Lecture 6 - Compressibility factor, ZP graph, corresponding states, Pitzer Lee-Kesler method

Topics for Today Compressibility * factor * The * Principle of Corresponding State * The be Reading Z : - . P graph Kesler method Sections 23,24 The Compressibility father Jefinition Z : th EXAMPLE Data : : molar Vol lz÷ = ideal gas 8.314 Calculate 7- of . water . come Jlmr ! as K sat . Land sat A- lbar THE 99.61 C = 37276k VLaO.oo1O4m31ky-zO.0o001874m3tno1VV-1.694m3Kg0.3o52m31molZL-f05Pakl.874xl05mYmoD@3l4mJg.k = kj () Z✓= ( 105Pa ) ( 8314 ( 372>6 0.3052 I my .k ) 0.0006045 mYmd ) ( 372.76k ) = 0.985 V@ 1bar . The i µ kea - gas Z state - P graph P o@T= V N@ 7 const const ] T SAT . rap ¥v & sat UQ ZL " 0 Pc > IT critical critical point e critical pressure T< To Corresponding States Zekuud Tr Pr : ¥ Th Pr , p = Principle ¥ of Lorre ) panting States atpeart 2 a to Universal Pr ,Tr , be function of for all molecules ZEZCTRP ) , . fat 3- Parameter Corresponding Form of 3- Mathematical States parametwpnnaplwflors ¥ZGr .rs#baefYstgtYhrgxiemxwhtm ) acentric Tabulated w= - 1- logoPr|yr=o - , nthtc along Pc : Appendix A Critical Properties of Selected Compounds Table A-1: Critical and related properties of selected species (sorted alphabetically by chemical formula). Name Argon Bromine Carbon tetrachloride Chloroform Dichloromethane Methyl chloride Methane Methanol Methylamine Carbon monoxide Carbon dioxide Acetylene R-134a R-134 Ethylene Acetic acid Ethyl chloride Ethane Ethanol Ethylamine Propylene Acetone Methyl acetate Formula Ar Br2 CCl4 CHCl3 CH2 Cl2 CH3 Cl CH4 CH4 O CH5 N CO CO2 C2 H2 C2 H2 F4 C2 H2 F4 C2 H4 C2 H4 O2 C2 H5 Cl C2 H6 C2 H6 O C2 H7 N C3 H6 C3 H6 O C3 H6 O2 Molar mass (g/mol) 39.948 159.908 153.822 119.377 84.932 50.488 16.043 32.042 31.057 28.010 44.010 26.038 102.032 102.032 28.054 60.053 64.514 30.070 46.069 45.084 42.081 58.080 74.079 PC VC ZC ω TC – – (K) (bar) (cm3 /mol) 150.86 48.98 74.57 0.291 −0.002 584.10 103.00 135.00 0.269 0.119 556.30 45.57 276.00 0.271 536.50 55.00 240.00 0.296 510.00 61.00 416.20 66.80 143.00 0.276 0.151 190.56 45.99 98.60 0.286 0.011 512.64 80.97 118.00 0.224 0.565 430.00 74.20 125.00 0.259 0.283 135.85 34.94 93.10 0.292 0.045 304.12 73.74 94.07 0.274 0.225 308.30 61.14 112.20 0.268 0.189 374.26 40.59 200.80 0.262 0.326 391.74 46.40 190.40 0.271 0.293 282.34 50.41 131.10 0.282 0.087 594.45 57.90 171.00 0.2 0.445 460.30 53.00 199.00 0.276 305.32 48.72 145.50 0.279 0.099 513.92 61.48 167.00 0.240 0.649 456.40 56.30 181.80 0.267 0.276 364.90 46.00 184.60 0.280 0.142 508.10 47.00 209.00 0.233 0.307 506.80 46.90 228.00 0.254 continued on next page 649 Pages for author errata mark-up only. Not for distribution. Thebe - Kester Method tuortingtothismethoditiscalwlatetasfllows Z=zH+wZ y f ' ' ' Ntt ' caklatednumencsk byketkeswr available & special Ofageneraimethod ftpwpenhs : , ' X=X0tw× from tables g araphs asafvmtionoftr ,Pr Aboveis Case hhiversalfmctiom and : Pitter Method ( separates the of effect Wfromthatof Tv ,Pr . 1.2 1.0 1.80 2.00 2.50 4.00 1.60 1.40 1.30 0.8 Z (0) 1.20 Tr = 0.85 0.6 1.15 1.10 1.05 0.90 0.4 0.95 1.00 0.2 0.0 0.0 0.5 1.0 Reduced pressure, Pr = P/Pc 1.5 2.0 1.5 4.00 2.50 2.00 1.80 1.0 Z (0) 1.60 1.40 1.30 Tr = 0.85 0.5 1.00 1.20 1.05 0.90 1.10 1.15 0.95 0.0 0.1 2 3 4 5 6 7 8 9 1 2 3 4 Reduced pressure, Pr = P/Pc 5 6 7 8 9 10 2 0.4 4.00 2.50 2.00 1.80 0.2 1.60 1.40 Z (1) 1.15 1.30 1.20 1.10 0.0 1.05 1.00 -0.2 Tr = 0.85 0.90 0.95 0.90 0.95 0.85 -0.4 0.1 2 3 4 5 6 7 8 9 1 2 3 4 Reduced pressure, Pr = P/Pc 5 6 7 8 9 10 2 Tabulate :@Pr=o Ndk Tr = 0.5 z0 z1 h0 h1 s0 s1 φ0 φ1 11 zo=t Z '=o Lee Kesler Tables Pr 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.4 1.6 1.8 2 2.5 3 3.5 4 0.0207 0.0413 0.0619 0.0825 0.1031 0.1236 0.1442 0.1647 0.1851 0.2056 0.2261 0.2465 0.2873 0.3280 0.3687 0.4092 0.5103 0.6110 0.7112 0.8110 -0.0090 -0.0181 -0.0270 -0.0360 -0.0450 -0.0539 -0.0628 -0.0716 -0.0805 -0.0893 -0.0981 -0.1069 -0.1243 -0.1417 -0.1590 -0.1762 -0.2189 -0.2611 -0.3028 -0.3440 -5.4592 -5.4528 -5.4464 -5.4400 -5.4335 -5.4270 -5.4206 -5.4141 -5.4076 -5.4011 -5.3946 -5.3881 -5.3751 -5.3620 -5.3489 -5.3357 -5.3027 -5.2696 -5.2362 -5.2027 -8.8689 -8.8708 -8.8728 -8.8747 -8.8767 -8.8787 -8.8808 -8.8828 -8.8848 -8.8869 -8.8890 -8.8911 -8.8953 -8.8996 -8.9039 -8.9082 -8.9194 -8.9308 -8.9424 -8.9543 -7.8416 -7.1562 -6.7585 -6.4786 -6.2632 -6.0886 -5.9421 -5.8162 -5.7060 -5.6082 -5.5205 -5.4410 -5.3018 -5.1832 -5.0801 -4.9894 -4.8025 -4.6558 -4.5366 -4.4375 -11.1958 -11.1907 -11.1856 -11.1805 -11.1755 -11.1706 -11.1656 -11.1607 -11.1559 -11.1511 -11.1463 -11.1416 -11.1322 -11.1230 -11.1140 -11.1051 -11.0834 -11.0625 -11.0424 -11.0231 0.0461 0.0235 0.0160 0.0123 0.0100 0.0085 0.0075 0.0067 0.0060 0.0055 0.0051 0.0048 0.0043 0.0039 0.0036 0.0034 0.0030 0.0028 0.0026 0.0026 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0012 0.0012 0.0012 0.0011 0.0011 0.0010 Tr = 0.6 z0 z1 h0 h1 s0 s1 φ0 φ1 0.1 0.0186 -0.0082 -5.1591 -7.5700 -7.2943 -8.8265 0.2714 0.0226 0.2 0.0371 -0.0164 -5.1531 -7.5730 -6.6097 -8.8233 0.1382 0.0224 0.3 0.0556 -0.0245 -5.1470 -7.5760 -6.2126 -8.8202 0.0939 0.0222 0.4 0.0741 -0.0326 -5.1409 -7.5791 -5.9333 -8.8172 0.0717 0.0220 0.5 0.0925 -0.0406 -5.1348 -7.5822 -5.7185 -8.8142 0.0585 0.0219 0.6 0.1109 -0.0487 -5.1287 -7.5853 -5.5445 -8.8113 0.0496 0.0217 0.7 0.1293 -0.0566 -5.1225 -7.5885 -5.3985 -8.8085 0.0433 0.0215 0.8 0.1476 -0.0646 -5.1163 -7.5917 -5.2732 -8.8057 0.0386 0.0213 0.9 0.1660 -0.0725 -5.1101 -7.5949 -5.1635 -8.8030 0.0350 0.0212 Pr 1 0.1842 -0.0803 -5.1039 -7.5982 -5.0662 -8.8004 0.0321 0.0210 1.1 0.2025 -0.0882 -5.0977 -7.6014 -4.9789 -8.7978 0.0297 0.0208 1.2 0.2207 -0.0960 -5.0914 -7.6047 -4.8999 -8.7953 0.0277 0.0207 1.4 0.2571 -0.1115 -5.0788 -7.6114 -4.7615 -8.7905 0.0246 0.0203 1.6 0.2934 -0.1268 -5.0662 -7.6182 -4.6436 -8.7859 0.0224 0.0200 1.8 0.3296 -0.1421 -5.0535 -7.6250 -4.5413 -8.7815 0.0206 0.0197 2 0.3657 -0.1572 -5.0407 -7.6320 -4.4512 -8.7773 0.0193 0.0194 2.5 0.4554 -0.1945 -5.0084 -7.6497 -4.2655 -8.7678 0.0169 0.0187 3 0.5446 -0.2312 -4.9758 -7.6679 -4.1197 -8.7593 0.0154 0.0179 3.5 0.6332 -0.2672 -4.9428 -7.6865 -4.0012 -8.7520 0.0145 0.0173 4 0.7213 -0.3026 -4.9095 -7.7054 -3.9025 -8.7455 0.0138 0.0166 0.1 0.8958 -0.1161 -0.2135 -0.4150 -0.2057 -0.4907 0.9054 0.9029 0.2 0.0344 -0.0148 -4.8483 -6.3597 -6.1402 -6.9508 0.4557 0.1183 0.3 0.0516 -0.0222 -4.8435 -6.3630 -5.7450 -6.9481 0.3091 0.1174 0.4 0.0687 -0.0294 -4.8385 -6.3664 -5.4675 -6.9456 0.2358 0.1166 0.5 0.0857 -0.0366 -4.8335 -6.3698 -5.2543 -6.9432 0.1919 0.1157 0.6 0.1027 -0.0438 -4.8285 -6.3734 -5.0819 -6.9410 0.1627 0.1149 0.7 0.1197 -0.0509 -4.8234 -6.3770 -4.9376 -6.9389 0.1419 0.1140 0.8 0.1366 -0.0579 -4.8182 -6.3807 -4.8138 -6.9369 0.1263 0.1132 0.9 0.1535 -0.0649 -4.8130 -6.3845 -4.7056 -6.9351 0.1142 0.1124 Pr 1 0.1703 -0.0718 -4.8077 -6.3883 -4.6097 -6.9334 0.1045 0.1116 1.1 0.1871 -0.0787 -4.8024 -6.3922 -4.5238 -6.9318 0.0966 0.1108 1.2 0.2038 -0.0855 -4.7970 -6.3962 -4.4461 -6.9303 0.0901 0.1100 1.4 0.2372 -0.0990 -4.7861 -6.4043 -4.3103 -6.9276 0.0799 0.1085 1.6 0.2704 -0.1123 -4.7750 -6.4126 -4.1948 -6.9254 0.0723 0.1069 1.8 0.3035 -0.1255 -4.7638 -6.4210 -4.0947 -6.9235 0.0665 0.1055 2 0.3364 -0.1385 -4.7524 -6.4297 -4.0067 -6.9219 0.0619 0.1040 2.5 0.4181 -0.1703 -4.7232 -6.4520 -3.8257 -6.9195 0.0538 0.1005 3 0.4991 -0.2013 -4.6932 -6.4751 -3.6839 -6.9187 0.0488 0.0972 3.5 0.5793 -0.2316 -4.6624 -6.4989 -3.5688 -6.9194 0.0454 0.0940 4 0.6588 -0.2611 -4.6310 -6.5233 -3.4729 -6.9213 0.0432 0.0909 0.1 0.9319 -0.0487 -0.1601 -0.2336 -0.1339 -0.2463 0.9360 0.9553 0.2 0.8539 -0.1160 -0.3448 -0.5415 -0.2943 -0.5784 0.8723 0.9061 0.3 0.0497 -0.0206 -4.5086 -5.2637 -5.2987 -5.4785 0.7139 0.3325 0.4 0.0661 -0.0272 -4.5072 -5.2658 -5.0257 -5.4743 0.5443 0.3303 0.5 0.0823 -0.0337 -4.5054 -5.2683 -4.8169 -5.4706 0.4427 0.3280 0.6 0.0985 -0.0401 -4.5035 -5.2710 -4.6486 -5.4674 0.3750 0.3258 0.7 0.1147 -0.0464 -4.5014 -5.2740 -4.5082 -5.4645 0.3268 0.3237 0.8 0.1307 -0.0526 -4.4990 -5.2773 -4.3881 -5.4620 0.2906 0.3215 0.9 0.1467 -0.0588 -4.4965 -5.2808 -4.2834 -5.4598 0.2626 0.3194 Pr 1 0.1626 -0.0648 -4.4937 -5.2845 -4.1910 -5.4579 0.2402 0.3174 1.1 0.1784 -0.0708 -4.4908 -5.2884 -4.1083 -5.4563 0.2220 0.3153 1.2 0.1942 -0.0767 -4.4878 -5.2925 -4.0337 -5.4550 0.2068 0.3133 1.4 0.2255 -0.0883 -4.4813 -5.3011 -3.9036 -5.4531 0.1831 0.3094 1.6 0.2566 -0.0996 -4.4742 -5.3102 -3.7934 -5.4520 0.1654 0.3055 1.8 0.2875 -0.1107 -4.4666 -5.3199 -3.6982 -5.4516 0.1518 0.3017 2 0.3182 -0.1217 -4.4586 -5.3299 -3.6147 -5.4519 0.1411 0.2981 2.5 0.3942 -0.1481 -4.4369 -5.3564 -3.4435 -5.4551 0.1221 0.2893 3 0.4690 -0.1736 -4.4131 -5.3845 -3.3100 -5.4609 0.1101 0.2809 3.5 0.5429 -0.1983 -4.3875 -5.4137 -3.2018 -5.4688 0.1020 0.2730 4 0.6160 -0.2222 -4.3606 -5.4438 -3.1118 -5.4784 0.0964 0.2654 0.1 0.9528 -0.0205 -0.1261 -0.1438 -0.0938 -0.1399 0.9547 0.9803 0.2 0.9015 -0.0442 -0.2641 -0.3075 -0.1988 -0.3005 0.9098 0.9597 0.3 0.8447 -0.0730 -0.4180 -0.5018 -0.3194 -0.4933 0.8650 0.9377 0.4 0.7800 -0.1118 -0.5956 -0.7507 -0.4634 -0.7439 0.8201 0.9137 0.5 0.7019 -0.1777 -0.8129 -1.1326 -0.6477 -1.1370 0.7745 0.8857 0.6 0.1006 -0.0396 -4.0739 -4.2544 -4.1450 -4.2692 0.6827 0.6326 0.7 0.1164 -0.0451 -4.0846 -4.2502 -4.0193 -4.2581 0.5951 0.6285 0.8 0.1321 -0.0503 -4.0936 -4.2483 -3.9124 -4.2495 0.5294 0.6245 0.9 0.1476 -0.0554 -4.1012 -4.2481 -3.8195 -4.2431 0.4784 0.6206 Pr 1 0.1630 -0.0604 -4.1076 -4.2492 -3.7377 -4.2383 0.4376 0.6169 1.1 0.1783 -0.0653 -4.1131 -4.2515 -3.6646 -4.2347 0.4044 0.6132 1.2 0.1935 -0.0701 -4.1176 -4.2546 -3.5989 -4.2323 0.3767 0.6096 1.4 0.2235 -0.0795 -4.1245 -4.2629 -3.4845 -4.2300 0.3334 0.6026 1.6 0.2531 -0.0885 -4.1290 -4.2733 -3.3877 -4.2303 0.3012 0.5959 1.8 0.2824 -0.0973 -4.1314 -4.2851 -3.3041 -4.2325 0.2763 0.5894 2 0.3114 -0.1059 -4.1322 -4.2980 -3.2309 -4.2362 0.2565 0.5831 2.5 0.3828 -0.1265 -4.1285 -4.3333 -3.0808 -4.2496 0.2217 0.5682 3 0.4527 -0.1463 -4.1187 -4.3712 -2.9635 -4.2668 0.1993 0.5543 3.5 0.5214 -0.1654 -4.1042 -4.4104 -2.8683 -4.2864 0.1842 0.5412 4 0.5892 -0.1839 -4.0863 -4.4502 -2.7889 -4.3073 0.1735 0.5287 Tr = 0.7 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 0.8 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 0.9 z0 z1 h0 h1 s0 s1 φ0 φ1 zgzi Lee Kesler Tables Tr = 1 z0 z1 h0 h1 s0 s1 φ0 φ1 0.1 0.9659 -0.0069 -0.1027 -0.0926 -0.0690 -0.0857 0.9669 0.9931 0.2 0.9300 -0.0140 -0.2118 -0.1910 -0.1436 -0.1771 0.9341 0.9862 0.3 0.8918 -0.0212 -0.3286 -0.2963 -0.2249 -0.2754 0.9015 0.9793 0.4 0.8509 -0.0285 -0.4551 -0.4101 -0.3147 -0.3821 0.8690 0.9724 0.5 0.8065 -0.0360 -0.5939 -0.5350 -0.4156 -0.4998 0.8366 0.9654 0.6 0.7574 -0.0435 -0.7497 -0.6748 -0.5318 -0.6324 0.8042 0.9585 0.7 0.7017 -0.0511 -0.9299 -0.8363 -0.6706 -0.7866 0.7715 0.9515 0.8 0.6353 -0.0588 -1.1506 -1.0336 -0.8472 -0.9766 0.7383 0.9446 0.9 0.5477 -0.0665 -1.4553 -1.3065 -1.1042 -1.2422 0.7039 0.9377 Pr 1 0.2918 -0.0789 -2.5738 -2.3825 -2.1674 -2.3106 0.6661 0.9306 1.1 0.2167 -0.0607 -3.3263 -2.8879 -2.8458 -2.8098 0.6185 0.9249 1.2 0.2237 -0.0609 -3.4410 -2.9516 -2.8926 -2.8683 0.5779 0.9201 1.4 0.2459 -0.0652 -3.5597 -3.0333 -2.8932 -2.9403 0.5135 0.9112 1.6 0.2710 -0.0706 -3.6278 -3.0931 -2.8622 -2.9910 0.4651 0.9030 1.8 0.2969 -0.0765 -3.6735 -3.1426 -2.8236 -3.0319 0.4274 0.8952 2 0.3229 -0.0824 -3.7064 -3.1861 -2.7838 -3.0670 0.3975 0.8878 2.5 0.3880 -0.0972 -3.7568 -3.2789 -2.6901 -3.1399 0.3441 0.8702 3 0.4523 -0.1118 -3.7815 -3.3584 -2.6089 -3.2003 0.3095 0.8538 3.5 0.5156 -0.1261 -3.7915 -3.4296 -2.5392 -3.2532 0.2858 0.8383 4 0.5780 -0.1401 -3.7918 -3.4952 -2.4789 -3.3011 0.2690 0.8235 0.1 0.9808 0.0040 -0.0728 -0.0404 -0.0415 -0.0375 0.9811 1.0039 0.2 0.9611 0.0084 -0.1478 -0.0804 -0.0847 -0.0749 0.9623 1.0079 0.3 0.9410 0.0134 -0.2253 -0.1198 -0.1297 -0.1121 0.9436 1.0123 0.4 0.9205 0.0190 -0.3053 -0.1584 -0.1767 -0.1488 0.9252 1.0170 0.5 0.8994 0.0254 -0.3883 -0.1958 -0.2258 -0.1850 0.9069 1.0220 0.6 0.8779 0.0326 -0.4744 -0.2318 -0.2773 -0.2201 0.8887 1.0274 0.7 0.8557 0.0407 -0.5639 -0.2657 -0.3315 -0.2540 0.8707 1.0332 0.8 0.8330 0.0499 -0.6573 -0.2970 -0.3885 -0.2861 0.8528 1.0394 0.9 0.8097 0.0603 -0.7547 -0.3250 -0.4487 -0.3159 0.8351 1.0462 Pr 1 0.7858 0.0719 -0.8567 -0.3489 -0.5124 -0.3428 0.8175 1.0534 1.1 0.7613 0.0848 -0.9636 -0.3679 -0.5799 -0.3661 0.8001 1.0613 1.2 0.7363 0.0991 -1.0756 -0.3811 -0.6514 -0.3851 0.7828 1.0698 1.4 0.6856 0.1310 -1.3155 -0.3877 -0.8069 -0.4082 0.7487 1.0889 1.6 0.6363 0.1637 -1.5729 -0.3704 -0.9762 -0.4134 0.7156 1.1105 1.8 0.5929 0.1891 -1.8345 -0.3498 -1.1487 -0.4171 0.6838 1.1339 2 0.5605 0.1990 -2.0787 -0.3607 -1.3076 -0.4469 0.6540 1.1575 2.5 0.5295 0.1651 -2.5367 -0.5907 -1.5866 -0.6803 0.5902 1.2069 3 0.5425 0.1095 -2.8072 -0.9339 -1.7270 -0.9915 0.5421 1.2376 3.5 0.5747 0.0639 -2.9673 -1.2428 -1.7921 -1.2621 0.5063 1.2542 4 0.6155 0.0304 -3.0655 -1.4887 -1.8198 -1.4733 0.4796 1.2620 0.1 0.9884 0.0072 -0.0547 -0.0165 -0.0275 -0.0189 0.9885 1.0072 0.2 0.9768 0.0147 -0.1102 -0.0320 -0.0556 -0.0373 0.9771 1.0145 0.3 0.9651 0.0225 -0.1667 -0.0466 -0.0843 -0.0551 0.9658 1.0221 0.4 0.9534 0.0306 -0.2240 -0.0600 -0.1136 -0.0722 0.9546 1.0298 0.5 0.9416 0.0390 -0.2823 -0.0722 -0.1435 -0.0887 0.9436 1.0378 0.6 0.9298 0.0477 -0.3414 -0.0831 -0.1741 -0.1043 0.9326 1.0460 0.7 0.9180 0.0567 -0.4016 -0.0925 -0.2054 -0.1191 0.9218 1.0544 0.8 0.9062 0.0661 -0.4627 -0.1004 -0.2373 -0.1329 0.9110 1.0631 0.9 0.8945 0.0757 -0.5247 -0.1068 -0.2699 -0.1458 0.9004 1.0720 Pr 1 0.8827 0.0857 -0.5877 -0.1114 -0.3031 -0.1576 0.8899 1.0811 1.1 0.8710 0.0959 -0.6516 -0.1143 -0.3370 -0.1683 0.8795 1.0905 1.2 0.8595 0.1063 -0.7163 -0.1154 -0.3716 -0.1779 0.8693 1.1001 1.4 0.8367 0.1276 -0.8481 -0.1124 -0.4423 -0.1937 0.8492 1.1201 1.6 0.8148 0.1491 -0.9823 -0.1027 -0.5150 -0.2052 0.8297 1.1410 1.8 0.7942 0.1699 -1.1178 -0.0879 -0.5887 -0.2134 0.8108 1.1626 2 0.7753 0.1894 -1.2530 -0.0701 -0.6626 -0.2196 0.7926 1.1848 2.5 0.7387 0.2259 -1.5765 -0.0337 -0.8393 -0.2402 0.7507 1.2413 3 0.7202 0.2397 -1.8569 -0.0442 -0.9900 -0.2904 0.7144 1.2955 3.5 0.7187 0.2339 -2.0819 -0.1144 -1.1073 -0.3773 0.6840 1.3439 4 0.7299 0.2171 -2.2555 -0.2277 -1.1943 -0.4884 0.6592 1.3852 0.1 0.9928 0.0080 -0.0427 -0.0041 -0.0194 -0.0106 0.9928 1.0081 0.2 0.9856 0.0162 -0.0857 -0.0075 -0.0391 -0.0208 0.9857 1.0162 0.3 0.9785 0.0245 -0.1290 -0.0101 -0.0590 -0.0305 0.9786 1.0245 0.4 0.9714 0.0330 -0.1726 -0.0119 -0.0791 -0.0399 0.9716 1.0330 0.5 0.9644 0.0415 -0.2165 -0.0129 -0.0994 -0.0488 0.9647 1.0416 0.6 0.9575 0.0501 -0.2606 -0.0131 -0.1199 -0.0572 0.9579 1.0503 0.7 0.9507 0.0589 -0.3051 -0.0124 -0.1406 -0.0652 0.9512 1.0591 0.8 0.9439 0.0677 -0.3498 -0.0109 -0.1615 -0.0727 0.9445 1.0681 0.9 0.9373 0.0766 -0.3947 -0.0085 -0.1826 -0.0797 0.9379 1.0772 Pr 1 0.9308 0.0855 -0.4398 -0.0053 -0.2039 -0.0862 0.9315 1.0864 1.1 0.9243 0.0945 -0.4851 -0.0013 -0.2253 -0.0922 0.9250 1.0958 1.2 0.9180 0.1035 -0.5305 0.0036 -0.2468 -0.0978 0.9187 1.1052 1.4 0.9059 0.1214 -0.6217 0.0155 -0.2902 -0.1077 0.9064 1.1245 1.6 0.8944 0.1391 -0.7130 0.0302 -0.3340 -0.1159 0.8944 1.1442 1.8 0.8837 0.1563 -0.8040 0.0470 -0.3778 -0.1227 0.8827 1.1643 2 0.8738 0.1729 -0.8942 0.0654 -0.4214 -0.1286 0.8715 1.1846 2.5 0.8537 0.2098 -1.1136 0.1127 -0.5280 -0.1417 0.8454 1.2363 3 0.8410 0.2381 -1.3176 0.1511 -0.6277 -0.1586 0.8221 1.2879 3.5 0.8361 0.2564 -1.5003 0.1693 -0.7169 -0.1854 0.8019 1.3381 4 0.8386 0.2654 -1.6586 0.1627 -0.7940 -0.2245 0.7846 1.3856 0.1 0.9955 0.0081 -0.0342 0.0029 -0.0144 -0.0065 0.9954 1.0081 0.2 0.9910 0.0162 -0.0684 0.0063 -0.0289 -0.0126 0.9909 1.0163 0.3 0.9866 0.0243 -0.1027 0.0101 -0.0435 -0.0186 0.9865 1.0245 0.4 0.9823 0.0325 -0.1371 0.0146 -0.0581 -0.0242 0.9821 1.0328 0.5 0.9780 0.0406 -0.1715 0.0195 -0.0728 -0.0296 0.9778 1.0413 0.6 0.9739 0.0488 -0.2060 0.0249 -0.0876 -0.0348 0.9735 1.0498 0.7 0.9698 0.0570 -0.2405 0.0308 -0.1024 -0.0396 0.9693 1.0584 0.8 0.9659 0.0652 -0.2750 0.0371 -0.1173 -0.0442 0.9652 1.0670 0.9 0.9620 0.0734 -0.3095 0.0440 -0.1322 -0.0486 0.9611 1.0758 Pr 1 1.1 0.9583 0.9546 0.0816 0.0897 -0.3439 -0.3783 0.0513 0.0590 -0.1472 -0.1622 -0.0527 -0.0566 0.9571 0.9531 1.0846 1.0935 1.2 0.9511 0.0978 -0.4127 0.0671 -0.1771 -0.0602 0.9492 1.1024 1.4 0.9444 0.1137 -0.4811 0.0844 -0.2071 -0.0669 0.9416 1.1205 1.6 0.9382 0.1294 -0.5491 0.1029 -0.2371 -0.0728 0.9343 1.1388 1.8 0.9326 0.1446 -0.6164 0.1225 -0.2668 -0.0781 0.9272 1.1573 2 0.9275 0.1593 -0.6829 0.1426 -0.2964 -0.0829 0.9204 1.1760 2.5 0.9176 0.1932 -0.8442 0.1936 -0.3687 -0.0938 0.9046 1.2231 3 0.9118 0.2224 -0.9963 0.2408 -0.4376 -0.1055 0.8906 1.2703 3.5 0.9103 0.2459 -1.1367 0.2793 -0.5018 -0.1202 0.8784 1.3170 4 0.9129 0.2639 -1.2638 0.3056 -0.5606 -0.1397 0.8680 1.3627 Tr = 1.2 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 1.4 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 1.6 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 1.8 z0 z1 h0 h1 s0 s1 φ0 φ1 Lee Kesler Tables Tr = 2 z0 z1 h0 h1 s0 s1 φ0 φ1 0.1 0.9972 0.0078 -0.0279 0.0071 -0.0111 -0.0042 0.9972 1.0078 0.2 0.9944 0.0155 -0.0557 0.0145 -0.0222 -0.0083 0.9944 1.0157 0.3 0.9918 0.0233 -0.0835 0.0223 -0.0333 -0.0122 0.9916 1.0236 0.4 0.9892 0.0310 -0.1113 0.0303 -0.0445 -0.0159 0.9889 1.0315 0.5 0.9866 0.0387 -0.1390 0.0387 -0.0556 -0.0195 0.9863 1.0396 0.6 0.9842 0.0464 -0.1666 0.0473 -0.0668 -0.0229 0.9836 1.0476 0.7 0.9819 0.0541 -0.1941 0.0563 -0.0780 -0.0261 0.9811 1.0558 0.8 0.9796 0.0617 -0.2216 0.0655 -0.0891 -0.0293 0.9786 1.0639 0.9 0.9774 0.0692 -0.2490 0.0749 -0.1003 -0.0322 0.9761 1.0722 Pr 1 1.1 0.9754 0.9734 0.0767 0.0842 -0.2762 -0.3034 0.0846 0.0945 -0.1114 -0.1226 -0.0351 -0.0378 0.9737 0.9713 1.0804 1.0888 1.2 0.9715 0.0916 -0.3304 0.1046 -0.1337 -0.0404 0.9690 1.0971 1.4 0.9680 0.1061 -0.3840 0.1253 -0.1558 -0.0453 0.9645 1.1139 1.6 0.9649 0.1203 -0.4369 0.1465 -0.1778 -0.0497 0.9601 1.1309 1.8 0.9622 0.1342 -0.4892 0.1681 -0.1996 -0.0539 0.9560 1.1479 2 0.9599 0.1476 -0.5406 0.1899 -0.2212 -0.0579 0.9521 1.1651 2.5 0.9561 0.1789 -0.6650 0.2438 -0.2740 -0.0672 0.9432 1.2082 3 0.9550 0.2069 -0.7825 0.2949 -0.3246 -0.0769 0.9355 1.2515 3.5 0.9567 0.2312 -0.8920 0.3404 -0.3725 -0.0878 0.9291 1.2944 4 0.9611 0.2517 -0.9928 0.3786 -0.4174 -0.1010 0.9240 1.3369 0.1 1.0004 0.0059 -0.0115 0.0144 -0.0042 -0.0011 1.0004 1.0059 0.2 1.0008 0.0117 -0.0228 0.0288 -0.0084 -0.0021 1.0008 1.0118 0.3 1.0013 0.0175 -0.0340 0.0432 -0.0125 -0.0032 1.0012 1.0177 0.4 1.0018 0.0232 -0.0451 0.0575 -0.0167 -0.0042 1.0017 1.0237 0.5 1.0024 0.0289 -0.0560 0.0718 -0.0208 -0.0052 1.0021 1.0296 0.6 1.0030 0.0345 -0.0669 0.0861 -0.0249 -0.0063 1.0026 1.0356 0.7 1.0036 0.0401 -0.0776 0.1003 -0.0290 -0.0073 1.0031 1.0415 0.8 1.0043 0.0456 -0.0881 0.1144 -0.0330 -0.0083 1.0037 1.0475 0.9 1.0050 0.0511 -0.0986 0.1285 -0.0370 -0.0093 1.0042 1.0535 Pr 1 1.1 1.0058 1.0065 0.0565 0.0619 -0.1089 -0.1191 0.1425 0.1564 -0.0410 -0.0450 -0.0103 -0.0112 1.0048 1.0054 1.0595 1.0654 1.2 1.0074 0.0672 -0.1291 0.1703 -0.0490 -0.0122 1.0060 1.0714 1.4 1.0091 0.0776 -0.1489 0.1978 -0.0568 -0.0142 1.0072 1.0834 1.6 1.0111 0.0879 -0.1680 0.2249 -0.0646 -0.0162 1.0086 1.0955 1.8 1.0131 0.0979 -0.1867 0.2517 -0.0722 -0.0182 1.0100 1.1075 2 1.0153 0.1076 -0.2048 0.2780 -0.0798 -0.0203 1.0115 1.1196 2.5 1.0215 0.1310 -0.2479 0.3418 -0.0982 -0.0255 1.0157 1.1497 3 1.0284 0.1529 -0.2876 0.4026 -0.1159 -0.0311 1.0203 1.1798 3.5 1.0362 0.1734 -0.3241 0.4600 -0.1330 -0.0371 1.0253 1.2098 4 1.0446 0.1925 -0.3574 0.5140 -0.1495 -0.0435 1.0309 1.2397 0.1 1.0011 0.0046 -0.0045 0.0162 -0.0022 -0.0005 1.0010 1.0046 0.2 1.0021 0.0091 -0.0089 0.0323 -0.0043 -0.0011 1.0021 1.0092 0.3 1.0032 0.0137 -0.0133 0.0484 -0.0065 -0.0017 1.0032 1.0138 0.4 1.0043 0.0182 -0.0175 0.0643 -0.0086 -0.0022 1.0043 1.0185 0.5 1.0055 0.0226 -0.0216 0.0802 -0.0107 -0.0028 1.0053 1.0231 0.6 1.0066 0.0270 -0.0256 0.0959 -0.0128 -0.0034 1.0065 1.0277 0.7 1.0078 0.0314 -0.0296 0.1116 -0.0149 -0.0039 1.0076 1.0323 0.8 1.0090 0.0357 -0.0334 0.1271 -0.0170 -0.0045 1.0087 1.0370 0.9 1.0102 0.0400 -0.0372 0.1426 -0.0191 -0.0051 1.0098 1.0416 Pr 1 1.1 1.0115 1.0127 0.0443 0.0485 -0.0408 -0.0444 0.1580 0.1732 -0.0211 -0.0232 -0.0057 -0.0063 1.0110 1.0122 1.0462 1.0509 1.2 1.0140 0.0527 -0.0478 0.1884 -0.0252 -0.0069 1.0133 1.0555 1.4 1.0166 0.0610 -0.0545 0.2183 -0.0292 -0.0082 1.0157 1.0648 1.6 1.0193 0.0691 -0.0607 0.2479 -0.0332 -0.0095 1.0181 1.0741 1.8 1.0221 0.0771 -0.0666 0.2770 -0.0371 -0.0108 1.0206 1.0833 2 1.0249 0.0849 -0.0722 0.3056 -0.0409 -0.0122 1.0232 1.0926 2.5 1.0323 0.1038 -0.0845 0.3752 -0.0504 -0.0158 1.0297 1.1158 3 1.0401 0.1219 -0.0947 0.4419 -0.0595 -0.0196 1.0364 1.1390 3.5 1.0482 0.1390 -0.1029 0.5057 -0.0683 -0.0238 1.0435 1.1621 4 1.0568 0.1554 -0.1091 0.5666 -0.0768 -0.0282 1.0508 1.1851 Tr = 3 z0 z1 h0 h1 s0 s1 φ0 φ1 Tr = 4 z0 z1 h0 h1 s0 s1 φ0 φ1 EXAMPLE A : 4m3tankwillbewedtostovenatura1gaslnosHyatiD@3OOK.HtheMaximnmsafepressnueis45bayWhatisthemax.massofbatvra1gasthatcanbestohed.7AnowerUsingthlLee-Kes1ermethok.So1utioni.Themo1esofcH4au.n = ¥91 c- From molar 300k Vol @ . , 45bar he Kesler P . V=z¥T Data city : Pta W= Mw= LK Tables Tyree ;4g Reduced Tr ,Pr Tc= 190 -56k Tr= -300 -5.99 190.55-1.574 0.011 PK -45 0.978=145.99 16.043 : 0.0857 Zz0[ 088272¥ 0.9308 [ V=ZRpI=5 0.0855 , .i3×i04mmI , inter = ZE potation zo=o 0.9246 .org , -1>2--0.9255 Na+y=¥=7797mul=125ks