The Pressure-Volume-Temperature Relationships of Propane Citation Nellis, Donald Charles (1938) The Pressure-Volume-Temperature Relationships of Propane. Master's thesis, California Institute of Technology. doi:10.7907/0vyq-6m71. https://resolver.caltech.edu/CaltechTHESIS:12102024-214146715 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): Sage, Bruce H. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1938 Funders: Funding Agency Grant Number American Petroleum Institute UNSPECIFIED Record Number: CaltechTHESIS:12102024-214146715 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:12102024-214146715 DOI: 10.7907/0vyq-6m71 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16914 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 11 Dec 2024 00:06 Last Modified: 11 Dec 2024 00:16 Thesis Files PDF - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

THE PRESSURE-VOLUME-TEMPERATURE RELATIONSHIPS OF PROPAME Thesis by Donald C. Nellis In Partial Fulfillment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena~ California 193g Introduction: To establish further the thermodynamic behavior of paraffin hydrocarbons, a study has been ma.de on the naturally occurring substance propane, a material which has already been considered along these lines to no small extent (6)*. Data of the type presented in this paper are of considerable use in many fields and particularly in natural gasoline practice. It is hoped that this new and more exact knowledge of the behavior of propane Will prove of direct value not only to industry but also to those interested in the study of the thermo~rnamic properties of materials from the theoretical point of view. The data presented include the pressure-volume-temperature relationships of propane and the corresponding compressibility factors. .Also given is information concerning the two-phase boundary conditions, and the results from a speci.al stu.dy in the vicinity of the critical point. The range covered in the work comprises that between 70°F and 520°F and the pressure interval from atmospheric pressure to· 3500 pounds per square inch. Expe~imen~~: The experimental data utilized in the derivation of the properties presented here come from three distinct and separat e sources: the Chemical Engineering Laboratory of the Calif ornia Institute of Teci'..nolo~; the Research Laboratory of Physical Chemistry of the Wiassachusetts Institute of Technology; and the Laboratory of the Linde Air Product s COlI!PallY, Buffalo, New York. * See literature citations at the close of the discussion. 2. The California Institute Laboratory, with which this writer has been associated, in its experimental work used propane obtained from the Phillips Petrole'U!Il Company. This propane was purified by fractionation in a glass col umn pac..'ced with glass rings of the type developed by Young (9). The work done at this laboratory on the propane was carried out on four separate experimental. set ups , and led. to the following quantities! pressure- volume-te~erature relations, Joule-Thomson coefficients, specific heats at constant pressure, and latent heats of vaporization. The pressure-·.,olilllle-temperat-ure work was done in the variable volume cell employed by Sage et al (7) in previous experimenta on eydrocarbons. A recent change in the apparatus has been the installation of a four- junction thermocouple of consta:ntan and copper to c ontrol more accurately the temperature of the oil bath, and a mu.lti-lead, single- junction couple of the same ty:pe to measure the temperature existing in the bomb. These calibrated thermocouples are accurate to two hundredths of a degree. Isotherms on r egion propane were run in the condensed liquidJ\ and some distance into the twophase region at intervals of 3o~F. In the critical area, isothermal runs sepE!,I"ated ,by 5° were made in order to observe more closely the behavior existent in that region. Two runs, one at 190° and the other at 220°F, were also made on the superheated gas to serve as the basis of calculation of the vol'llmes in the entire superheated region. (Adsorption of the superheatE:d gas on the walls of the apparatus at teIIJ>eraturas lower than 19()°F was found to be an iIIJ>ortant factor; hence, direct measurements of the vol-wnetric relationships in that area could not be ma.de. ) For the condensed liquid work the temperature range from 70°F to 250°F was coverad, up to pressures of 3500 pounds per square inch. 3. A recent publication in the series of articles on the subject , "Phase Equilibria in lzy'drocarbon Systems" (4). describes the Joule-Thomson apparatus employed at the California Institute Laboratory to obtain the data necessary for the determination of the Joule-Thomson coefficients of superheated gaseous propane. The values presented in that paper have been used in the calculations attendant on this work. Another of the above-mentioned series of publications (S) outlines the adiabatic expansion equipment used to measure the specific heats at atmospheric pressure of gaseous propane. These , together with the Joule- Thomson coefficients, offer a means of calculation of C * throughout the p superheated gas region as explained in reference (4). The adiabatic calorimeter of Sage and Lace'J (5) afforded a direct measurement of the latent heat of vaporization of propane in the temperature range lOO~F to 160°F. In additionJ measurements were ma.de on this apparatus to give the specific heat of the saturated liquid (5). The data of the Massachusetts Institute of Technology (1) (Beattie and co-workers) gave the pressure-volume-temperature information fo1· propane in the range of temperatures from the critical point to 527°F, and specific vol1lIIles from O. 036 to O. 36 cubic feet per pound. This work, however, extended down only to pressures in the neighborhood of 500 poim.ds per square inch. This same laboratory made a special study of the region in the immediate neighborhood of the critical point (2), and ari•i ved at certain conclusions as to the values of the critical pressure, temperature, and vol'Ullle of propane. * See Nomenclature. 4. Investigators at the Linde Air Products Compacy Laboratoey (3) have determined the vapor pressure of propane up t o 120°F as well as the latent heats of that substance up to 70°F. Calculations: The condensed liquid region of propane was established in ~ vol'Ul!letri c behavior on the basis of four sets of runs, ma.d.e at the California Institute laboratory. These experimental values were plotted at constant temperature against pressure, smoothed, and then cross-plotted ~t constant pressure against temperature. The maximum deviation 4 t-ae ~ of the experimental points from the corresponding finally accepted values was not more than 0.2%. From these runs good vapor pressure data were also obtained~ below 190°F. Figure 1 is a plot of volume against pressure for the condensed liquid. The pressure-volume-temperature relationships in the superheated gas inacc11ra cy region had to be attacked indirectly because of the ~ of experimental data in that area, due to the difficulties mentioned above. of the relationship { 1:JT = -;II already referred to (4) , and O p Cp However, use is made employing the Joule-Thomson data calculated from the recent values of 0 p at atmospheric pressure (8) and the Joule-Thomson coefficients by progressive !)T as computed was smoothed against temperature and pressure and ( ~7, calculated from the relationship liVP = -t! ijT :Ta • After pl~ttl.ng (~,4 against both temperat=e approximate integration (4). (~ and pressure to smooth, an integration was ma.de . This was carried out employing the values of 6?. (the compressibility factor), calculated at 220°F, fr om the volumetric isotherms previously mentioned, as a bas i s. These integrated 0.05 ai 0.045 _J a: w a. >-' L.. 0.040 j u w :; ::, _J 0.035 0 > 0.030 400 800 1200 · 1600 PRESSURE Figure 1. LB. PER 2000 2400 2800 SQ. IN. Volumetric Behavior in the Condensed Liquid Region. 5. ~ valuesv wh ich were found to give a consistent set of data, are plotted in Figw-e 2. Ha~ing these values of the compressibility factor it was then an easy matter to calculate the cor:cesponding volumes from the primary definition of -c ( i!: = P;J:) . The accuracy of these volumes and a?- , s naturally depends entirely upon the values of /.,/ r · and C p atm employed in the early calculation as well as the validity of the two isotherms at 190°F and 220°F, vmich served as a basis for the integration. It is probable that the maximum . inaccuracy f or the volumes and r'J in the superheated gas region is no t more t han 0.5%. Since the overlapping of the data of :Bea.ttie, et al (1), which extends down to the critical temperature (206e3°), with that done at the California . . it Institute, is only slight from the point of view of temperature> and,..was, in addition, close to critical where the change of volume with pressure and temperature is great, some difficulty was encountered in fitting the two sets of data together. However, by suitable cross-plotting they were effectively joined and a smooth overall effect obtained. Values of .z were then calculated from these voli.1111es 1 up to 2000 pounds per square inch , and plotted, ince z at pressure equal to zero .is unityD these curves of ~ versus pressure at constant terrperature were drawti t o ,mity at zero pressure. This bridged the gap in the pressure range O to 500 pounds per square inch for temperatures above 2B0°F. whellJno data were available. These extrapolated values were assumed temporarily to be correct. Values of t} for these curves of -c against temperature were obtained graphically and smoo~hed. (1i) T was then calculated from the relation; 0.9 0 .8 0.7 :,;Ifi;'.cr " N 0.6 0.5 600 PRESSURE Fi gure 2. 700 LB. PER SQ. IN. Compressibility Factor in the Superheated Gas Region. 6. Above 1500 pounds per SQ.ua.re inch and the critical temperature9 and throughout the condensed liquid region. ( { -i)p was obtained graphically. smoothed and (: H) , These values of /4l::.) from i_J T/ p I} T This q"Ua.D.tity wa.s = derived :from the eqp.a.tion, f a I! ) V - /. e '{_~ T • \tf WT \ o T/ p T were then plotted with those obtained as above ct!) and smoothed. The agreement of the two sets of data in the overlapping area is shoVlll in Figm·e 3s To (1 :) T of the superheated gas region these smooth values were joined by a process of smoothing and CDoss-plotting putting the emphasis from the point of view of accuracy on the former. There was a somewhat Jll&'ked change in the finally accepted values of (1~) T at high temperatures and below 500 pounds per square inch as a result of this process. This could easily be tra ced to the original extrapolation of the high tenperature curves o:f a versus pressure to zero press"Ure. such as could be expected in the values of rather large discrepancies from accuracy of ~ Small errors, from such a method, made for (~) p and, hence9 (1 ~) T at these low pressures. These smooth and now assumed correct values of ~ ~) T from 22oci to 520«, and from 0 to 800 pounds per square inch were used in the calciJ.lation of new (If./2 quantities fo1• this region. An integration was carried. out on these to obtain the correspondi~ e 's, using a~ at 220,i;, 'Up to 500 po1.lllds Above that pr essure .zJ at 310° were employed., r ef erence to a pressure of 800 pounds per square inch. These~values at 31ocr were per square inch as a basis. obtained by connecting the new values at 310°F below 500 pounds pressure with the previous values above 1000 pcrunds at 31o~F. This procedure had . ~~ t the overall effect of establl.shing the l ower pressure Mel all the way o 520@F and satisfactorily connecting it with the previously derived volumetric data in the superheated gas region. 1000 1200 1400 PRESSURE Figure 3. 1600 1800 2000 2200 LB. PER SQ. IN. in the High Teirg? erature Region. The next step was the calculation of e for pressures above 2000 pounds per square inch at temperatures above critical and for the condensed liquid region. The entire compressibility factor picture for pro- pane could then be pieced together except for a small r egion around the critical point. A thorough smoothing and cross-plotting process having been gone through f or the whole, with the above exception, it could then be said that vol'll11les might be calculated with as much accuracy as could be expected z from the corresponding Tbis was done and the volumes obt ained are values. presented as final results in the tables. The ac curacy from 250° to 520°F below 500 pounds per square inch is of the order of 0.5% and above 500 pour1ds per square inch of 0.2%. The vapor pressures of propane, which were used in the calculations in the superheated gas region, were taken at low temperatures from the ~ta of Dana and colleagues (3), above 70°F from a composite of the values indicated by four different sets of California Institute runs, and at the critical state and immediat ely adjacent thereto fr om the work at the Massachusetts Institute Laboratory (2). These three independent sets of data were plotted together and found to agr ee well as shown in Figure 4. Points were read. off this curve at even temperatm·es and called for the moment P'. was then used to smooth these E, = P the 1 - P 1 , where _!: 11 ideal II P1 A mathew.atical points effectively. method Tha relation is the residual vapor press'Ul'e and log10 PI (PI vapor pressure at temperature • t) equals b a - T • is Here the If value of 11 a 11 was taken as 5.47211, I\ 11 b 11 as 1788.132. The residual vapor pressures so calcu.lated were plotted against temperature and smoothed, the srr:.ooth value ~ being calcv.lated back to give the finally accepted vapor p1·essures . 7 I O CIT .o, LINDE 7QQ I - - - - 9 MIT C R ITICAL -- P_ 6 00 ~ 0 50 0 I Ul a: w a. ~ 40 0 w a: :::, Ul Ul w a. a: 30 0 / 200 100 ~ V 40 / V I I V 80 120 TE MPERATURE - Figu:t' e 4. 160 O 200 F. Va;por Pressure cwve 8. AS mentioned previously the critical region is a difficult one to establish because of the fact that the change of volume with temperature and pressure is so greatn being infinite at the critical point itself. Howevers advantage was taken of the fact that plots of pressure against temperature at constant volume are nearly straight lines. Curves of this the s tate nature we1·e drawn for the area near" critical~ using as their basis the published Y.iassachusetts Institute data (1,2), three sets of runs at the California Institute, and the established data at states farther removed from critical. The plot covered the range of pressure from 4oo to 14oo pounds per square inch and of temperature from 160° to 370°F. These curves were smoothed and vah1es read f r om them . were accepted asfinala shows the nature of the plot obtained. calculated. Corresponding Figure 5 e ~ were also Of much material aid in establishing the two phase boundaries in the vicinity of the critical point was a plot of the average density of the two phases against temperature which is very nearly a straight line f1&BetieB as shown in Figure 6. l3y this means a value of the critical vol'UID.e of 7.199 cubic feet per pound was derived as compared to the value proposed by Beattie et al (2) of 7.093, who claimed one per cent accuracy. The critical pressure (617.4 pounds per square inch) and critical temperature . , ...s,. (206.3@F) of these investigavi:OBtS were accepted. This procedure filled in all that remained unknown as to the volumetric behavior of propane. The accompanying tables present the data along with the corresponding values of the compressibility factor 2 . Values for the two phase bo'Ulldary conditions are given as well as vapor pressures. Figure 7 is a plot of the compressibility factor over the entire region studied. The volumetric ~ehavior in the critical region is shown in Figure 8. z d <I) CI w a. ai 700 ...J W· CI :::, <I) <I) w CI a. 200 210 220 230 TEMP~RATURE Figure 5. 240 O 250 260 F. Pressure-Temperature Diagram at Constant Volume in the Vicinity of the Critical Point. ~ 2e ~' 0 ~ 0 24 "' ~ 20 I\ er w a. ~ 16 i----- ~ 12 \ --- __rCRITICAL ) e 4 L--- W 100 ' 0 130 .'/ 190 160 TEMPERATURE Figure 6. / O 220 F. Density of the Two-Phase Eoundar ies. i2\f'. a: II N PRESSURE Figure 7. LB. PER SQ. IN. Compressibility Factor-Pressure Diagr~ 500 Figure 8. 550 600 650 700 PRESSURE LB. PER SQ . IN. 750 800 Specific Vol'Wne-Pressure Diagram in the Vicinity of the Critical Point. 9. Latent Heat of Vaporiza.tio!f,: The latent heat of vaporiz a tion for propane f r om 70°F to the cr:i.tical temperature wa s calculated by making use of the Jlapeyron equat ion: L•A if,(~) 'H-. J,t'f. In addition, values of the latent hea t. eniploying a s a reference the Clap eyron value at 70°F , were computed by graphically integra ting the exoression : AL .. .., - ,, I ~ r..p· r(~H:.\ LI fr).f~-j•' -( 0 1-1.) re/Jn-.1;,. ]th) (C l<>+ ~,+. + , ld-:J., - Ct> ilJ elt- let-. ,..,.) These two sets of latent heat values are plotted in Figure 9 a long wUh the values of this quant ity eXperiment ally mea sured by the Linde Laboi·a tory and the California Institute. Sumnarz: The pressure-volume-temperatu.re relations of propane have been est abllshed for the r ange of temperature from 70° to 520°:E' and of pressure from a tmospheric pressure to 3500 po,l11ds per square inch. The corresp onding corm_.?ressibility factors h ave been determined and a special study in the vicinity of the critica l st a te has been made. The accura C"'J of the tabula ted values in the condensed liquid region is 0.1%; in the s1.1perhea ted gas area 0. 5%; and in the critical region , 0.5%. Above the critical temperatur e, the accuracy i s O. 5% below 500 pounds per square inch pressure and 0.2% above that pressure. The vapor pressures are accur a te to a probable 0.3 pound per square inc.ii. When published these dat a will be included with those for the enthalpy and entropy of propane under corresponding conditions which will be ca lcula ted by this writer. -0--0-0- 125 ai ...J a: w 0. 100 ::i r: [lJ !;i: w 75 I I- z w !;i: _j 50 25 o C.LT. -0- LIND E 9 CLAPEYRON 8 INTEGRATED 60 VALUES 100 Figure 9. 180 140 T EMPERATURE O F. Latent Heat of Vaporization. 10. Ac]cnowledgments: This study was made possible through the financial assistance of the American Petroleum Institute a s part of the extended program of Research Project 37. I wish to express rw personal thanks to Dr. B. H. Sage for his encouragement and technical a ssistance in the preparation of this paper. Much credit is due to J ames Reynolds who made some of the experimental runs and to Louise Reaney who helped in many of the calculations. 11. Nomenclature b Gas constant per pound(= 0.24319 for propane) Cp Specific heat at constant pressure (Etu per pound per OF) H Enthalpy (Etu per pound) L Latent heat of vaporization (Btu per pound) M Y~leci~lar weight (44.06 for propane) P Press,ira (pounds per square inch) PI "Ideal II vapo1· pressure 1: Residual vapor pressure R Gas constant per pound mole (= 10.715) t Temperature, degrees Fahrenheit, °F T Temperature, degrees Rankine, V Specific volume (cubic feet per pound) _._ facto"~ (- .TIM) Compress1•b"1.l"1~y RT Joule-Thomson coefficient 0 R (= t°F + 459. 6°) 12. Literature Cited (1) Beattie, James A.• Key, William C., and Kaminsky. Joseph, J. .Am. Chem. Soc. a ~ ' 1589 (1937). (2) Beattie, James A., Poffenberger, Noland and Hallock, Canfield, J. Chem. Phys., l, 96 (1935). (3) Dana, L. I., Jenkins, A.C .• Burdick, J. N. and Timm, R. c., Refrigerating Eng., 12, 387 (1926) (4) Sage, B. H. 9 Kennedy, E. R., and Lacey, W. N., Ind. Eng. Chem., ~. 601 (1936). (5) Sage, B. H. • and Lacey, W. N., Ibid., £1.. 1484 (1935). (6) Sage, B. H., Schaafsma, J. G.. and Lacey9 W. N., Ibid., 26, 1218 (1934), and literature cited (7) Sage. B. H., Webster. D. c.. and Lacey, W. N., Ibid.,~. 658 (1937). (8) Sage, B. H., Webstera D. C., and Lacey, W. N., Ibid.,~. 1309 (1937). (9) Young, W. G., and Jasaitis, Z. , J. Am. Chem. Soc.9 ~, 377 (1936). TABLE I SPECIFIC VOLUME OF PROPANE Superheated Gas Region Cu. ft. per lb. Pressure 700 100" 130~ 160° 190"' 2200 2500 28010 F' 14.7 s.629 9.142 9.651 10.158 10.662 11.164 11.668 12.169 25 5.013 5.322 5.628 5.932 6.. 234 6.532 6.830 7.127 50 2.428 2.594 2.756 2.915 3.071 3.226 3.378 3.530 100 1.121 1.220 1.313 1.401 1. 486 1.569 1.650 1.730 0.7527 0.8257 o.s925 0.9553 1.016 1.073 1.129 200 .5772 .6355 .6881 • 7371 •7836 .8280 250 .4224 .4782 .5256 .56s5 .6087 .6466 300 .3686 .4151 .4554 .4917 .5253 350 .2865 .3341 .3730 .4074 .43so 400 .2705 .3105 .3434 .3726 450 .2180 .2607 .2930 .3209 500 .1741 .2196 .2521 .2791 .1842 .2184 .2444 (lo. /•1· ;,,,.) 150 550 TABLE II SPECIFIC VOLUME OF PROPANE Condensed Liquid Region Cu. ft. per lb. 700 Press-ure lbs. per sq. in. X 200 300 400 500 600 700 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 10-a 3.195 3.178 3.164 3.152 3.140 3.129 3.11s 3.100 3.078 3.05s 3.038 3.020 3.002 2.984 2.969 2.955 2.942 2.930 X 100° 130° 160° 190° 2200 25o(!ll 2800 F' 10-a X 10-2 X lQ-B X 10-2 X 10-2 X 10- 2 X 10- 2 18.882 21.550 16 .. 959 13.468 8.606 5.991 5.090 4.697 4.463 4.298 4.176 4.074 3.978 3.. 898 3.823 3.3gg 3.368 3.349 3.331 3.314 3.29g 3.282 3.256 3.228 3.200 3.172 3.146 3.124 3.102 3.084 3.065 3.o49 3.033 3.619 3.5s1 3.546 3.519 3.. 494 3.471 3.431 3.3s7 3.350 3.314 3.283 3.254 3.. 227 3.205 3.184 3.163 3.. 145 3.969 3.s92 3.g2g 3.775 3. 731 3.659 3.589 3.530 3.478 3.433 3.395 3.364 3.334 3.308 3.284 3.26o 4.428 4.258 4.141 3.986 3.856 3.755 3.. 679 3. 619 3.564 3.518 3.480 3.443 3.4o9 3.37g 15.120 7.673 5.130 4.531 4.229 4.059 3.933 3.839 3.758 3.690 3.636 3.584 3.. 539 3.499 14.106 10.031 5.826 4.843 4.455 4.245 4.103 3.997 3.910 3.s34 3.765 3.702 3.645 TABLE III SPECIFIC VOLUME OF PROPANE High Te~erature Region Cu. ft. per lb. Pressure lbs. per sq. in. 14.7 50 100 200 300 400 500 6oo 700 800 1000 310° 34oo 370° 400C! 4300 460° 490° 520° F 14.17 14.67 12.67 13,.67 15.17 15.67 16.. 17 13.17 4.130 4.429 3.680 4.279 3.981 3.831 4.577 4.727 2.04o 1.886 2.117 2.269 1.809 1.963 2.193 2.345 1.114 0.8710 0.9129 0.9539 0.9942 1.034 1.074 1.153 .6451 .6165 .7oos .7282 .6731 .5571 .5873 .7556 .424o .4704 .4474 .5144 .4925 .3992 .5359 .. 5573 .4026 .4208 .3842 .3032 .3252 .. 43ss .3457 .3653 .2781 .2391 .2594 .3123 .3446 .3287 .. 36o4 .2955 .2124 .2460 .2614 .2298 .2762 .2906 .1930 .3048 .2091 .2234 .1583 .25o4 .1771 .2372 .1937 .2633 .. 1102 .1441 .1285 .1711 .. 1832 .1579 .1947 .2059 (All values below are x 10-2 ) 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 7.581 6.017 5• 3ll~ 4.930 4.673 4.490 4.346 4.. 222 4.118 4.023 9.161 7.127 6.080 5.487 5.109 4.855 4.660 4.498 4.359 4.242 10.59 s.271 6.921 6.. 105 5.589 5.. 248 4.99g 4.. 795 4.626 4.491 11.85 9.361 7.786 6.776 6.117 5.681 5.367 5.120 4.921 4.754 13.03 10. 40 8.651 7.472 6.683 6.143 5. 760 5.466 5.231 5.037 14.. 09 11.36 9.482 8.185 7.272 6.622 6.17g 5.841 5.567 5.335 15.09 12.24 10.29 8.891 7.867 7.13g 6.621 6.232 5.91g 5.654 16.05 13.10 11.04 9.547 8.459 7.675 7.1o4 6.656 6.289 5.. 979 TAJ3LE IV COMPRESSIBILITY FACTOR OF PROPANE Superheated Gas Region 700 100° 1300 160° 190° 220° 2500 280f!!I F 14.7 o.9s49 o.9s75 o.9s94 0.9910 0.9921 0.9930 0.9939 0.9946 25 .9731 .9777 .9813 .9842 .9865 .98s1 .9s95 .9906 50 .9427 .9530 .9610 .9672 .9720 .9759 .9787 .9s12 100 .s704 .8966 .9155 .929s .9409 .9495 .9563 .9619 .8297 .8637 .8885 .9071 . 921s .932g .9417 200 .8051 .8435 .8711 .8920 *9081 .9207 250 . 7364 .7935 .8317 .8599 .8818 .89s7 300 •7338 . 7883 .8266 .8547 .8762 350 .6655 . 7403 . 7899 .s263 .8524 400 .6849 .7515 .7960 .8286 450 .6210 .7099 .764o .8028 500 .5509 .6645 .7305 .775s . 6129 .6960 .7474 Pressure lbs. per sq$ in. 150 550 TABLE V COMPRESSIBILITY FACTOR OF PROP.ANE High Temperature Region Pr essure 1bs. per sq. ine 3100 34o~ 370° 400° 4300 460@ 490° 520° F 14.7 0.9951 0.9956 o.996o 0.9964 0.9967 0.9971 0.9974 o. 9977 50 100 200 .9s32 .9663 .9307 .8929 .8532 .8101 .7665 • 7217 .6764 .5887 .9s50 .9700 .9389 .9061 .8721 .8362 .8004 .9865 .9732 .9456 .9168 .8870 .8568 .8268 .9879 .976o .9511 .9257 .9000 .9890 .9784 .9560 • 7972 • 7682 . 714o .6560 .6149 .6003 .6052 .6233 .6503 .6812 .7130 .9911 .. 9s25 .9644 -. 9460 .9283 .9110 .8954 .8809 .8676 .8430 .8167 .7952 . 7800 .7700 • 7665 • 7728 ~7884 .8096 .8329 .. 8570 .9921 .9842 .9680 • 7646 .7284 .6608 .5889 .5498 .5472 .5643 .5912 .6242 .9901 .9806 .96o5 .9401 .9200 .9001 .8818 .8646 .8485 .8191 .7s77 . 7616 .7420 .. 7320 .7316 • 7403 300 400 500 600 700 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 .5063 .4822 .4969 .5268 .5618 .5, 98 .6385 .6768 .7150 .7524 .6591 .694o .72s6 .. 7635 "7453 •7791 .8737 .8482 .s238 .8000 .7555 .7os8 .6717 .6518 .6482 .6584 .6794 .7060 .7347 $7650 .7960 e9334 .9106 .8879 .8662 .8457 .8262 .7908 .7528 .7212 .699s .6907 .6950 .. 7099 .7322 .7580 • 7859 . 8149 .7597 • 7835 .8090 .8350 .9515 .. 9357 .9209 .9077 .s956 .8842 .8643 .8424 .8249 .8109 .8015 • 7989 .8054 .. 8200 ~8382 a8579 .s7s4 TABLE VI PRESSURE-VOllJME-TEMPER.ATURE RELATIONS OF PROPANE IN CRITICAL REGION Coll!)ressibility Factor Above Pressure (lbs. per sq.in.) below 210° 2200 0.2251 81Oel 0.2393 866.o 0.2768 1016.5 .2044 662.0 .2171 707.1 .2498 s25.s .2815 944.2 0.060 .2297 619.s .2399 651.2 .2667 734.5 .2927 818.O 0.070 .2670 617.6 .2761 642.3 .3011 710.8 .3247 778.O .37os 914.o 0.080 .3049 617.2 .3136 63s.3 .3367 695.6 .3589 752.3 .4017 866 .. 6 0.100 613.2 630.0 .3869 .4071 672.s .4261 714.6 .4630 799.0 .4592 594.9 .4659 606.9 .4827 63s.2 .4995 670.1 .5320 734.5 200° 2050 0.045 0.2009 716.2 o. 2.eo6 792.4 0.050 .1831 .2002 647.0 Volume Cu. ft. per lb. 587.5 206.3° = Crit .. .3787 2300 250° F 0.125 575.0 .4570 590.9 0.150 .5147 550.4 .5231 563.6 .5252 567.0 .5312 576. 7 .5467 602.4 .5617 628.O .5903 679.1 0.175 .5695 522.0 .5767 532.6 .5785 535.3 .5s3s 543.2 .5972 564.o . 6099 584.5 .6346 625.8 0.200 . 6109 490.0 .6181 499.5 .6199 501.9 .6247 508.6 .6376 526.9 . 6488 544.o .6727 5so.4 . 448$1 T.A.BLE VII TWO-PHASE BOUNDARY RELA.TIONS OF PROPAl~E Temp. e:F. Volume (Sat.Liq.) z (Sat. Liq.) Volume z (Sat. Gas) (Sat .. Gas) 70 3.207 X 10- 2 3.130 X lQ-2 0.8474 o. 8270 100 3.391 4.715 .5528 .7685 130 3.631 6.926 .3656 .6974 160 3.!983 10.13 .2399 .6100 190 4.634 15.42 .1491 .495g 200 5.136 18 .. 60 .1168 .4230 205 5.995 22.62 .08945 .3376 206.3 = Crit. 7.199 27 .. 45 .07199 .2745 100 3.125 2.498 1&0672 o. 8531 200 3.422 5.020 .5206 .7592 300 3.7o4 7.646 .3272 .6754 400 4.038 10.65 .2264 .5972 500 4.502 14.36 .1628 .5192 600 5.562 20.70 .1010 .. 3759 615 6.540 24.85 .08006 .30l-l-2 617.4 = Crit. 7.199 27.45 . 07199 .2745 Pressure lbs. per sq. in. TABLE VIII VAPOR PRESSURE VAIDES FOR PROPANE Temp. °F. Pressure Lbs. per sq. in. Pressure Lbs . per sq.in. Temp9°F. 10 46.5 79.0 125.7 189.2 273.5 383.2 474.8 525.5 580.8 609.9 100 150 200 250 300 350 400 54.8 40 70 100 130 160 1$0 190 200 205 206.3 = Grit. 617.4 82.4 104.3 122.4 450 138.0 151.7 163.9 175.0 500 185'.1 550 6oo 617.4 194.5 = Crit. 203. 3 206.3 TABLE IX CRITIC1lli CONSTANTS OF PROPANE Terr~erature = 206.3°F. Pressure = 617.4 lbs. per sq.in. Volume = 7.199 X 10-2 cu. ft. per lb.