Calculate the fugacity

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Prompt/Given Information: Consider a reversible isothermal expansion of vapor benzene at 450 K from 1 to 0.1 MPa. Assume that the PVT behavior of benzene obeys van der Waals equation of state.                                      P = (RT)/(V - b) - a/V2            for benzene: a = 1884514 (cm6 * MPa)/mol2 and                                  b = 119.47 cm3/mol For your convenience, at 450 K and 0.1 MPa the volume of vapor benzene is 37025 cm3/mol, and at 450 K and 1 MPa it is 3312.4 cm3/mol. R = 8.314 (MPa*cm3)/(mol*K). Note: 1 cm3*MPa/mol = 1 J/mol   Question: What is the change of internal energy? What would be the change of internal energy if the gas was ideal?

Compute the fugacity and chemical potential for CO2 at 323 K and 5 bar. At these conditions, CO2 is described by the virial equation of state truncated at the second virial coefficient. Assume that the interaction potential between CO2 molecules can be described by the spherically symmetric square-well potential.