FIGURE 2. 175 150 200 °F. SPECIFIC VOLUME OF THE PROPANE-PEN'l'ANE MIXTURE AS A FUNCTION OF TEMPERATURE VOL. 28, NO. 4 point is striking. At the higher pressures, temperature has a much smaller effect upon the thermal expansion. The principal interest in this pressure-volume-temperature work is a comparison of the actual measurements with those predicted from the laws of ideal solutions. One of the assumptions which must be validated before these laws are applicable is that of additive volumes . Figure 3 shows the percentage deviation of the volumes predicted by the laws of ideal solutions from the experimental volumes as a function of temperature for a series of pressures . This percentage deviation was obtained from the expression: . t· (0.7941 V, + 0.2059V5 - V)(IO0) P er cen t d evia 10n = V where Va, V&, V = specific volumes of propane, pentane, and the mixture, respectively The deviation from additivity is negligible at the lower temperatures, but as the critical temperature of propane is approached the deviation becomes appreciable. It is also apparent from Figure 3 that the assumption of additive volumes is much more closely followed at the higher pressures than at pressures in the neighborhood of the bubble point. However, in all cases the deviation is small except near the critical temperature and pressure of propane, where deviations of over 100 per cent are encountered. Another interesting correlation which the data permit is a comparison of the observed bubble point with that predicted from Raoult's law and from the laws of ideal solutions. In the following table the experimentally determined bubble-point pressures (in pounds per square inch absolute) for a series of temperatures are shown for comparison with similar values based upon ideal solutions and upon Raoult's law : 70° F. 100° F. 130° F . 160° F. 190° F. 220° F. Exptl. 106.4 162 . 0 231.5 322 441 590 Ideal soln. 107. 9 162. 7 234. 3 334 Raoult's law 109. 8 165. 8 239. 8 333 459 0.61 isopentane; n-pentane, 99.3 with 0.7 isopentane. The In each case the agreement is satisfactory at the lower temcompositions of mixtures discussed hereafter are given in peratures but becomes poor at higher temperatures, approachterms of the proportions of these three samples, referred to as ing the critical temperature of propane. propane, n-butane, and n-pentane. The mixture chosen for the pressure-volume-temperature work was composed of 79.41 mass per cent propane and 20.59 mass per cent n-pentane. This mixture was chosen as representing the mixture of 2.0 1 - - - - - - + - - - - - + - - - - - + - - -- -+ - - + - - + - - - + - + - - - t - - - i those studied which would be expected to deviate most widely from the laws of ideal solutions; it was z composed of the two constituents of most widely Q 1divergent properties and with the maximum con<0: 1.51------+-----+----+---.<11-----+-l-----al--l----l > centration of the constituent nearest to its critical w 0 state. The study included the effect of pressure upon volume at seven temperatures spaced between 1z 1.0 1 - - - - - - f - - - - - l - - - - - - f - - V"j<----f-------,'-+-----f-+--+---l 70° and 220° F. In each case the volume of the w u system was increased to about three times its volume a: w at bubble point. Figure 1 shows the results of these a. measurements in the vicinity of the bubble point. The 0.51-----1----1-~"---l--,,.L'-----+---~,-£-t--------,,''--+-----l much larger decrease in pressure with increase in volume in the two-phase region for the higher temperatures is apparent. The rapid increase in compressibility of the liquid as bubble-point pressure is approached at the higher temperatures can be clearly •r. TEMPERATURE seen. Figure 2 shows the isobaric variation in volume FIGURE 3. DEVIATION FROM EXPERIMENTAL VALUES OF SPECIFIC of the liquid with temperature; the rapid increase in VOLUMES QI,' THE PROPANE-PENTANE MIXTURE CALCULATED FOR foEAL thermal expansion with temperature at the bubble SOLUTION APRIL, 1936 INb US\RiAL AND ENGINEEilING CHEMISTRY / ,/ A'.::::,...--,L.\--__:::~:::j---;/r/ 500 200 Heat contents were determined from the internal energy values by use of the relation: H=E+pv In the two-phase region the isothermal changes in entropy were determined by graphical integration of the expression: 175 6.T. "<;- .l,._ ~ 150 (oP) (oS) oV = oT w r a: :, I- <( 125 a: a. ::; v The changes in entropy with temperature were determin ed by integration of the equation: w w =Cv (oS) oT v T ,-. 100 The determination of the effect of pressure upon heat content and entropy in the condensed region was carried out in exactly the same manner as previously described (6). The results of the calculations 0.08 0.05 0.06 0.07 0.04 0.02 003 fo r the two-phase region are shown B.T.U. PER LB. PER °F. S-0.0009 (T-60) in Table I; the pressure, heat conFIGURE 4. TEMPERATURE-ENTROPY DIAGRAM FOR THE PROPANE-PENTANE MIXTURE tent, and entropy are given as functions of the total volume of the system for a series of temperatures. Table II presents the specific Still another assumption which must be fulfilled by an volumes, heat contents, and entropy as functions of pressure ideal solution is the additivity of the heat contents. In other for the condensed region at the same series of temperatures. words, there must be no change in internal energy upon mixThe temperature-entropy plane offers the best method of ing. Experimental verification of this assumption is not presenting the thermodynamic data in graphical form. Beeasy, since high precision in the determination of specific heat cause of the small isothermal changes in entropy as compared is laborious and difficult of attainment. For this reason a to the changes with temperature, a function of entropy is comparison of this nature was not attempted, although the used in Figure 4 in order to show these isothermal variations specific heat data indicate agreement within the limits of on a better scale. The use of this function is based upon a their accuracy, as will be shown later. device to exaggerate graphically the small isothermal changes The pressure-volume-temperature data along with the and still allow plotting on a reasonable scale the larger changes specific heat data to be discussed later furnish sufficient inin entropy with change of temperature. For this purpose the formation to determine the thermodynamic properties of this values shown are merely differences, at constant temperature, mixture throughout the pressure and temperature range inbetween the entropy and the function 0.0009 (t - 60), where vestigated. The methods of calculation used have already tis the temperature in ° F. To obtain the value of the entropy been described in detail (6). However, because of the small for a given state, the value of the abscissa is read from Figure 4 change in pressure with increase in volume in the two-phase and the quantity 0.0009 (t - 60) for the temperature in region, a modification of the previous procedure had to be question is added to it. The inversion of the Joule-Thomson used. In the two-phase region, volume was used as the coefficient in the condensed region at the higher temperatures independent variable instead of pressure. The isotherm al is evident from the shape of the lines of constant heat changes in internal energy with volume were determined by content. The large positive Joule-Thomson coefficient in the graphical integration of the expression: two-ph ase region is in agreement with that expected from the values for propane and pentane. The behavior is in distinct contrast to that found for mixtures of crude oil and natural gas (3). In such mixtures the Joule-Thomson coefficients The changes in internal energy with temperature were dewere small and inverted in the two-phase region. The intermined by graphical integration of the following expression: version of curvature of the constant-pressure lines in the con- TABLE I. PROPERTIES IN THE Two-PHASE R EGION FOR PROPANE-PENTANE MI XTU RE CONTAINING 79.41 MASS PER CENT PROPANE - 7 0 ° F.----- •• P h ~--100° F .- - ~ ~ Ph 0.035 0.040 0 .045 0 .050 106 .3 2.67 0.03472 106.1 3 .48 0.03623 105.9 4.27 0 .03773 105 . 7 5. 07 0.03923 160.8 160.5 160 .2 159.9 0.055 0.060 0.065 0 . 070 105.5 5.87 0.04073 105.3 6.65 0 .04222 105.2 7.45 0.04371 105.1 8.23 0.04519 159.6 26. 14 0 .07696 159.3 27.20 0.07886 159.1 28.25 0.08075 159. 0 29 .30 0 . 08262 a • 21.84 22.92 24 . 00 25. 01 -1 30° F . ~ ~-160 ° F .- ~ p h s 0 .06927 232.6 41 .75 0.10309 0.011 21 232. 0 43_21 0.10558 0.07314 231.4 44.66 0.10805 0.01506 230 .9 46. 10 0.11049 p h - - 190° F. ~ ~ - 2 2 0 ° F . ~ p 323.1 64. 22 o:1 39 j9 440:1 32 1. 7 66.18 0.14237 437 . 5 320. 3 68.11 0 . 1455 1 434.4 h p h 85. 77 0 . 11111 88.47 0.17597 91.1 2 0.1 8009 483 114.3 230 .4 47.52 0 .1 1291 319.0 70 . 02 0.14861 43 1.5 93.72 0.18413 229.9 48.93 0.11530 317 .6 71.90 0 .15 167 428.7 96 .25 0 . 18808 229.4 50.32 0. 11768 316.3 73.75 0 .15468 426.1 98.74 0.19195 229 .0 51.70 0.12002 315.1 75.58 0.1 5765 423.6 101 . 16 0.1 9573 = specific volume, c u. ft./lb.; P = pressure, lb./sq . in. abs.; h = heat content, B. t. u ./lb.; s = entropy , B. t. u./lb.l° F. abs. o :2 i440 47 5 117.62 0.21965 468 121 . 00 0 .22473 462 124.26 0 .22963 457 127.42 0. 23437 VOL. 28, NO. 4 INDUSTn.JAL AND ENGINEERING CHEMISTRY 492 • TABLE II. ~ pa PROPERTIE S IN CONDENSED REGION FOR P ROPANE -PENTANE MIXTURE CONTAINING 79.41 Pim C ENT PROPANE MAss -70 ° F.- - ~ ~v h s -100 ° F .- - ~ v h S ~ --1 30° F. - - ~ ~ -- 160° F . ~ ~ - -190° F . ~ h v s V h S h V ~ 2 20° F.~ S V h S Satd. 0.03042 1.94 0 . 03333 0 . 03199 21. 19 0 . 06810 0 . 03377 41.38 0.10248 0.03606 62.64 0 . 13665 0.03958 85.54 0.171 41 0.04580 111.95 0 .2098 200 0.03033 1. 97 0.03239 0 . 03194 21.19 0.06770 . .. .. .... ... ... ..... . .. . . 400 0 . 0301 5 2. 08 0 .03047 0 . 03166 21.22 0 . 06566 0 . 03342 41 20 0.10040 0 03576 62.29 0.1 3526 ... .. . . .. .... . ... . 600 0.02995 (2.31 ) 0.02865 0.0314 0 21.28 0 . 06375 0 . 03302 41.09 0.09812 0 0351 1 61.59 0.1 32 01 0 . 03836 84. 07 0.167 29 0.04548 111.71 0.20938 800 0.02979 2.4 2 0.0269 1 0 . 0311 8 21.43 0 .06195 0 . 03268 41.06 0 . 09601 0 034 58 61.11 0.1 29 15 0.03730 82.64 0.16291 0 . 04165 107.99 0.20176 1000 1250 1500 1750 0.02964 0.0294 6 0.02930 0.02915 2 . 65 0 .02526 0 .03007 2 1.63 0 . 06024 0 . 03239 41. 11 0. 09405 0.0341 3 60.81 0 .12658 0.03650 81.57 0.1 59 19 0 . 03987 105.65 0.19607 2.98 0.02329 0.03072 21 92 0 . 05821 0.03205 41 25 0.09178 0.03365 60.61 0.12369 0.03572 80. 64 0.1551 9 0.03830 103 . 67 0.19050 3 .36 0.02142 0.03050 22 27 0 . 05630 0 . 03176 41 49 0 . 08967 0.03322 60.55 0.12107 0.03507 80.03 0.15173 0 . 03730 102.33 0.18598 3.77 0 . 01964 0 . 03029 22 66 0 .05447 0.0314 8 41.78 0 . 08769 0 . 03284 60.60 0.11 867 0.03452 79.65 0 . 14869 0 . 03658 101 . 41 0.182 12 2000 2250 2500 2750 3000 0.02902 0.02888 0.02876 0.02866 0.02857 4.22 0.017 93 0 . 03011 23. 08 0 .05274 0.03123 42 13 0.08583 0.03 25 0 60.7 3 0.11644 0.03406 79. 44 0.14595 0.0359 1 100.76 0.1787 2 4.69 0.01629 0.02994 23.54 0 . 05108 0 . 03101 42.53 0.08405 0 . 0322 1 60.94 0.11437 0.03366 79 .38 0 . 14343 0 . 03535 100.32 0.17564 5 . 19 0.01 471 0.0297 7 24.02 0 . 04948 0 . 03080 42 .97 0.08236 0.03192 61.23 0.11243 0.03330 79.41 0.1 4110 0 . 03486 100.02 0 . 17280 5.72 0.01320 0 . 02963 24.53 0 .04794 0 . 03061 43.44 0.08075 0.03167 61.56 0.11059 0.03298 79.53 0.1 3892 0 . 03443 99.82 0 . 1701 5 6.27 0.01175 0 . 02948 25. 07 0.04637 0 . 03041 43.94 0.079 21 0 . 03144 61.95 0.10886 0.03267 79 . 71 0.1 3687 0.03403 99.72 0.16767 162 .0 Satd. pressure 106. 4 322 23 1. 5 441 590 a The letters indi cate tlie sa me properties as those in Table I. densed region of Figure 4 is due to the fact that the rapid increase in the specific heat at constant pressure outweighs the effect of pressure upon the isothermal change in spec ific heat. This latter effect causes the lines of constant higher pressures to recede from the bubble point line as the temperature is increased . Specific Heat Measurernen ts Frnm the pressure-volume-temperature study upon the mixture discussed, the authors consider that the deviation from the behavior of ideal solutions in the case of the other more favorable mixtures would be small enough to permit calculation of the required specific heat conversions. These corrections to the specific beat at constant volume in the twophase region are applied in two steps. First the change in specific heat at constant volume with volume must be evaluated over the range from the volume at which the specific heat measurements were made to the volume at bubble point. This change was determined by graphical integration of the following expression: 2 = T (o P) ( oCv) oV r 0T 2 v The change from specific heat at constant volume at the two-phase side of bubble point to the specific heat at constant pressure on the condensed side of bubble point must also be determined. This was clone by evaluation of the following expression: C',,13 = C\13 + r(!;).J:~t + r(!;).n(:nn It should be reali zed that there is an abrupt discontinuity in C,, in passing from one side of the bubble point condition to the other. That is, the value of Cv for condensed liquid very close to the bubble point is definitely different from that for t he liquid in equilibrium with an infinitesimal amount of gas phase, even though the two states are almost identical. The values of in these two conditions would be denoted uy C' ,,8 and C"•n' in which the subscript B refers to bubble point and the superscripts ' and " indicate the presence of one or two phases, respectively. The two correction calculations indicated were carried out fo r each experimental point., and the values of specific heat at constant pressure, C' vn , obtained. With the exception of mixtures with more than 70 mass per cent propane, the two corrections together were not more than 2 per cent of the specific heat. The lowest curve in Figure 5 shows the results of the experimental work done on n-pentane. These values for the specific heat at constant pressure of the saturated liquid are distinctly lower than the values previously reported (5) for the specific heat at a constant pressure of 1000 pounds per square inch. The earlier values were determined by the adiabatic expansion method (6) which becomes unreliable when the thermal expansion is small. The values of (oT / oP), which were used in these earlier determinations were checked c. 0.9 0.8 -d I I 0 .7 YA y ~ I -d 0.6 100 125 150 TEMPERATURE 175 200 °F. FIGURE 5. SPECIFIC HEA'r A'l' CoNS'l'A N'r PREssu nE FOR Co N DENSED MIXTURE OF' PROPANE A N D n-PBN TA NE AD.IA CENT '1'0 B UBBLE POIN1' 100 125 15 0 TEMPERATURE 175 0 2 00 F. FwuRE 6. SPECIFI C HEA'r A'l' CoNSTAN'l' PRESSURE OF PRoPANE-n-B uTANE SYSTEM FOR CONDENSED LIQUID ADJACENT ·ro BUBBLE POJN'l' APRIL, 1936 INDUSTRIAL AND ENGINEERING CHEMISTRY . - Cl. u 493 . - a. u 20 MASS 40 60 PERCENT PROPANE 60 TEMPERATURE FIGURE 7. SPECIFIC HEAT AT CONSTAN'l' PRESSURE OF MIXTURES OF PROPANE AND n - PENTANE FOR CONDENSED LIQUID ADJACENT TO BUBBLE POINT with the present apparatus with higher precision and were found in satisfactory agreement. This indicates that the discrepancy in the earlier reported specific heats was due to uncertainty in the isobaric thermal expansion at 1000 pounds per square inch. The results of these experimental studies for the twocomponent systems propane with n-pentane and propane with n-butane are shown in Figures 5 and 6. At the lower temperatures the agreement of the curves drawn through the experimental points for the mixtures is within experimental error of that predicted from the laws of ideal solutions. However, in the case of mixtures of propane and pentane at the higher temperatures, this is not the case. Figure 7 shows the isothermal change in specific heat as a function of the composition at a series of temperatures for mixtures of propane and n-pentane. The points plotted in this figure were read from the curves shown in Figure 5. As can be seen from the straight-line relationship throughout the composition range at 70° and 100° F ., these solutions have little or no change in internal energy upon mixing. At the higher temperatures the curvature becomes marked, showing that the heat contents are not additive in this region and hence the solutions do not follow the laws of ideal solutions accurately at these temperatures and pressures. In the case of mixtures of n-butane and n-pentane, the specific heats of the pure components differ by an amount small enough so that the magnitude of the experimental error of the present work renders results from the mixtures inconclusive. However, determinations made upon three mixtures indicated accord with the behavior of ideal solutions within the experimental error. To gain further insight into the behavior of propane in solutions as its critical temperature is approached, another set of specific heat measurements was made on mixtures of propane and crystal oil. In order to make the necessary specific heat conversions, the pressure-volume-temperature data already published for these mixtures (4) were used. The corrections were applied in the same manner as was described earlier. Figure 8 shows the experimental points for several mixtures of propane in crystal oil as a function of temperature. The curve shown for crystal oil was taken from published data (2). Figure 9 shows the isothermal change in specific heat at constant pressure for the condensed liquid at the bubble point as a function of composition for a series of temperatures. The points plotted in this figure were read from the curves shown in Figure 8. In this case the divergence °F. FIGURE 8. SPECIFIC HEAT AT CONSTANT PRESSURE OF PROPANE- CRYS'l'AL OIL SYSTEM FOR CONDENSED LIQUID ADJACEN'l' TO BUBBLE POIN'l' . - Cl. u 20 MASS 40 60 PERCENT PROPAN E 60 FIGURE 9. SPECIFIC HEAT AT CONSTANT PRESSURE IN PROPANE-CRYSTAL OIL SYSTEM FOR CONDENSED LIQUID ADJACENT TO BUBBLE POINT AS A FUNC'l'ION OJ<' COMPOSITION from the straight line is apparent even at the lower temperatures but is marked only at the higher concentration of propane. At the higher temperatures, however, the curvature of the isotherms is appreciable at all concentrations, and the divergence from ideal solutions would be expected to be large. Acknowledgment The authors express their indebtedness to the American Petroleum Institute for financial support, the work having been done as a part of its Research Project 37. They wish to thank W. N. Lacey, director of the project, for his criticism and advice. J. E. Sherborne and D. C. Webster assisted in the measurements and calculations, respectively. Literature Cited (1) Sage, B. H., and Lacey, W. N., IND. ENG . CHEM., 27, 1484 (1935). (2) Ibid., 28, 106 (1936). (3) Ibid., 28, 249 (1936) . (4) Sage, B. H., Lacey, W. N., and Schaafsma, .J. G., Ibid., 26, 874 (1934) . (5) Ibid., 27, 48 (1935). (6) Sage, B. H., Schaafsma, .J. G., and Lacey, W. N., Ibid ., 26, 1218 (1934). RECEIVED September 19, 1935. Pn1NTED JN U. S. A. II. SPECIFIC BEATS OF LIQUID HYilROCAP.BC1'1$ a. Theoretical Consid.erations Numerical data for specific heats of the pure normal alkanes are necessary in a tabulation of the thermodynamic properties of these compounds. The functions of state most used in engineering calculations are pressure, volume, temperature, entropy and enthalpy. During any process in which a material undergoes a change in temperature, the heat absorbed can not be calculated from P-V-T data alone. Thermal values for any change in state may be calculated, with the aid of the physical data, once the thermal quantities have been obtained for some one process (for instance, a change at constant volume). The heat qua.nti ties used in isothermal changes of state are calculated by integration of one of the Second Law relations: The isobsxic specific he at applies directly in many problems, and is the value most fre~uently tabulated; but it is difficult to measure calorimetrically, either in a system of constant mass or under conditions of steady-state flow. The isentropic process or method of adiabatic ex- pansion is best applied to ga.ses near atmospheric pressure, where the thermal expansion is large. For liquids, a l ar ge pressm·e drop is nec- essary for.reliap.le values. This method makes use of the relation : 1 Lewis and Randall, Thermodynamics, p.137. 1 2. Joule-Thomson coefficients for the liquid state are too small to be determined satisfactorily by experimental methods. Measurements on gases have been made by investigators on this research project (A.P.I. 37) with gratifying accuracy. From these data the specific heat is calculated by l the equation : -;;:. -1 (dV) _ y cl T 'F Liquid specific heats are probably best obtained by measurements in an adiabatic calorimeter. begun by Sage 2 The author has carried. on an investigation, 3 and Backu.s, of values of the isochoric specific heats of a number of pure compounds and mixtures of known composition. Accepted expe~imental points have not differed from the mean by more than 2 percent 4 • As a result of correlations of the data for the different materials studied, , curves have been located for which the maximum relative error is about 0.5 percent. Agreement of our values with those of two other investi- gations, carried on by Parks and Huffman at Stanford University and Dana of the Linde Air Products laboratories, indicates that our absolute error is less than 1 percent. The apparatus used has been described by Sage and La cey and will be reviewed in the next section. The liquid to be investiga ted is at its own vapor pressure, a small amount of the gas phase being always present. Experimental values have been converted so as to apply to the condensed liquid at a constant pressure equal to that of saturation. The reported values apply, well within experimental accuracy, over a pressure range of 100 pounds per square inch. It is believed that the data for this region adjacent to bubble point are more directly useful than values at 1 2 3 4 Lewis and Randall, Thermodynamics, pp.68, 133. Sage, B.H. and Lacey, W.N., Ind.Eng.Chem., _gz, 1484 (1935). Backus, R.S., M. s. Thesis in Chemical Engineering, C. I. T., 1935. For measurements on n-pentane, the 25 points used in plotting the curve deviated by less than 1 percent. Only two points were rejected. 3. some constant higher pressure which might be taken as an arbitrary gasis. Too, acldi tional correction terms would increase the probably error of the results. From the two-phase constant volume specific heats, the isobaric values for condensed liquid at bubble point are calculated with the use of P-V-T data by means of equations given in the foregoing article. The d.eriva,tion of these equations is included here to ind.icate the physical significance of the various terms. A five-step cycle is used, giving results identical with those obtained through purely mathematical analyses. In the accompanying figure, T while V3 2 is only infinitesimally higher than T 1 , "4 {double-primed denotes two phases) differs from VB {at bubble ' point) by a finite amount. T Co.-,c:) ~ .-,se-d L,' q.,._,c{ V Three relations are used in evaluating the enthalpy changes for the d.ifferent steps: dH = ~;; ) T -=- Lv ::: qs T vdp -+ y T T (~ ) ( In the Clapeyron equa ti on for the dT ~ Vi:, 11 la.tent" ( ; ; )r - v8 ) heat of v a.porization, sul,script ] refers to the state of the satura ted gas, or dew point. enthalpy or heat content are given as follows. The changes in (Subscript M denotes a,n average value over the temperature change; i.e., the v;:;,lue at T + ~ . 2 4. ! is the quality, or t he fraction of the total .material tha t is in the gas phase.) = H 2. ::: = - 8 f £_/? ) ( V, 3 - V " ) T, ... Id L.p) 13 (VB '(:c;(' . ._ \__c:(T ' H"'t- - rl ~ = c""dT V H, - H..,. :::- LI X 4 He, - HI v ' d p = 1 M - c: d T - v'' ~ )~ ( V, E - V") T, Second-order infinitesimals a.re of course neglected throughout. Adding, V, 8 ( - ( ~ V ,, ) ' ITT): 4T £.£ )c1 dT o{T I equating to zero; and dividing by dT, there is obtained the expression: II The derivatives of the pressure may be written as partials at constant VE, without changing their values; this gives a symmetrical form to the two similar terms. A correction by the Bureau of Standards l of this form is identical with that derived for the work on ammonia, and used by the Linde laboratories in their study of the lighter paraffins at l0\7 tempera ture. The saturation specific heat at bubble point is calculated as an intermediate step. = cl) L:... X ... - Q (.d T) )V\ / Cpa -= 1 C...B LI ;,( / + 6. T + -1 @ T )~ Lx T Cd"V)/Pa d'T Osborne and Van Du.sen, Bur. Stds. :Bull., 11, 397 (1918). dT 5. This deriva tion is rigorous only for a pure compound. A similar treatment could be applied to a multi-component system, taking into account the change in pressure during the isothermal vaporization; but it would be impracticable to obtain physical data for every mixture investigated. For ideal solutions the partial enthalpies are equal to the enthalpies of the respective eomponents in the pure state. Addition of the correction terms for the pure substances should provide a fairly good basis for conversion even if the assumption of ideality is widely in error; and it turns out, both from the physica1 measurements on the pentane-p:ropane mixture and from the specific heat data obtained, that most mixtures of normal hydrocarbons ere closely ideal. The "specific heat 11 for any particular type of process is a function of the state of the system. Values mey- be deterrnin'e d for every process 1 which satisfies either an actual or an empirical physical relation • Thus, two pg, ths not included in the cycle are shown in the figu.re: is the isochoric specific heat of the two-phase mixture adjacent to bubble point. 1Q,:a = CB is the specific heat for liquid under a changing volu.rne equal to the bubble-point values at each temperature; the saturation specific heats c may be calculated for a mixture of any constant quality. The 8 three terms in the conversion equation provide a step-wise correction, in ' their respective order, to CVB" . to CB, and to CP.B. b. Experimental Methods The adiabatic calorimeter used for specific heat measurements was not designed or installed by the author, whose principal construction work on the equipment has been in maintenance repairs. Eut it is felt that a short description of the assembly has its place here. 1 11 Specific heat 11 data in the literature are often of limited application in those cases where the authors have failed to report specifically the process on which the values are based. 6. In any ac~arate calorimetric method, heating due to other sources than that measured mu.st be eliminated as completely as ~ossible. The bomb upon which measurements were made was placed in a chromium-plated brass jacket so constructed as to minimize the three types of heat transmission. Conduction could take place only along the fine steel wires (Number 36, A. W.G.) by which the bomb was supported in a ring resting upon trunnions. Convection and conduction through the space between bomb and jacket were prevented by evacuation of the chamber to a pressure between 10-· and 10..s millimeters of mercury by means of a Cenco Ryvac pump and a diffusion pump using Apiezon-] oil. Radiation was largely eliminated by polishing the two metallic surfaces and by maintaining the oil bath surrounding the brass jacket at a l temperature within 0.02°F. of that of the bomb. The differential ther- mocouple used had one junction on the surface of the bomb and the other in the oil bath outside of the jacket. A light beam, deflected by the mirror of a high-sensitivity galvanometer in series with the couple, operated a photo-electric cell; this in turn operated a relay on one of the heater circuits in the oil bath. The quantities of continuous and control heat were adjusted manually by means of rheostats. A tnermostated air bath, surrounding the oil bath, was enclosed by double walls of an insulating wallboard. The front panel was removable, and included a window of two panes of glass ~1th dead air space between them. l The fluctuations of oil bath temperature due to opening and closing of the control heater circuit are largely damped out by the brass jacket, the inner surface of the latter remaining at much more nearly constant temperature than the value stated. 7. 11 In order to insure both thermal and pha se equilibrium within the l bomb, the latter was oscillated about the axis of the trunnions. To accomplish this movement without a stuffing box through the vacuu.m j acket wall, an iron bar was mounted on the shaft inside the jacket. This bar served to oscillate the bomb by following the movement of the electromagnet outside the jacket. 11 The construction and opera tion of the mag- netic clutch are indicated in Figures 1, 2 and 8. The original b-amb could not be used for measurements at hi gh tempera tu.res on the more volatile mixt-ures because it had not been designed for pressures greater than 1000 pounds per square inch. It became neces- sary to build a new bomb, very similar in general design and in its dimensions, weight, and heat capacity, but designed to withstand an internal pressure of 3000 pounds per square inch. The new bomb was formed from a solid piece of alloy tool steel (Seminole). After heat treat ment by Dr. D. s. Clark of the California Institute, this material had a yield strength of 200,000 pounds per square inch. Fred C. Henson Company mach- ined this roughly to shape, then gr~.md it accurately to a thickness, for the side wall, of 0.040 inch, and for the end walls, of 0.045 inch. 2 bombs were 2 inches in diameter and 4 inches in body length • Both They were fitted with diaphragm valves, which could be removed for filling with liquid. The ends were threaded and sweated on to the central cylinder. A thermocouple well and two sta inless steel tubes for the heater leads were soldered into the bomb wall. Subsequent use of the bomb showed that these soldered joints were the weakest points. After continued use, the s older would rupture at pressures of from 1000 to 2000 pounds per s qUP. re inch; 1 The quota tions a re from the article by Sage a nd Lacey, Ind. Eng.Chem., £2, 1484 {1935) • :a The volumes of b oth bombs were thus about 10 cubic inches or 160 cubic centimeters. 8. BOMB CALORIMETER Figure 1. Bomb Calorimeter Figure 2. Bomb Calorimeter 9. this occurred because its elasticity under increased tempera ture and pressure is small compared to that of steel. The heat capacity of each of the bombs was determined by filling it with hydrogen at a pressure near atmospheric, and measuring current impu.t and temperature rise in the usual way. For most of the materials studied, this was about 40 percent of the total heat capacity. The bomb- well thermocouple was calibrated by recording the observed voltage and the temperature of the oil bath when the control galvanometer indicated no difference between bomb and bath. This temperature was obtained on a calibrated mercury-in-glass thermometer on which all readings are believed accurate to 0.02°F. The quotient of temperature by potentiometer scale reading was plotted against the scale reading itself, and a smooth calibration curve was drawn which established an accuracy of the temperature differences observed of within 0.005°F. From voltage readings which in- dicated the voltage and current of the bomb heater circuit, the electrical heat was calculated. These were taken at frequent intervals during each run, and any variations were integrated against the time. To quote again from Sage and Lacey, 1•1n making a determina tion with the calorimeter, a sample was placed in the bomb, the weight of materials added being ascertained by weighing the bomb. 11 and the jacket space was evacuated. The apparatus was assembled, ~efore each run the temperature of the sample was determined, "readings being repeated at 5-minu te intervals until found constant. Current was passed through the heater element in- side the bomb for about 20 minutes, (measured to within about 0.3 second). About 6 to 8 minutes after stopping the current, tempera ture readings were again taken until a constant value was o'btained 1~ The amounts of heat energy added as a result of agi ta.ti on, or transferred because of heat leakage to or from the jacket, were found to be entirely negligible. 10. Five normal hydrocarbons and nine binary mixtures were mea sured thermally by the author. Previ ous work had been done on ethane, propane l and butane by :Backus and by J. E. Sherborne , but uncertainty in their values was reduced by the new measurements and by correla tion of the data for the pure compounds. Data for ethane, obtained with the new bomb, are shown in Figure 3. The experimental values do not agree as accurately as our other calorimetric measurements because of the l arge specific volume of the material over the temperature range investigated, the less rapid attainment of equilibrium by the gas, and the smaller temperB.ture increment required because of the more rapid change in value. For the specific volume shown, the hea t capacity of the bomb amounted to of the total. volumes. 50 to 70 percent Confirmatory runs were made upon ethane for three other These data were not used directly and are not shown in the figure, but they were of value in locating and shaping the curve of Figure 3. The specific volume of QC764 cubic feet per pound was used in 2 this curve because it a pproaches the value for the critical state. In the critical region, Op is of little use because it is very large. The isochoric specific hea t which has been measured was used directly in calcula ting the thermodynamic properties of ethane. The discontinuity shown on the plot was calculated by means of the expression: l 2 Other measurements have been made with this calorimeter by W.R. Mendenhall upon isobutane and of three additional binary mixtures; by Eackus on mixtures of crystal oil with propane and butane, and on several crude oils; and by J. A. Davies (M.S. Thesis in Chemical Engineering, C.I.T., 1936) upon ethane-crystal oil mixtures. The cri tiea.1 constants of ethane have been determined by this laboratory to be 718.1 pounds per square inch and 0.07553 cubic feet per pound at 90.6°F. 11. ll11.250 J/ l.000 ---- ...,...0.0164 I (,).J~ 1-- > u I I I 0.750 I ~~ 0 0.500 70 80 90 TEMPERATURE Figure 3. 100 t-- 110 120 °F Specific Heat of Ethane in the Critical Region at a Constant Volume near the Critical Volume . • 12. The tempere. ture was located by reference to the P-V-T dat::i,, and was found to be 90.5°F. At this point the liquid. phase disappears completely, and the specific volume is equal to the specific volume tabulated for the satursted gas. Because essentially the vaporization process has been com- pleted, it is expected that the single-phase specific heat will be smaller than that for the two phases. 1 This is substantiated by the equa.tion above • The experimental values dropped rapidly in this region and confirmed the temperature and discontinuity calculated. It should be noted that a break in the curve might also occur at the same temperature for another value of specific volume at which point saturated liquid would completely fill the bomb after having expanded to take up the volume previously occupied by gas. These relations may be indicated gra,phically: T Curves for the isobaric specific heats of propane, n-butane, and n-pentane have been published by Sage and Lacey, and in the foregoing reprint. If the experimental data alone are used as a basis, the sh8.pe assigned to the curves is somewhat axbitrary. A plot of the nature of Figure 5, correlating values for the homologs of the paraffin series, indicates the true curvature rather closely. The curves shown in Fig:ure 4 were plotted on the basis of this correlation and fit the experimental l The pressure deriva tive along saturation is greater than that at cons tent volume for the superheated gas. The thermal ex pans1on • f or th e saturated vapor is negative. 13 . Cp 6 PARKS & HUFFMAN 0. 5 ~;:....>=::;;;;i::.:;.::::::::~..:::J------+--__..j_::0~A•.: :_:_.P::_ 1. ~37+--_____..j 0 200 150 100 50 TEMPERAnJRE ° F. Figure 4. Isobaric Specific Heat for Coniensed Liquid adjacent to Bubble Point. Dotted curve for Propane shows values predicted from Figu111e 5. Values are for straight-chaih hydrocarbons. 0 .7 I I c, I I I I I 0.6 0.2 Figure 5. 0.4 0.6 0.8 Isobaric Specific Heat for Condensed Li quid for Normal ilkanes of from 3 to 10 Carbon atoms. 14. points well. The smoothed values tabula ted in section IIc likewise show this curvature. Low-tempera ture specific hea t determinations have been made on l propane and butane by Dana and co-workers, and on all the normal alkanes :a of four to twelve carbon atoms by Paxks, Huffman and co-workers. The agreement between Dana's values and ours is shown in Figure 8 of the paper by Sage and Lacey. The data of Parks and Huffman are plotted in Figure 4 of this thesis, showing excellent agreement for butane and pentane. The deviation for values of decane is a.bout equal to the sum of the experimental uncertainties (2 percent), indicating that the true va.lues probably fall between the two sets of data. This fact has influenced the location of the curves for decane. Data for the mixtures of propane with butane and with pentane are published in the reprint. For three mixtures of butane a,ncl pentane and two mixtures of pentane and decane, the experimental values did not ind.icate that the solutions were ideal. The agreement with theory in the case of mixtures of propane with pentane and with crystal oil indicates that the deviation in the other mixtures investigated is probably due to experimental inaccuracy. c. Correlation of the Data Each member of the homologous series of normal aliphatic hydrocarbons differs from the next in its physical properties by an increment which is some progressive function of the size of the molecule. The properties of a mixture of two widely separated components always fit into the series fairly near the point represented by the 11 molar 11 weight of the mixture. The isobaric specific heat of the bubble-point liquid shows this cha.racteristic gradation, both when plotted against temperature (Figure 4) and when 1 Dana, Jenkins, Burdick and Timm, Ref. Eng.,~, 387 (1926). 2 {For heptane) Parks, Huffman and Thomas, J . .A.C.S., .§g, 1032 (1930); for pentane) Parks and. Huffman, J.A.C.S., _§g, 4381 (1930); (for all others) Huffman, Parks and Barrnorei J.A.C.S., ~' 3876 (1931). 15. shown one. reduced temperature l plot (Figure 5). ' Ideal solutions may be assumed without loss of accuracy as compaxed to the experimental specific heat data available. Correlations of da.ta consist of generalizations which allow the prediction of behavior from a minimum of information. In the preceding section, there was mentioned the use of Figure 5 in approximating the true curva- ture for the plots of Figure 4. This section will describe two bases for prediction of specific heat values, by means of the Theory of Corresponding States and by use of an empirical equation derived by the author to fit the curves drawn through the experimental data obtained. In its most literal interpretation, the Theory of Corresponding States establishes the reduced temperature and pressure scales as coordinates upon which the specific or molal values of a certain property for all members of a homologous series may be shown by a single line. Reference to Figure 5 shows that strict application of the theory is inadmissible. At the same heat time predictions can be made of the isobaric specificAthroughout the range of composition and tempera tu.re shown, to an accuracy of within 3 percent, by extrapolation of the experimental values on the basis of this theory. The soli d lines have been fitted to the actual data; the 'broken lines are extrapolated. Ordinarily, the theory applies best in the critical re gion. For these curves the accuracy of extrapolation is not improved because Cp becomes infinite at the critical point. This is shown thermodynamically by reference to the First Law expression: + l The reduced' temperature is obtained by dividing the absolute temperature by the absolute value of the critical temperature. The values of the critical temperature for the series through octane wer e taken from the International Critical Tables (.~, 248). For nona.11e and decane, the temperatures were estimated from charts by Warren K. Lewis to be respectively, 597°K. (616°F.) and 625°K. (665°F.). 16. The critical point is the upper limit of the two-phase region, throughout which the thermal expansion is infinite. The critical isobar on the tem- perature-volume plane thus becomes tangent to the dome. Previous to the initiation of this research project, little experimental work had been done on the range of materials and at the temperatures shown in Figure 4. Empirical equations 1 for heavier oils do not apply ' by better than 10 percent to this region. An equation for the range from 3 to 10 carbon atoms and from 600F. to 160°F. has been derived empirically. It includes linear and quadratic terms in! to account for the curvatures, and a power function of the molecular weight to explain the separation of the curves. While the function :a used is arbitrary , it is improbable that this llOillber of parameters can . be used in a more satisfactory form than that obtained. The expression takes the following form: CI p:il Mis the molecular weight of the compound or mixture. The average deviation 3 from smoothed experimental curves is 1 percent, the maximum deviation about twice that amount. This equation may be extrapolated back linearly from 60°F. to 0°F. with about the same accuracy, the quadratic term being omitted. 1 Bureau of Standards, Misc.Pu.bl., .[Z, 26 (1929). Also Fortsch and Whitman, Ind. Eng.Chem., 1§, 795 (1926). These expressions cover a wide range of ma.terials, both paraffins and naphthalenes, with an average deviation of 2 percent over the temperature range from 50°F. to 4300'.Ji1. Specific heat is given as a. linear function of the temperature, and the composition vaxiable used is the specific gravity at 60°F. 2 It is entirely possible that future developments in the structura.1 theories of matter will lead to the derivation of such correlative equations, leaving only the coefficients to be determined experimentally. 3 The calculated points are compared with the most reliable values in the table on page 17. 17. ISOBARIC SPEC U1 IC HEATS OF NORW.AL ALIPHATIC HYDROCARBONS For Condensed Liquid Adjacent to Bubble Poiht Smoothed experimental data ire shown. Parenthetical values are calculated from the equation: I CP:8 4 2 = 0.490 + 0.0006t + M"9 (380,000 + 66 (t-60) ) PURE COMPOUNDS 190°a 220°a (. 757) 160° .888 (.867) .600 ( .593) .632 ( .630) .668 ( .678) .709 (. 736) .756 (. 804) .546 ( .546) .565 ( .568) .587 (.594) .610 (.624) .636 (. 659) .660 ( .697) .530 (.533) .546 ( .551) .564 ( .569) .583 ( .587) .604 (.605) .627 (.623) .734 (. 745) .809 (. 833) .906 (. 939) 70° .624 ( .635) 100° .674 (.680) Butane .572 ( .567) Pentane Dedane Prope.ne 130° .750 SOLUTIONS 47.1% c~ (by weig t) .598 ( .591) Propane-Butane .640 .682 (. 624) (. 676) Propane-Pentane 24.2% c:t18 .565 (. 557) .592 ( .582) .620 ( .614) .654 (.654) .702 (. 702) 48.4% .583 ( .574) .616 ( .602) .653 ( .644) .702 (. 698) (. 765) .609 (.605) .654 (. 642) .705 (.701) .792 (.783) .961 b (. 887) 79.16/; .778 a The empirical equation of fit was derived only for tempera tures of 160°F. and below. b The difference between the experimental and calculated values for this point is due mainly to deviation from ideal solution. Refer to Figure 7 in the reprint. 18. The exponent of the molecular weight was found more accura tely to be 3.50 + 2 0.0002 (t - 85) • as is desired. This was rejected as too unwieldy for such a correlation Use of this exponent would require recalcula tion of the - - coefficients of Mand the quadratic int. • Specific heat data for the more volatile liquids in the series of normal aliphatic hydrocarbons are now known with reasonable accuracy throughout a wide temperature range. Further experimental work in this field may be most advantageously directed toward the development of more accurate experimental methods. 19. III. HEAT OF VAPORIZATION OF ISOBUTANE a. Theoretical Considerations Accurate pressure-volume-tempera,ture de,ta. are the most usual source of values of the latent heat of V&-poriza.tion. These may be ce,lcula ted by an application of the Second Law of Thermodynamics to give the rel ation known as the Clapeyron equation: Calorimetric measurement of t he heat of vaporization provides a serviceable check upon the physical data. Frequently the volume of the saturated vapor can not be accurately obta ined from the measurements in a compression tube because of adsorption effects ana. the difficulty of attaining complete equilibrium In such cases an independent det er mination of the heat of vap- orization is of use in calcula ting the enthalpy, entropy and speci f ic volume for the dew-point gas. In the limiting case of very small vapor pres sures, the dew-point volume approaches infinity. then negligible. The volume of the bubble-point liquid is Perfect ga s laws may be assumed, with the introduction of the specific gas constant l• = Thus, in the limiting case, =- - h d J,,, pe d (;) Experimentally the slope of the logarithm of vapor pressure against reciprocal absolute temper a.ture has been found to be nearly constant under these conditi ons. Thus L will approach asymptotically to a limiting V maximum value as the tempera.tu.re is decreased. As the temperature in- crea ses, the l a tent heat becomes appreciably smaller because of the contribution of the liquid volu~e, and the deviations of the vapor from a perfect gas. 20. At the critical point the phase boundary has disappeared, the specific volumes of gas and liquid are identical, and the heat of vaporization must vanish. The slope of the latent heat plot near the critical tempera- ture may be evaluated in terms of the physical properties and is found to have very large negative values: LV F( v =- l> - vet) + Of these three difference terms, the first two vanish at the critical point. The thermal expansion of the dew-point vapor becomes negatively infinite, while that of the bubble-point liquid goes to infinity in the positive direction. These are the slopes along the saturation curve on the volumey IQ'. V L~ 9 v.,'ci temperature plane. T This knowledge of the behavior of the heat of vapor- ization at low tempera tures and ih the critical region is of use in fitting a curve to the experimental data. Essentially, the experimental determination of latent heats of vaporization consists in maintaining isothermal conditions, adding a measured amount of electrical energy, and weighing the guantity of material which has vaporized. If the hydrocarbon under investigation is held in a constant volume, not all of the material vaporized is removed from the boundary of the system. A volume ju.st equal to that of the liquid which has evaporated is now filled with a.n additional quantity of gas. The experimental values 2L must the r efore be corrected as shown in the equ a tion: w ( (+ ) An additi onal correction must be applied to the quantity of heat measured if the tempera tur es a t the beginning and end of the run axe not identical. From the observed input, the product of the temperature rise by the avera.ge heat capacity of bomb and contents must be subtracted. The best recent ex:tBrimental determinations of latent heats of vaporization have been made at the Bureau of Standards 1 2 and the Linde laboratories. The latter investigation was made at temperatures bet ween 0°F. and 50°F. a..~d included the two butanes, on which measurements have been made in this investigation. T'.ae values of Dana and co-workers have been of as sistance in shaping our curves, and will be shown along with our points on the plots of the next section. b. Experimental Methods The calorimeter described in part II, used for specific heat measurements, was converted into an instrument suitable for the measurement of hea ts of v aporization. The extent of the auxiliary equipment installed may be seen by comparing Figure 6 with Figure 1. A vapor line was sealed into the bomb, brought out through the wall of the vacuum jacket and through a motor-operated valve to a manifold which could be opened to a receiving bomb thermostated by an oil bath. One arm from the line bet ween the bomb and the valve led to a mercury trap, which was connected by an 3 oil line to the l aboratory's pressure balances. 1 2 3 Osborne and Van Du.sen, Bur. Stan. Bull., 14, 439 (Sci.Paper No. 315) (1918). Dana , Jenkins, :Burdick and Timm, Ref.Eng., 111, 387 (1926). Pressure readings could have been ta.ken to supplement the temperature readings. Actually they were made only when testing the assembly for leaks by filling with air at pressures around 400 pounds per squaxe inch. Pressure measurements will be more necessary in case this calorimeter is adapted for investiga tion of heats of solution. 22 . M i- I V - " I AIR - - OIL VAC -~ --- -- - v!~ I, -~ I< I<: I< I<: .,.> > > > \~ VAPO RIZATION ASSEMBLY Figure 6. -up 23. Figure 7. Condensation Assembly. The steam-jacketed vapor line comes down at the left to the pressure trap. Steam outlet lines are also shown. A lagged vapor line goes to the right, leading through the throttling valve, which is also jacketed. The valve is operated by the direct-current motor, the spur gears, and a friction clutch. A long-necked w~i ghing bomb is attached by a standard fitting, its temperature being controlled by the thermostated condenser bath. The valve opening to vacuum is shown between the receiving bomb and the agitator motor for the bath. Behind the motor is the mercury agitator, enclosed in a brass jacket. 24. The bomb instailed was the one previously used for low-pressure specific heat measurements. of the bomb. The diaphragm valve was removed from the top A 1/16 inch tube of stainless steel was doubled, the two arms were soldered together, and the tube was seaied into a fitting which was threaded into the top of the bomb. The tube was soldered onto the end of a 1/8 inch copper tube, around which was fitted a 1/4 inch copper tube; saturated steam at about 280°F. was introduced into the outer line to prevent condensation of the vapor. The trap, the motor-operated valve and connecting lines on the outside wall were also heated with steam, as is indicated by diagrammatic jacketing in Figure 6. Control of the rate of flow was needed to maintain isothermal conditions within the bomb, electric heat being added at a constant measured rate. The tempera ture of the bomb and the differential temperature be- tween the bomb surface and the oil bath were whown by light beams ~eflected from high-sensitivity galvanometers onto ground-glass millimeter scales. Vapor flow was regula ted by variation of the opening of the throttling valve, by means of a t wo-way switch installed on the potentiometer bench • in front of these scales. The pressure differential had to be adjusted carefully, and was established by manual adjustment of a mercury regulator which thermostated the oil bath condenser surrounding the receiving bomb. The difference in temperature between the calorimeter jacket and the condenser bath was measured by a thermocouple and was indicated by an additional galvanometer beam on the control bench. The throttling valve was operated by a 100-volt direct current motor rated at about 40 watts. The direction of the motor (and of the current) was governed by means of two relays actuated by two separate 110-volt alternating current circuits either of which coul d be closed by the switch on the control bench. The motor was connected by the spur gea.rs shown in Figure 7 to a friction clutch on the valve stem. 25. Figure e. :alorimeter, sh~ -dng onb n.nc ste:~ n-jr cketed ve.:s,or line. Figure 9. Interior of the Calorimeter. heater and thermocouples are shown. Leads to 26. The outlet tube from the bomb led from the vapor space through the liquid in order to avoid entrainment of liquid and superheating of the vapor before leaving the bomb. Liquid which might have been condensed in the bend of this tube was removed by making a short run to vacuum before each vaporization measurement. The amount of superheating was found to be neg- ligible on a trial run in which the bomb thermocouple was removed from the well and was mounted on the outlet tube just above the bomb; fluctuations in its tempera ture were compared with those of the bomb surface relative . to that of the Jacket l the bomb temperature. and were found to vary not more than O.Ol°F. from The variation in the bomb temperature was therefore recorded for each run as a measure of the superheating. Maximum devi ation during accepted runs was less than 0.1°F., and integrated averages were around 0.03°F., a difference too small to require correction of the heat content of the vapor. Leaks through soldered joints and valve packing presented a major difficulty in putting the apparatus into operation. These could be de- tected by a continued drop in the observed bomb temperature of the order of O.Ol°F. per minute. Since on experimental runs heat was added for 20 to 30 minutes, it was impossible to compensate or correct accurately for any loss of material. Finally all leaks were found and sealed. c. Data Obtained After numerous experimental difficulties had been overcome and the apparatus was in the form described above, four runs were made upon normal butane. The agreement with the values obtained by calculation from phy~ sical data is evident from Figure 10. workers are also shown. Points obtained by Dana an d co- ]ecause of the good agreement, and because the remaining data for n-butane were ready for publication, no a dditional work wa.s done on this compound. Twenty measurements were then made on isobutane, thirteen, of these 1 The oil bath surrounding the jacket was maintained at constant temperature by means of a potentiometer circuit operated ·by a thermocouple between the 27. ai _J a: "'a. :i ,-: ai z 0 "" --"--~ 150 ~ -~ r------ 125 r------ j:: <!. ' N ci. 0 a. ~ L._ 0 ~ "'I 100 ~ - - VALUES REPORTED - - - - CLAPEYRON EQUATIO N - 0 DIRECT p OA~A ET AL MEASUREMENT 75 100 125 150 TEMPERATURE Figure 10. ~ I 175 200 225 °F Latent Heat of Vaporization of Normal :Butane. 28. points giving the agreement shown on the large-sea.le plot of Figure 12. The points rejected were in most cases known from observed experimenta l conditions not to be trustworthy. The shape of the curve plotted was ob- tained by reference to the critical behavior and to Dana's points, as shown in Figure 11. Relative accuracy of the plotted curve is within 0.3 percent, and the probable absolute deviation is not greatly in excess of this amount. In the case of isobutane, the latent heat measurements were much more reliable than the values calculated from the physical data, and indicated errors of several percent in the l atter. l (p.26) oil and an ice bath, actuating the photo-electric -circuit for control of the heat added to the oil bath. Small fluctuations in the bomb temperature made the differential temperature unsuitable for control. 29. ~ ai _j ~ [5120 ~ Q. ::i I-' ~ ', ai 1- 80 '' ''' <{ w " I 0 DANA ET AL '' - ' A.P.1. 37 1- z \ '\ \ \ ~ 40 I I <{ I _j I I I I I 100 50 150 Figure 11. a: lt ::i 130 ai ~ ~ ~ G" 0 t-' 120 ~ 1z w I- <{ _l ~ 110 I"._ 0 ~ 100 150 125 TEMPERATURE Figure 12. °F. Eatent Heat of Vaporization of Isobu~ane. 140 ~ ai _J 250 200 TEMPERATURE 175 °F. Latent Heat of Vaporization of Isobutane. 30. ACKNOWLEDGEMENT The American Petroleum Institute gave financial support to this investigation under its Research Project 37. Professor William N. Lacey, director of the project, has helped the writer to obtain the theoretical background necessary to carry on the work. Dr. :Bruce H. Sage has dis- played a continued active interest in the measurements taken, and had a large part in the development of the equipment used. Donald C. Webster also worked on the design and generously assisted in teJdng photographs of the apparatus. Miss Jeanne Thomson prepared the typewritten copies of this thesis which are submitted. Working under the National Youth Administration, W. D. Yale, B. W. Dunbar and D. C. Nellis contributed in the insta1lation and maintenance, and F. H. Moore traced several of the drawings. To all of these the author wishes to convey his appreciation.