How to calculate pressure in thermodynamics

[JT0532]

How to construct a P vs. T graph using the Peng-Robinson EOS in thermodynamics? The only condition existed is the temperature range from 150 to 520 K. The prof told me that to look for P at a fixed T and then see if the fugacities match, but how exactly can I do it?

The goal is to model the same figure as the attached file.

Please show me some hints since I don't know where i should start. Much appreciated.

 

[nilesh_pat]

The first step is to determine the parameters of the Peng-Robinson EOS. Depending on the fluid you are modeling, these parameters will need to be determined through experiments or taken from literature. For this example, we will assume that the fluid is propane and use the following parameters: • A = 0.45724 • B = 0.07780 • R = 0.08206 • Critical Temperature (Tc) = 369.8 K• Critical Pressure (Pc) = 42.48 bar Next, we need to set up the temperature range and calculate the reduced temperature (Tr) for each temperature. The temperature range is 150-520 K and the corresponding Tr values are 0.3987-1.4053 respectively. Then, we need to calculate the reduced pressure (Pr) at each reduced temperature. This can be done by solving the Peng-Robinson equation for a given reduced temperature. Finally, the P vs T graph can be constructed by plotting the calculated Pr values against the corresponding Tr values. I have attached a sample figure which shows a P vs T graph constructed using the Peng-Robinson EOS. I hope this helps!