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The Journal of Chemical Thermodynamics Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide I....
Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide I. The homogeneous gas and liquid regions in the temperature range from 217 K to 340 K at pressures up to 9 MPa
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Cilt:
22
Yıl:
1990
Dil:
english
Sayfalar:
14
DOI:
10.1016/00219614(90)90172m
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M2508 .I. ~‘kttr. Tilrrttt~td~nurni~~.~ 1990, 32. 827840 Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide I. The homogeneous gas and liquid regions in the temperature range from 217 K to 340 K at pressures up to 9MPa W. DUSCHEK, R. KLEINRAHM, and W. WAGNER lnstitut ,ftir Thermo trnd Fluid&twm’k. Ruhrlftliversitiir Bochum, D4630 Bochum, Federal Rrphlic of’ Gcrtnatl~* Comprehensive (p. p. T) measurements on pure carbon dioxide have been carried out in the singlephase region (362 values) and along the entire coexistence curve (202 values). The results reported in this first pdper cover the homogeneous gas and liquid region in the temperature range from 217 K to 340 K at pressures up to 9 MPa. Comparisons with experimental results of previous workers and values calculated from three current equations of state for carbon dioxide are presented. A truncated virial equation has been established in order to determine reliable values for the second and third virial coefficients. This equation represents the density of carbon dioxide in the entire temperature range investigated at densities up to 35 per cent of the critical density with an uncertainty of less than kO.01 per cent. The second and third virial coefficients have been determined with an uncertainty of less than 0.4 per cent and 3 per cent, respectively. 1. Introduction The IUPAC Thermodynamic Tables Project Centre at Imperial College is committed to revise its tables on carbon dioxide, (I) because the equation of state used for establishing these tables shows quite large systematic deviations from experimental (p, [I, T) and caloric values, especially along the coexistence curve and in the critical region. Moreover, the equation has a rather complicated structure; it consists of an analytic farfield equation and a nonanalytic nearcritical equation which are combined by a switching function. To overcome these difficulties a new equation of state will be developed by Wagner et ul. which will de; scribe the entire thermodynamic surface of carbon dioxide within the experimental uncertainty of the most reliable data, and it is hoped that this will contribute to the revision of the IUPAC tables. 002 I ~~9614/90!090827 + I4 $OXQ’O (’ 1990 Academic Press Llmited 828 W.DUSC~~K.R.KL~lN~A~M.ANDW.WA~N~R The aim of this work, reported in two papers, is to provide a reliable set ol (pressure p, density p, temperature 7) values for the establishment of this new equation of state. This first paper presents comprehensive (p, p, T) m~dsurementson pure carbon dioxide in the homogeneous gas and liquid region including the largest part of the critical region in the temperature range from 217 K to 340 K at pressures up to 9 MPa. A truncated virial equation has been established for the density range up to 0.35p,, where pCis the critical density. This equation provides accurate values for the second and third virial coefficients. The second paper, which will be published shortly,‘2’ reports the measurement and correlation of the saturatedliquid and vapour densities together with the vapour pressure along the entire coexistence curve of carbon dioxide. 2. Ex~rimental A new apparatus has been developed especially for accurate measurements of the saturatedliquid and vapour densities of pure substances together with the vapour pressure along the whole coexistence curve from the triplepoint temperature to the critical temperature. Moreover, the apparatus is also suitable for density measurements of the homogeneous gas or liquid phase including the largest part of the critical region. As a first application of this new measuring principle, comprehensive measurements on pure methane were carried out along the coexistence curve,C3)in the critical region,t4) and in the homogeneous gas region in the temperature range from 273 K to 323 K at pressures up to 8 MPa.“’ The essential details of the new apparatus were given in a previous paper.‘“) Therefore, only the principle is briefly described here. The new method for density measurements is based on a buoyancy principle. However, instead of the usual single sinker, two sinkers of identical massand surface area but with a considerable difference in volume are used. With this “TwoSinkerMethod” all the effects (such as buoyant forces on the whole suspension device of the sinkers, surface tension at the suspension bar or wire when measuring liquid densities, adsorption on the surface of the sinker when measuring gas densities, etc.) which reduce the accuracy of the density measurement when only a single sinker is used, are automatically compensated. The operational range of the apparatus covers a density range from 1 kg.rnw3 to 2000 kg.m3 at temperatures from 50 K to 350 K and pressures up to 9 MPa. 3. Results The ex~rimentai results are listed in table 1. Figure 1 shows a general view of the (p, p, 7’) surface investigated. Together with the results of the coexistence curve,(‘) our fp, p, T) values cover the whole region from the triplepoint temperature 216.580 K up to 340 K at pressures up to 9 MPa. To check the reproducibility, some of the measurements at selected points were repeated at different times. (p, p, 7’) MEASUREMENTS TABLE 829 DIOXIDE 1. The new (p, p. T) results for carbon dioxide, where 7‘ is the temperature pressure, and (t the density P kgm ON CARBON p_ ’ MPa g._ kg.m .’ P MPa 6’ kg.&” P,, M&i (IPTS68). p the f’ k8.m a P MPa T = 217.OOOK 7.6998 0.30 I57 10.4212 0.40145 7.4658 0.29732 T = 2’0.000 K 0.50117 15.2795 0.52443 I 167.07 0.54999 1169.26 0.55060 1171.41 0.56023 I 173.52 0.57076 I I75.b2 0.84976 7.5582 7.5584 10.2263 12.8291 12.9840 0.50040 13.0039 13.6636 14.3933 14.4107 14.6872 14.9918 ‘0.601 b 0.80248 21.9848 0.30082 0.30082 0.40069 0.49489 0.58069 1.00854 2.01454 2.99935 4.00289 5.003 10 I 177.66 1177.67 1179.77 1181.75 1183.69 5.99942 6.00137 7.02108 8.00754 9.ooo99 2.00103 3.00527 4.01025 5.00086 5.01018 1103.70 1106.63 1109.47 1 I 12.22 h.0(1947 7.00344 7.99734 8.99168 1026.66 1030.85 1030.88 8.00975 9.00264 8.99182 T = 130.000 K T = 233.150 K I 125.20 4.18767 T=24O.OOOK 6.8644 11.6769 11.6931 18.026 I 24.73 1I 0.30146 0.50123 0.50191 0.75036 0.99563 24.8452 24.8196 24.8808 32.4117 1089.26 0.99968 1.00086 100094 1.25430 1.39221 43.8169 1.70011 45.4953 1.75083 10.6426 10.6441 22.246 I 35.1470 49.9066 0.50166 0.50174 1.00132 1.5Otuo 1.99984 49.9288 63.7136 999.298 1002.06 1007.49 2.00050 2.40015 2.50328 2.99454 4.00312 79.6880 1.99695 79.7116 1091.27 1094.51 1097.66 1100.70 1100.72 T = 250.000 K 1060.39 5.4’111 T=16O.OOOK 1007.51 1012.60 1017.49 1022.08 1022.16 4.00864 5.00422 6.00106 6.9895 1 7.00288 7‘ = 170.000 K 3.99757 T = 170.854 K 964.780 6.51519 T = 280.000 K 9.7448 9.7556 9.7682 20.289 1 31.5094 43.7964 57.4040 57.4173 0.49940 0.49994 0.50057 1.00415 1.50162 2.~7 2.50027 2.50080 72.8188 90.8340 112.986 113.043 113.081 113.174 119.453 121.299 3.00040 3.50066 3.998 13 3.9993 1 3.99998 4.00184 4.12011 4.15312 883.776 884.040 884.963 887.947 893.824 893.850 904.700 914.288 4.17593 4.19778 4.26165 4.50556 4.99745 4.99941 6.00474 6.99882 914.342 923.003 923.033 93 1.024 931.036 7.00457 8.00188 8.00408 9.00489 9.00444 830 W. DUSCHEK, R. KLEINRAHM, TABLE I’ kg.rn~” P MPa P kg.m ’ P Mki AND W. WAGNER Icontinud P kg,m ’ P MPa i’ kg.m f’ ’ MPa T = 290.000 K 121.510 148.435 162.312 4.50097 5.OQOO9 5.20003 170.459 809.375 820.785 5.30035 5.49993 6.00191 133.288 159.618 180.018 197.238 5.00165 5.50058 5.80119 6.00253 207.53 I 219.262 219.890 228.344 6.10178 6.19719 6.20172 6.25870 OSooO8 0.50160 1.00002 1.00082 1.50058 2.00029 2.50033 2.50094 3.00014 3.50413 4.00323 92.1169 109.006 128.415 128.427 128.729 151.976 182.514 207.120 229.741 229.756 229.874 4.00479 4.50382 5.00027 5.00042 5.00768 5.50135 6.00240 6.29972 6.50087 6.50097 6.50182 124.162 145.606 171.954 207.412 226.453 252.357 269.688 280.797 293.694 309.851 4.99849 5.49965 6.00038 6.50079 6.69891 6.90208 7.00137 7.05172 7.09884 7.14270 314.141 323.309 325.446 331.014 333.938 600.519 600.781 601.868 609.168 612.809 7.15194 7.16853 7.17176 7.1790s 7.18248 7.18860 7.18895 7.19073 7.20465 7.21303 590.276 637.039 65 1.065 7.42907 7.60179 7.6985 1 663.052 680.447 694.008 7.80385 8.00237 8.20090 201.362 228.113 252.470 267.961 6.50093 6.80026 7.00161 7.0997 1 302.214 340.420 381.839 411.522 7.24972 7.33621 7.37163 7.37861 196.981 222.254 242.965 271.117 301.056 340.340 6.49447 6.80256 6.99838 7.19596 7.33643 7.44187 380.549 425.015 457.121 458.769 500.808 538.848 7.49175 7.51379 7.52183 7.52240 7.53233 7.55051 839.252 839.306 854.305 7.00067 7.00245 8.00234 867.022 9.00495 6.30105 6.50039 7.oooo3 7.0238 1 777.111 789.901 8 10.664 7.50565 8.00337 9.00808 6.50311 6.55677 6.60111 6.60195 6.65044 6.65109 6.65386 6.65485 6.68294 6.70113 6.70629 267.417 689.670 698.293 705.810 719.160 738.464 738.480 753.263 781.251 6.70801 6.80343 6.89846 6.99384 7.20323 7.60186 7.60290 7.99844 9.0059s 7.25415 7.30091 7.30553 7.31010 7.39793 7.50267 7.60618 7.79927 8.00099 8.00079 715.518 724.424 724.588 732.562 739.658 739.855 746.462 8.20408 8.40044 8.40390 8.60203 8.7981 S 8.80322 9.00279 8.40309 8.60319 8.80096 731.240 9.0@030 7.38024 7.38062 7.38513 7.41761 615.196 7.50320 7.60489 7.79972 7.90003 8.00208 8.19993 8.40123 700.399 710.316 710.331 7 18.849 8.60505 8.80646 8.80785 9.00315 T = 297.000 K 729.431 740.392 761.227 762.050 T=3OO.OOOK 9.0474 9.0755 18.5804 18.5964 28.6868 39.4268 50.9440 50.9593 63.3803 77.0682 92.0693 230.044 237.683 244.772 244.958 253.982 254.109 254.672 254.887 261.074 265.578 266.927 T = 303.000 K 626.379 637.386 638.338 639.260 653.794 666.769 677.015 692.239 704.875 704.879 T = 304.135 K 705.414 715.133 723.595 T = 304.155 K 471.100 504.680 538.950 580.859 T = 305.000 K 580.682 631.516 645.770 657.283 674.794 688.725 (~3p, 7I MEASUREMENTS TABLE P kg.m 3 P MPa P MPa ON CARBON DIOXIDE 831 I conrind f’ kg.m 3 119.472 161.456 189.397 210.456 227.182 247.025 5.00316 6.00166 6.49998 6.80075 6.99948 7.19471 213.926 300.229 340.559 340.741 378.329 419.963 T = 307.000 K 7.39908 459.791 7.54425 499.467 7.689 19 539.678 7.69003 578.468 7.769 10 610.837 7.82210 639.48 1 155.020 179.356 210.444 210.721 225.923 225.944 243.525 6.00051 6.49351 6.99664 7.wO47 7.20093 7.20120 7.40085 264.673 211.154 291.371 308.364 328.085 328.532 328.685 7.60095 7.70092 7.80074 7.90252 8.OGQ70 8.00275 8.00335 6.98123 6.99890 7.20004 7.20024 7.40087 240.312 258.473 268.556 219.937 292.317 7.59762 7.8~30 7.90016 8.00300 8.10420 8.4539 8.4910 17.2596 26.4470 36.0748 46.2109 0.5omo 0.503~ 1.00138 1.50097 2.00056 2.50066 56.9151 68.2227 68.2550 80.3370 93.2587 107.238 3.OOO96 3.49961 3.50096 4.00107 4.50012 5.00052 7.9173 16.1154 24.5834 33.3506 42.4800 51.9809 0.50035 1.00141 1.50120 2.00013 2.50024 3.00024 61.8900 61.9796 72.3113 83.1986 94.4446 94.6447 3.50035 3.50477 4.00339 4.50478 4.998 12 5.00679 ~._fl_ MPa i’ kg.m ’ P MPa 7.86014 7.89878 7.9548 1 8.05164 8.19623 8.40578 649.470 658.07 1 658.518 673.107 685.360 8.50344 8.60071 8.60535 X.80t97 9.00075 8.10090 8.20079 8.3ooO3 8.40050 8.40624 8.50172 8.601 17 570.374 588.407 588.550 603.289 8.70179 8.80180 8.80265 8.9030X 8.201.57 8.30093 8.40270 8.50311 8.60122 409.059 436.766 437.166 467.349 494.667 8.70488 8.80109 8.802 18 8.90506 9.00463 5.50056 6.COO96 6.50054 7.00056 7.coO87 7.50199 232.038 232.100 259,881 284.322 313.692 8.00130 ~.~201 8.40143 8.69853 9.00190 5.50059 6.Gixl34 6.50113 7.00068 7.00108 7.49995 178.691 178.701 196.289 215.394 ~‘~36 8.00077 8.49859 8.99873 T = 310.OOOK 353.211 385.694 427.346 474.756 477.239 516.354 547.104 T = 313.000K 197.476 198.527 211.058 211.074 224.961 305.593 320.8 18 338.630 358.872 381.660 T = 320.000 K 122.435 139.157 157.741 178.788 178.800 203.232 T = 340.000 K 106.512 t 19.199 132.678 146.982 146.997 162.259 The carbon dioxide used for the measurements was supplied by Messer Griesheim, F’.R.G. (purity: x(C0,) > 0.999991,where x denotes mole fraction; impurities: ~(0,) <: 1.5x lO‘j; x(NJ < 3.2 x 10m6; s(H,O) < 1.7 x lo? x(C0) < 1.2x 10 ‘; xthydrocarbons) < 0.9 x 10m6;$oil) < 0.7 x 10 “). The experimentai uncertainties of the single measuring values p, p, and T were discussed in the previous paperf3’ with this result: the uncertainty in pressure is less than 0.006 per cent or 30 Pa, whichever is greater, in density less than 0.015 per cent 832 W. DUSCHEK. R. KLEINRAHM. AND W. WAGNER 220 K I FIGURE 1. General view of the investigated (R,p. T) surface. The isotherms were calculated from the Bender equation of state”” and the coexistence curve was calculated from new correlation equations of the vapour pressures and of the saturatedliquid and saturatedvapour densities.“’ or 0.0015 kg.rnm3,i whichever is greater, and in temperature less than 0.003 K. On this basis the total uncertainty in density or in pressure was calculated by applying the Gaussian errorpropagation formula; the rehability of these total uncertainties given below is estimated to be about 95 per cent. Thus, the total relative uncertainty in density Ap/p of the (p, p, T) measurements has been determined to be less than _+0.015 per cent to kO.025 per cent in the t The uncertainty in the density of the CO, measurementsis slightly lower than that given in reference3 becausea considerably improved magneticsus~nsion balance was used to measure the buoyant force on the sinkers. To transmit the suspension force from the pressurized measuring cell to &he balance at ambient atmosphere, a new magnetic suspension coupling was developed by L6sch.‘b) It consists of an upper electromagnet fixed at the balance and of a lower permanent magnet connected by a wire with the cage for the two sinkers in the measuring cell. Between the two magnets a highstrength metal disk was placed, separating the pressure region from the ambient atmosphere. (p, p, T) MEASUREMENTS ON CARBON 833 DIOXIDE temperature range from 220 K to 290 K and from 320 K to 340 K at pressures up to 9 MPa. In the temperature range around the critical temperature (T, = 304.136K), namely from 297 K to 313 K, the total uncertainty increases to kO.035 per cent for densities less than 240 kg.rnm3 and to +0.020 per cent for densities greater than 650 kg. m 3 (critical densit y pc = 467.6 kg. m 3). In the enlarged critical region (T = 297 K to 313 K and p = 240 kg.m 3 to 650 kg.mm3), relatively large deviations in density correspond to rather small deviations in pressure. Therefore. the total uncertainty in pressure is more suitable for comparisons than the uncertainty in density. The total relative uncertainty in pressure Ap/p of the (p. I’. T) values in this region is less than +O.OlO per cent to f0.020 per cent. Based on the new experimental results, a truncated virial equation has been established to determine values for the second and third virial coefficients. The equation represents the measured densities in the temperature range from 2 I7 K to 340 K at densities up to 0.35~~within their reproducibility of better than f0.005 per cent. The form of the truncated virial equation is with the compression factor Z = (p. M)/(p . R. 7) = p/(p,. R. T), the molar gas constant R = (8.31451+_0.00021)J.K~’ .molF ’ ,“’ the molar mass of carbon dioxide M = (44.0098f0.0016) g.mol1,‘8’ t = T,/T, 6 = p/p,, the critical temperature T, = 304.136K, (2) the critical density p, = 467.6 kg. rn~ 3,(2) the amountofsubstance density P,, = p/M, and the coefficients ai and exponents ri and ti given in table 2. The structure of the equation has been found by using a new optimization method. developed by Setzmann and Wagner.(9’ The estimated uncertainty of this equation is less than F0.01 per cent, with a reliability of about 95 per cent. This estimation is based on an error analysis described in previous papers.‘5.lo’ Equation (1) corresponds to a virial equation Z = 1+ B( T)p, + C( T)p; + D( T)p;, truncated after the fourth virial coefficient. Numerical values for the second virial coefficient B and the third virial coefficient C calculated from this equation are listed TABLE i fi 2. Exponents and coefficients of equation ( I) f, 1 2 5.5 7 4 8.5 9.5 10 0.98158714 0.13329505 0.76096097 0.90567895 0.71016170  0.18302968 0.78864293 0.23562227 ~ 0.15649249 x x x x IO ’ IO1 10 I 10 ’ x IO’ x 10’ x 10’ 834 TABLE W. DUS(‘HEK. K. KLEINKAHM. AND W. WAGNEU 3. Second and third virial coef~cicnts of carbon dioxide together with their lln~~~~~in[l~~ T/K 220 240 260 280 300 320 340 B/&m” mol ‘)  747.52) I .o ~ ‘02. I 3 )0.X ~ I h8.‘7 ) 0.7 142.lt&o.h  121.35&0.5  104.49 + 0.4 90.5710.3 C’.‘(cm ‘. mol ‘)1 sta+ I55 4753,140 4360& 130 3996i 120 in table 3 together with their uncertainties.,+ The uncertainties of the virial coefficients have been determined in a way similar to that described in the methane paper.‘5’ In order to get an impression of how the way of determining the second and third virial coefficients influences their numerical values and, accordingly, also their uncertainty range, the following fitting procedures have been performed in addition to that leading to equation (I): (a) truncated virial equations have also been fitted to the (p, p, 7’) surface Iimited not only by the maximum density ~~~~= 0.35~~(as has been done for obtaining equation l), but also by pmaxvalues of 0.3p,, 0.2pE,and 0. IQ,; (b) truncated virial equations have not been fitted to the (p, p, T) surface at once but only to the (p, p, 7’) values of the single isotherms limited by the different prnBxvalues mentioned under point (a). The results can be summarized as follows. For temperatures T 3 280 K, the values for B and C obtained from all these attempts agreed with each other within the uncertainties given in table 3. For T < 280 K, however, there were large differences between the C values obtained from the entire surface fit (corresponding to equation 1) and the C values evaluated from the fits to single isotherms only. At 220 K, for instance, equation (1) yields a value for C which is about six times greater than that resulting from the isothermal fit. We suppose that the C values calculated from equation (1) (or from a surface fit in general) are more reliable than values obtained from an isothermal fit, at least for temperatures where the isotherms in the homogeneous gas region are extremely short because of the phase boundary. In spite of the high accuracy of our (p. p. T) values, but keeping in mind the discrepancies discussed above, we list in table 3 only values of the third virial coefficients for T > 280 K. It should be pointed out that most of the C values for T < 280 K, which can be found in literature, are based on (p, p, Tf measurements which are more inaccurate than ours. 4. Discussion A comparison of the new (p, p, T) values outside the critical region with several selected measurements of other workers is presented in figures 2 and 3 (relative $ It should be noted that a density calculation using only these values of B and C, and neglecting the influence of the term which includes the fourth virial coefficient. describes the densities in the temperature range from 280 K to 340 K within the limits of uncertainty of +O.Ol per cent only at pressures below 2.5 MPa. (p,p, T) MEASUREMENTS I).? 0. 1 ?I” ’ ’ ’ ’ _._._.. 1 ON CARBON I . I I I , , , l3i I; ._._.... 835 DIOXIDE , , I 1 _,_._.__... ._._._._._......xx\\ 0 .. ._._.....~ .\ \\\\\\\\““’ 0 0 _ I. \\\\\\\\\Fi\ A\ \’ 0,““” 0 0 a I \.\ 0 .\\ 0 . \,o,,... .~.\ ;\. ~~. \’ ‘.‘.\ .\~“‘>““ 0.1 I II (I.? FIGURE 2. Relativedensity deviations of experimental (p,p, T) values and of calculated densities of carbon dioxide from values pEslCcalculated from the equation of state by Pitzer and Schreiber.” ” 0, This work. Y. Vukalovich et LI/.;(~~) b4, Golovskii and Tsymarnyi:‘17’ Q, Popov and Sayapov;“8’ V, Kirillin er al.;“9’ #, Holste et CZ~.;“~’0, Rasskazov et LI~.“~’ 0. Jaeschke (refractiveindex measurements):“”    , phase boundary;“’  ., values calculated from Bender’s equation of state;“”  n , values calculated from Ely et al.‘s equation of state. ‘13’ The experimental results of the experimentalists named above cover a temperature range of +3 K around the temperature values given in these diagrams. deviations in density). Both figures show the deviations between the measured values and the values calculated from the equation of state established by Pitzer and Schreiber.” ” The equation yields for this part of the (p, p. T) surface essentially the same values as the IUPAC equation (l) does because, for this region, Pitzer and Schreiber fitted the equation only to values from the IUPAC table. In the critical region, however, they fitted their equation not to values from the IUPAC table but 836 W. DUSCHEK. R. KLEINRAHM, AND W. WAGNER 0. I 2P 7 < I 2 = = II 0.1 0.3 FIGURE 3. Relativedensity deviations of experimental (p.p, T) values and of calculated densities of 0, This carbon dioxide from values pcnlecalculated from the equation of state by Pitzer and Schreiber.“” et a1.;“4’ r$ , Michels and Michels;“6’ W. Golovskii and work, [3, Ely et al.;‘13’ < , Vukalovich Tsymarnyi;“‘) ~3, Popov and Sayapov;“8’ V. Kirillin et 01.;“~‘#, Holste et al.;‘*” 0, Rasskazov et &‘2” + , Jaeschke (refractiveindex measurements);““’ G , Jaeschke (Burnett measurements);‘22’ W, values    , phase boundary;‘*’ .  , values calculated from Bender’s equation of state;“” calculated from Ely et al.‘s equation of state. (I31 The experimental results of the experimentalists named above cover a temperature range of k 3 K around the temperature values given in these diagrams. to recent experimental values. In addition to the experimental results, the figures also show the plot of values calculated from the Bender equation”” and from the formulation of Ely et ~1.“~’ Furthermore, both figures illustrate the unce:tainty of the new (p, p, T) values and contain the position of the phase boundary calculated from a new vapourpressure equation.‘2’ (p, p. T) MEASUREMENTS ON CARBON DIOXIDE 837 FIGURE 4. Relativepressure deviations of experimental (p.p, T) values and of calculated pressuresof carbon dioxide from values pEalccalculated from the equation of state by Pitzer and Schreiber.fil’ 0, This work; c[l, Ely et ~1.;“~’ < , Vukaiovich et LI~.;“~)$, Micheis and Michels;“6) 4, Popov and Sayapov;““’ v, Kirilhn et ~1.;“~’#, Holste et a1.;1201 0, Rasskazov et &@” 9, Michels et &z51 x , Wentdo@”   , phase boundary;“’  ‘, values calculated from Bender’s equation of state:“” D, values calculated from Ely et al.‘s equation of state.“3’ The figures make clear that none of the three equations of state is able to describe the new Cp,p, T) values within the estimated experimental uncertainty. In general, the deviations amount to as much as kO.15 per cent; at higher tem~ratures they even increase to 10.3 per cent. The results of the other experimentalists agree mostly within their claimed uncertainty (in general +0.05 per cent to f0.2 per cent) with 838 W. DUSCHEK. o.;l ’ ’ ’ R. KLEINRAHM. AND W. WAGNER ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 1 0.3 0 /’ ‘. ‘. 0.; ! 100 I 3’0 I ‘. /‘ \ /’ / I‘\ ..A’I .300 400 i i /‘ I , ~ 500 [ 4 , (100 , , 700 , SOII FIGURE 5. Relativepressure deviations of experimental (p, p, T) values and of calculated pressures of 0, This carbon dioxide from values p..,. calculated from the equation of state by Pitzer and Schreiber.‘” et ~1.;““’ $. Michels and Michels;“6’ ‘$7. Kirillin et a/.;“9’ work; q , Ely et ~1.;“~’ < , Vukalovich #, Holste et CI~.;‘~~’q, Michels et t11.;(~s’x , Wentdorf? . . values calculated from Bender’s equation of state;” ”  n . values calculated from Ely et al.‘s equation of state.‘j3’ our (p, p, T) values. In comparison with our measurements, however, the values of the other workers exhibit greater scatterings (Vukalovich et CIL)“~.‘~’ or larger systematic deviations (Michels and Michels at 320 K,‘16’ Golovskii and Tsymarnyi,” 7’ Popov and Sayapov, (r8’ Kirillin et ~1.~‘~‘). In the temperature and pressure range considered in this paper, the measurements of Holste et LJ~.,‘“” Rasskazov et al.,‘21’ and JaeschkeCz2’ agree with our values within f0.05 per cent, (p. 11.T) MEASUREMENTS ON CARBON DIOXIDE 839 whereas the values of Ely ef ul. ‘l 3, deviate slightly systematically up to 0.08 per cent at 320 K which is, however, within the uncertainty given for these values. The experimental results of Vukalovich et u/.(23) and Kholodov et ~11.‘~”were considered. but not selected because of great systematic deviations. Most of the experimental results of this work in the critical region are compared in figures 4 and 5 (relative deviations of pressure) with selected measurements of other workers and also with values calculated from the three equations of state mentioned above. Just as outside the critical region, these equations are not able to represent our values in the critical region; the deviations of the calculated values amount to several times the total uncertainty in pressure of the new results. Our (p, /j, T) values agree very well with those of Ely et al. ‘13’ at 305 K and 310 K and agree only slightly less well with those of Holste et al. (20) The values of Michels et ~1.“~’ and of Wentdorft2@ show deviations which are almost parallel below our values. These systematic deviations are probably caused by an uncertain relation between their temperature scale and the IPTS68. A temperature shift of 0.025 K would bring Wentdorf’s and Michels et ul.‘s results into better agreement with the (p. p, T) values of this work. Such a value of the temperature shift is also in reasonable accordance with those suggested by Ely ef ~1.,“~) Albright et ,,1.,“” and Levelt Sengers and Chen.‘28’ The result of these comparisons can be summarized by the statement that the three discussed equations of state are not able to represent the new (p, p. T) results and those of other workers in that part of the singlephase region measured by us. The results of the other experimentalists agree mostly within their claimed uncertainty with our values, but in view of the values of these uncertainties, the observed scatterings, and tendencies of their measured values, it becomes apparent that these results are less suitable for establishing an equation of state which shall be of really high accuracy. When considering the discussion and the conclusions with regard to the (p, p, 7’) values, it does not seem to be reasonable to compare in detail the new values for the virial coefficients, listed in table 3, with those evaluated from the experimental results of the other authors. Therefore, the virial coefficients derived from the new (p. 0. T) values have been compared only with the virial coefficients given by Holste et ‘11.““’ and by those experimentalists which have been examined and listed by Dymond and Smith (“’ Our second virial coefficients clearly agree within their uncertainties with those of Holste et ~1.‘~‘) and with those of Waxman et ul. ‘30’ Values of the third virial coefficients given in the literature are rather poor and great deviations exist between the values listed in reference 29. Taking into account these differences, the values for C of Holste et al.(“) are in satisfying agreement with our values given in table 3: the! deviate up to 470 (cm3. mol 1)2 at 280 K. The authors acknowledge the assistance given by all who contributed to this work. especially H. Brugge and R. Gilgen for performing a part of the measurements. Hunter Brugge from the Chemical Engineering Department of the Texas A & M University, College Station, U.S.A., had spent half a year in our group. We are also grateful to H.W. Lasch for the development of the new version of the magnetic 840 W. DUSCHEK. R. KLEINRAHM, AND W. WAGNER suspension coupling which was the main reason that we were able to increase the accuracy of the density measurement. Above all, we thank the Deutsche Forschungsgemeinschaft for financial support of our work. REFERENCES I. Angus. S.: Armstrong, B.; de Reuck, K. M. ~nternationui Thertil~~~~,~~anli~T&es y/the Fluid State. Vol. 3: Carbon Dio.xide. Pergamon Press: Oxford. 1976. 2. Duschek, W.: Kleinrahm, R.: Wagner, W. J. Chem. Thermodynamics 1990, 22, 841, 3. Kleinrahm, R.; Wagner, W. J. Chem. Thermodynamics 1986, 18. 739. 4. 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