I need a help to plots pressure vs. Temp at equilibrium from the attached paper and in the same graph another plot using Peng Robinson model.

Question

Hanadi 2023-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/2060354-i-need-a-help-to-plots-pressure-vs-temp-at-equilibrium-from-the-attached-paper-and-in-the-same-gra

编辑： Torsten 2023-12-15

采纳的回答： Sam Chak

BF01448209.pdf

在 MATLAB Online 中打开

plot (p, T)

# in the same figure, plot using the model from the paper for P and T and compare it with Peng Robinson model. at equilibrium

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Answer 1

Sam Chak 2023-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/2060354-i-need-a-help-to-plots-pressure-vs-temp-at-equilibrium-from-the-attached-paper-and-in-the-same-gra#answer_1371184

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I'm not an expert in gas laws, but when the data is available (for example, in the fictional dataset below), you can plot the graph as desired. I cannot find any equilibrium in this sample dataset. Additionally, I'm unfamiliar with the Peng–Robinson model because the formula is not provided. I am unsure if this Peng–Robinson equation in this Wikipedia article is the same. If you provide the parameters in your question above, you can also plot it on the same graph for comparison purposes, using the 'hold on' feature.

data = [

223.160 0.0929

233.159 0.1486

233.159 0.1487

243.146 0.2285

243.156 0.2283

253.151 0.3380

253.152 0.3367

253.154 0.3378

253.154 0.3379

263.147 0.4832

263.149 0.4830

263.152 0.4830

263.152 0.4833

273.146 0.6710

273.150 0.6710

273.150 0.6712

273.151 0.6714

283.144 0.9088

283.144 0.9092

293.141 1.2047

293.141 1.2056

293.184 1.2066

298.144 1.3774

298.183 1.3800

303.139 1.5678

303.139 1.5679

303.139 1.5692

303.181 1.5701

303.181 1.5705

313.136 2.0075

313.136 2.0077

313.136 2.0078

313.136 2.0080

313.136 2.0082

313.136 2.0089

313.136 2.0090

313.136 2.0094

317.148 2.2090

318.138 2.2606

319.638 2.3411

323.133 2.5360

323.133 2.5363

323.133 2.5364

323.133 2.5368

323.133 2.5369

323.133 2.5370

323.250 2.5436

328.138 2.8398

328.176 2.8419

333.130 3.1700

333.130 3.1706

333.130 3.1710

333.130 3.1712

333.130 3.1715

333.251 3.1801

334.252 3.2505

335.134 3.3127

336.252 3.3967

337.133 3.4605

337.133 3.4621

338.252 3.5472];

%% extract the data

T = data(:,1);

P = data(:,2);

%% plot the graph

plot(P, T), grid on

title('Temperature vs. Pressure')

xlabel('Pressure (MPa)'), ylabel('Temperature (K)')

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Torsten 2023-12-14

编辑：Torsten 2023-12-15

在 MATLAB Online 中打开

My guess is that the universal gas constant is not correct for the units used for P and rho in the Peng-Robinson equation-of-state.

M = [280.148 0.8087 50.98

282.148 0.8176 50.98

303.139 0.9086 50.93

333.130 1.0324 50.86

343.127 1.0732 50.83

353.125 1.1133 50.81

363.122 1.1517 50.78

373.118 1.1917 50.76

393.115 1.2687 50.71

413.111 1.3464 50.66

433.108 1.4198 50.61

453.105 1.4983 50.55

463.105 1.5352 50.53

473.104 1.5694 50.50

298.144 1.3543 88.74

313.136 1.4815 88.68

333.129 1.6423 88.60

353.125 1.7971 88.51

373.120 1.9469 88.42

393.115 2.0934 88.33

413.111 2.2368 88.25

433.108 2.3777 88.15

453.106 2.5158 88.06

463.105 2.5782 88.02

473.103 2.6462 87.97

323.133 2.4778 187.16

333.130 2.6918 187.07

343.128 2.8973 186.98

353.125 3.0955 186.90

363.123 3.2897 186.80

373.120 3.4793 186.71

383.117 3.6659 186.62

393.115 3.8500 186.52

403.113 4.0315 186.43

413.096 4.2113 186.33

423.110 4.3893 186.24

433.108 4.5653 186.14

453.106 4.9132 185.94

473.104 5.2557 185.75

328.136 2.7507 217.07

333.130 2.8804 217.02

343.128 3.1307 216.92

353.125 3.3720 216.81

363.122 3.6070 216.70

373.120 3.8369 216.60

383.117 4.0627 216.49

393.115 4.2851 216.38

403.113 4.5046 216.27

413.111 4.7215 216.16

423.110 4.9359 216.05

433.108 5.1482 215.93

443.107 5.3590 215.82

453.106 5.5681 215.71

473.104 5.9819 215.48

338.133 3.4746 346.47

343.128 3.7078 346.38

353.125 4.1544 346.21

363.122 4.5877 346.04

373.120 5.0116 345.87

383.117 5.4282 345.69

393.115 5.8368 345.52

403.113 6.2456 345.34

413.111 6.6476 345.16

423.110 7.0463 344.98

433.108 7.4415 344.80

443.107 7.8342 344.62

453.106 8.2232 344.43

473.104 8.9952 344.06

339.483 3.6320 449.66

343.128 3.8638 449.58

353.125 4.4800 449.35

363.122 5.0833 449.13

373.114 5.6791 448.90

383.117 6.2699 448.67

393.115 6.8559 448.44

403.110 7.4375 448.21

413.111 8.0157 447.98

423.110 8.5901 447.74

433.108 9.1613 447.51

453.106 10.2950 447.03

473.104 11.4172 446.54

339.283 3.6298 567.41

339.383 3.6364 567.41

340.252 3.7060 567.38

341.246 3.7847 567.35

342.253 3.8643 567.32

343.254 3.9436 567.30

343.254 3.9433 567.30

353.256 4.7442 567.01

363.255 5.5492 566.73

373.237 6.3547 566.44

383.258 7.1616 566.15

393.259 7.9540 565.85

413.261 9.5565 565.26

433.262 11.1515 564.66

453.263 12.7424 564.05

473.265 14.3170 563.43

333.145 3.1762 704.48

336.133 3.3908 704.38

338.133 3.5423 704.31

339.133 3.6316 704.28

340.128 3.7323 704.24

341.132 3.8353 704.21

342.132 3.9397 704.17

343.128 4.0445 704.13

353.115 5.1362 703.78

373.120 7.4227 703.05

393.115 9.7631 702.32

413.111 12.1260 701.57

433.108 14.4957 700.81

453.203 16.8750 700.03

339.133 3.6695 756.32

343.126 4.1431 756.16

353.125 5.3898 755.78

363.122 6.6820 755.39

373.120 7.9998 754.99

383.124 9.3353 754.60

393.115 10.6792 754.20

403.124 12.0331 753.79

413.111 13.3882 753.39

423.110 14.7467 752.98

433.108 16.1064 752.56

439.963 17.0384 752.28

335.140 3.3660 848.73

338.133 3.8158 848.60

343.128 4.5902 848.38

348.130 5.3874 848.16

353.133 6.1998 847.94

363.122 7.8533 847.50

373.120 9.5370 847.05

383.117 11.2391 846.60

393.133 12.9576 846.14

413.111 16.4039 845.22

416.116 16.9240 845.08

333.130 3.5409 924.19

338.133 4.4970 923.95

343.118 5.4717 923.71

348.130 6.4679 923.47

353.128 7.4740 923.23

358.128 8.4908 922.98

363.114 9.5120 922.73

368.125 10.5448 922.49

373.121 11.5796 922.24

378.123 12.6205 921.99

383.104 13.6591 921.74

393.115 15.7549 921.23

328.142 3.3843 988.22

333.130 4.5304 987.96

338.133 5.7026 987.70

343.128 6.8878 987.43

348.163 8.0951 987.17

353.125 9.2934 986.90

358.128 10.5115 986.64

363.122 11.7320 986.37

368.129 12.9609 986.10

373.120 14.1900 985.83

378.123 15.4247 985.56

383.117 16.6599 985.29

306.530 1.8664 1145.32

308.181 2.4621 1145.25

313.180 4.2649 1144.94

318.178 6.0758 1144.59

323.177 7.8960 1144.31

328.176 9.7266 1143.96

333.175 11.5449 1143.64

346.031 16.2723 1142.82];

T = M(:,1);

P = M(:,2);

rho = M(:,3);

[P,I] = sort(P);

T = T(I);

rho = rho(I);

v = 1./rho;

R=8.3143/(120.02e-3)*1e-6; %MJ/(kg*K)

Tc= 339.45; %K

Pc= 3642.77e-3; %MPa

w= 0.2986;

k= 0.37464+1.54266*w-0.26992*w^2;

alph = (1+k*(1-sqrt(T/Tc))).^2;

a = 0.45724*R^2*Tc^2*alph / Pc;

b = 0.0778*R^2*Tc^2 / Pc;

pPR = R*T./ (v-b) - a ./(v.^2+2*b*v-b^2);

hold on

plot(P,T)

[pPR,I] = sort(pPR);

plot(pPR,T(I))

hold off

Sam Chak 2023-12-15

在 MATLAB Online 中打开

Thanks, @Torsten, for showing the plots. There is a discrepancy in the formula for the parameter 'b' in the Peng–Robinson equation of state, and the one supplied by the OP. I'm unsure which one is correct. Please edit the code as necessary.

%% Data

M = [280.148 0.8087 50.98

282.148 0.8176 50.98

303.139 0.9086 50.93

333.130 1.0324 50.86

343.127 1.0732 50.83

353.125 1.1133 50.81

363.122 1.1517 50.78

373.118 1.1917 50.76

393.115 1.2687 50.71

413.111 1.3464 50.66

433.108 1.4198 50.61

453.105 1.4983 50.55

463.105 1.5352 50.53

473.104 1.5694 50.50

298.144 1.3543 88.74

313.136 1.4815 88.68

333.129 1.6423 88.60

353.125 1.7971 88.51

373.120 1.9469 88.42

393.115 2.0934 88.33

413.111 2.2368 88.25

433.108 2.3777 88.15

453.106 2.5158 88.06

463.105 2.5782 88.02

473.103 2.6462 87.97

323.133 2.4778 187.16

333.130 2.6918 187.07

343.128 2.8973 186.98

353.125 3.0955 186.90

363.123 3.2897 186.80

373.120 3.4793 186.71

383.117 3.6659 186.62

393.115 3.8500 186.52

403.113 4.0315 186.43

413.096 4.2113 186.33

423.110 4.3893 186.24

433.108 4.5653 186.14

453.106 4.9132 185.94

473.104 5.2557 185.75

328.136 2.7507 217.07

333.130 2.8804 217.02

343.128 3.1307 216.92

353.125 3.3720 216.81

363.122 3.6070 216.70

373.120 3.8369 216.60

383.117 4.0627 216.49

393.115 4.2851 216.38

403.113 4.5046 216.27

413.111 4.7215 216.16

423.110 4.9359 216.05

433.108 5.1482 215.93

443.107 5.3590 215.82

453.106 5.5681 215.71

473.104 5.9819 215.48

338.133 3.4746 346.47

343.128 3.7078 346.38

353.125 4.1544 346.21

363.122 4.5877 346.04

373.120 5.0116 345.87

383.117 5.4282 345.69

393.115 5.8368 345.52

403.113 6.2456 345.34

413.111 6.6476 345.16

423.110 7.0463 344.98

433.108 7.4415 344.80

443.107 7.8342 344.62

453.106 8.2232 344.43

473.104 8.9952 344.06

339.483 3.6320 449.66

343.128 3.8638 449.58

353.125 4.4800 449.35

363.122 5.0833 449.13

373.114 5.6791 448.90

383.117 6.2699 448.67

393.115 6.8559 448.44

403.110 7.4375 448.21

413.111 8.0157 447.98

423.110 8.5901 447.74

433.108 9.1613 447.51

453.106 10.2950 447.03

473.104 11.4172 446.54

339.283 3.6298 567.41

339.383 3.6364 567.41

340.252 3.7060 567.38

341.246 3.7847 567.35

342.253 3.8643 567.32

343.254 3.9436 567.30

343.254 3.9433 567.30

353.256 4.7442 567.01

363.255 5.5492 566.73

373.237 6.3547 566.44

383.258 7.1616 566.15

393.259 7.9540 565.85

413.261 9.5565 565.26

433.262 11.1515 564.66

453.263 12.7424 564.05

473.265 14.3170 563.43

333.145 3.1762 704.48

336.133 3.3908 704.38

338.133 3.5423 704.31

339.133 3.6316 704.28

340.128 3.7323 704.24

341.132 3.8353 704.21

342.132 3.9397 704.17

343.128 4.0445 704.13

353.115 5.1362 703.78

373.120 7.4227 703.05

393.115 9.7631 702.32

413.111 12.1260 701.57

433.108 14.4957 700.81

453.203 16.8750 700.03

339.133 3.6695 756.32

343.126 4.1431 756.16

353.125 5.3898 755.78

363.122 6.6820 755.39

373.120 7.9998 754.99

383.124 9.3353 754.60

393.115 10.6792 754.20

403.124 12.0331 753.79

413.111 13.3882 753.39

423.110 14.7467 752.98

433.108 16.1064 752.56

439.963 17.0384 752.28

335.140 3.3660 848.73

338.133 3.8158 848.60

343.128 4.5902 848.38

348.130 5.3874 848.16

353.133 6.1998 847.94

363.122 7.8533 847.50

373.120 9.5370 847.05

383.117 11.2391 846.60

393.133 12.9576 846.14

413.111 16.4039 845.22

416.116 16.9240 845.08

333.130 3.5409 924.19

338.133 4.4970 923.95

343.118 5.4717 923.71

348.130 6.4679 923.47

353.128 7.4740 923.23

358.128 8.4908 922.98

363.114 9.5120 922.73

368.125 10.5448 922.49

373.121 11.5796 922.24

378.123 12.6205 921.99

383.104 13.6591 921.74

393.115 15.7549 921.23

328.142 3.3843 988.22

333.130 4.5304 987.96

338.133 5.7026 987.70

343.128 6.8878 987.43

348.163 8.0951 987.17

353.125 9.2934 986.90

358.128 10.5115 986.64

363.122 11.7320 986.37

368.129 12.9609 986.10

373.120 14.1900 985.83

378.123 15.4247 985.56

383.117 16.6599 985.29

306.530 1.8664 1145.32

308.181 2.4621 1145.25

313.180 4.2649 1144.94

318.178 6.0758 1144.59

323.177 7.8960 1144.31

328.176 9.7266 1143.96

333.175 11.5449 1143.64

346.031 16.2723 1142.82];

%% Data extraction

T = M(:,1); % extract Temperature data

P = M(:,2); % extract Pressure data

rho = M(:,3); % extract Density data

[P, I] = sort(P); % sorted Pressure [MPa]

T = T(I); % sorted Temperature [K]

rho = rho(I); % sorted Density [kg/m³]

v = 1./rho; % specific volume [m³/kg]

%% Parameters

R = 8.314462618/(120.02e-3)*1e-6; % Gas constant [MJ/(kg*K)]

Tc = 339.45; % Critical Temperature [K]

Pc = 3642.77e-3; % Critical Pressure [MPa]

omega = 0.2986;

kappa = 0.37464 + 1.54266*omega - 0.26992*omega^2;

alpha = (1 + kappa*(1 - sqrt(T/Tc))).^2;

a = 0.45724*(R^2*Tc^2)/Pc; % parameter a in P–R EoS (Wiki)

% b = 0.07780*(R^2*Tc^2)/Pc; % parameter b (defined by OP)

b = 0.07780*(R*Tc)/Pc; % parameter b in P–R EoS (Wiki)

%% Peng–Robinson equation of state

pPR = (R*T)./(v - b) - (a*alpha)./(v.^2 + 2*b*v - b^2);

%% Graphing

hold on

plot(P, T), grid on

[pPR,I] = sort(pPR);

plot(pPR, T(I)), grid on

hold off

xlabel Pressure, ylabel Temperature

legend('Data', 'Peng–Robinson', 'location', 'SE')

Hanadi 2023-12-15

编辑：Hanadi 2023-12-15

在 MATLAB Online 中打开

Thank you for the plot.

I have another question related to the same article... table 1 is showing vapor pressure (TWO Phases at equilibrium). How can I plot the graph including also PR model.... I need to compare them... similar to the last graph that you plot ...This the data from table 1

Temp. (K)
223.160 233.159 233.159 243.146 243.156 253.151 253.152 253.154 253.154 263.147 263.149 263.152 263.152 273.146 273.150 273.150 273.151 283.144 283.144 293.141 293.141 293.184 298.144 298.183
303.139 303.139 303.139 303.181 303.181 313.136 313.136 313.136 313.136 313.136 313.136 313.136 313.136 317.148 318.138 319.638 323.133 323.133 323.133 323.133 323.133 323.133 323.250 328.138 328.176 333.130 333.130 333.130 333.130 333.130 333.251 334.252 335.134 336.252 337.133 337.133 338.252
Press. (MPa)
0.0929 0.1486 0.1487 0.2285 0.2283 0.3380 0.3367 0.3378 0.3379 0.4832 0.4830 0.4830 0.4833 0.6710 0.6710 0.6712 0.6714 0.9088 0.9092
1.2047 1.2056 1.2066 1.3774 1.3800 1.5678 1.5679 1.5692 1.5701 1.5705 2.0075 2.0077 2.0078 2.0080 2.0082 2.0089 2.0090 2.0094 2.2090 2.2606 2.3411 2.5360 2.5363 2.5364 2.5368 2.5369 2.5370 2.5436 2.8398 2.8419 3.1700 3.1706 3.1710 3.1712 3.1715 3.1801 3.2505 3.3127 3.3967 3.4605 3.4621 3.5472

Torsten 2023-12-15

编辑：Torsten 2023-12-15

在 MATLAB Online 中打开

@Hanadi

We need to know how to compute the density at saturation conditions in order to apply PR (i.e. compute pressure from temperature and density).

@Sam Chak

Thank you for finding another error in the OPs coding.

For comparison, it might be better to plot Pressure against Temperature:

%% Data

M = [280.148 0.8087 50.98

282.148 0.8176 50.98

303.139 0.9086 50.93

333.130 1.0324 50.86

343.127 1.0732 50.83

353.125 1.1133 50.81

363.122 1.1517 50.78

373.118 1.1917 50.76

393.115 1.2687 50.71

413.111 1.3464 50.66

433.108 1.4198 50.61

453.105 1.4983 50.55

463.105 1.5352 50.53

473.104 1.5694 50.50

298.144 1.3543 88.74

313.136 1.4815 88.68

333.129 1.6423 88.60

353.125 1.7971 88.51

373.120 1.9469 88.42

393.115 2.0934 88.33

413.111 2.2368 88.25

433.108 2.3777 88.15

453.106 2.5158 88.06

463.105 2.5782 88.02

473.103 2.6462 87.97

323.133 2.4778 187.16

333.130 2.6918 187.07

343.128 2.8973 186.98

353.125 3.0955 186.90

363.123 3.2897 186.80

373.120 3.4793 186.71

383.117 3.6659 186.62

393.115 3.8500 186.52

403.113 4.0315 186.43

413.096 4.2113 186.33

423.110 4.3893 186.24

433.108 4.5653 186.14

453.106 4.9132 185.94

473.104 5.2557 185.75

328.136 2.7507 217.07

333.130 2.8804 217.02

343.128 3.1307 216.92

353.125 3.3720 216.81

363.122 3.6070 216.70

373.120 3.8369 216.60

383.117 4.0627 216.49

393.115 4.2851 216.38

403.113 4.5046 216.27

413.111 4.7215 216.16

423.110 4.9359 216.05

433.108 5.1482 215.93

443.107 5.3590 215.82

453.106 5.5681 215.71

473.104 5.9819 215.48

338.133 3.4746 346.47

343.128 3.7078 346.38

353.125 4.1544 346.21

363.122 4.5877 346.04

373.120 5.0116 345.87

383.117 5.4282 345.69

393.115 5.8368 345.52

403.113 6.2456 345.34

413.111 6.6476 345.16

423.110 7.0463 344.98

433.108 7.4415 344.80

443.107 7.8342 344.62

453.106 8.2232 344.43

473.104 8.9952 344.06

339.483 3.6320 449.66

343.128 3.8638 449.58

353.125 4.4800 449.35

363.122 5.0833 449.13

373.114 5.6791 448.90

383.117 6.2699 448.67

393.115 6.8559 448.44

403.110 7.4375 448.21

413.111 8.0157 447.98

423.110 8.5901 447.74

433.108 9.1613 447.51

453.106 10.2950 447.03

473.104 11.4172 446.54

339.283 3.6298 567.41

339.383 3.6364 567.41

340.252 3.7060 567.38

341.246 3.7847 567.35

342.253 3.8643 567.32

343.254 3.9436 567.30

343.254 3.9433 567.30

353.256 4.7442 567.01

363.255 5.5492 566.73

373.237 6.3547 566.44

383.258 7.1616 566.15

393.259 7.9540 565.85

413.261 9.5565 565.26

433.262 11.1515 564.66

453.263 12.7424 564.05

473.265 14.3170 563.43

333.145 3.1762 704.48

336.133 3.3908 704.38

338.133 3.5423 704.31

339.133 3.6316 704.28

340.128 3.7323 704.24

341.132 3.8353 704.21

342.132 3.9397 704.17

343.128 4.0445 704.13

353.115 5.1362 703.78

373.120 7.4227 703.05

393.115 9.7631 702.32

413.111 12.1260 701.57

433.108 14.4957 700.81

453.203 16.8750 700.03

339.133 3.6695 756.32

343.126 4.1431 756.16

353.125 5.3898 755.78

363.122 6.6820 755.39

373.120 7.9998 754.99

383.124 9.3353 754.60

393.115 10.6792 754.20

403.124 12.0331 753.79

413.111 13.3882 753.39

423.110 14.7467 752.98

433.108 16.1064 752.56

439.963 17.0384 752.28

335.140 3.3660 848.73

338.133 3.8158 848.60

343.128 4.5902 848.38

348.130 5.3874 848.16

353.133 6.1998 847.94

363.122 7.8533 847.50

373.120 9.5370 847.05

383.117 11.2391 846.60

393.133 12.9576 846.14

413.111 16.4039 845.22

416.116 16.9240 845.08

333.130 3.5409 924.19

338.133 4.4970 923.95

343.118 5.4717 923.71

348.130 6.4679 923.47

353.128 7.4740 923.23

358.128 8.4908 922.98

363.114 9.5120 922.73

368.125 10.5448 922.49

373.121 11.5796 922.24

378.123 12.6205 921.99

383.104 13.6591 921.74

393.115 15.7549 921.23

328.142 3.3843 988.22

333.130 4.5304 987.96

338.133 5.7026 987.70

343.128 6.8878 987.43

348.163 8.0951 987.17

353.125 9.2934 986.90

358.128 10.5115 986.64

363.122 11.7320 986.37

368.129 12.9609 986.10

373.120 14.1900 985.83

378.123 15.4247 985.56

383.117 16.6599 985.29

306.530 1.8664 1145.32

308.181 2.4621 1145.25

313.180 4.2649 1144.94

318.178 6.0758 1144.59

323.177 7.8960 1144.31

328.176 9.7266 1143.96

333.175 11.5449 1143.64

346.031 16.2723 1142.82];

%% Data extraction

T = M(:,1); % extract Temperature data

P = M(:,2); % extract Pressure data

rho = M(:,3); % extract Density data

[T, I] = sort(T); % sorted Temperature [K]

P = P(I); % sorted Pressure [MPa]

rho = rho(I); % sorted Density [kg/m³]

v = 1./rho; % specific volume [m³/kg]

%% Parameters

R = 8.314462618/(120.02e-3)*1e-6; % Gas constant [MJ/(kg*K)]

Tc = 339.45; % Critical Temperature [K]

Pc = 3642.77e-3; % Critical Pressure [MPa]

omega = 0.2986;

kappa = 0.37464 + 1.54266*omega - 0.26992*omega^2;

alpha = (1 + kappa*(1 - sqrt(T/Tc))).^2;

a = 0.45724*(R^2*Tc^2)/Pc; % parameter a in P–R EoS (Wiki)

% b = 0.07780*(R^2*Tc^2)/Pc; % parameter b (defined by OP)

b = 0.07780*(R*Tc)/Pc; % parameter b in P–R EoS (Wiki)

%% Peng–Robinson equation of state

pPR = (R*T)./(v - b) - (a*alpha)./(v.^2 + 2*b*v - b^2);

%% Graphing

hold on

plot(T, P), grid on

plot(T, pPR), grid on

hold off

xlabel Temperature, ylabel Pressure

legend('Data', 'Peng–Robinson', 'location', 'SE')

Hanadi 2023-12-15

final request can you plot (pressure vs. density) from the previous data using the paper data and PR?

Torsten 2023-12-15

编辑：Torsten 2023-12-15

We corrected your PR equation and we plotted pressure vs. temperature for the paper data and PR. I think it's time now that you start doing your part of the work.

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