A supercritical fluid Xis used as a solvent. The critical point is T=500 K and P=200 bar, so the process must be carried out at exceedingly high temperatures and pressures. At the end of the process a turbine is used to return the supercritical fluid to lower pressures. It enters the turbine at T=550 K and P=300 bar and leaves the turbine at T=300 K and P=1 bar.

Question

This equation of state can be used to model the supercritical fluid at the conditions we are examining in this problem:

Z = 1 + bPT Where b= 1.5 x 10-6 bar-1K-1

The ideal gas heat capacity is Cp*=5R, and can be considered constant, and the acentric factor is ?=0.4.

A) Estimate the change in molar enthalpy the compound X experiences when it goes through the turbine, using the equation of state above.
B) If you were going to use the Peng Robinson equation to model X at T=550 K, what values of the parameters a and b would you use?
C) Another solvent Y is geometrically and structurally similar to X. Y has critical temperature of 425 K and critical pressure of 150 bar, and no other data for Y is available. What is your best estimate of the constant b for compound Y in the equation of state Z = 1 + bPT?

Answer 1

Put the EOS in terms of V:



Take partial derivative with respect to T at constant P:









Assuming Y has the same Z at critical point:



Note however that typically compounds have Z significantly below 1 (e.g., 0.2-0.3) at their critical point. This is a simplified EOS concocted for exam purposes and is not used in practice.

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