A chemical engineering company is evaluating the behavior of methane at high pressures and temperatures, typical of natural gas processing. You are to use equations of state to predict the molar volume of methane at a temperature of $400K$ and a pressure of $10$MPa. Assume the critical properties of methane are:

Tasks:

Calculate the molar volume of methane using:

a$.$ Peng$-$Robinson $($PR$)$ equation

b$.$ Swoave$-$Redlich$-$Kwong $($SRK$)$ equation

c$.$ Redlich$-$Kwong $($RK$)$ equation

Discuss how the choice of equation of state impacts the predicted behavior of real gases based on the molar volume values obtained.

Find the molar volume of methane at $400K$ and a pressure of $20$MPa using the PR equation.

Discuss how the molar volume values would change if the temperature or pressure were significantly increased, based on the behavior described by the Peng$-$Robinson equation.