Compressibility Factor of Gas with Truncated Virial Equation

Question

(A) Give the expression of the compressibility factor Z (Z = PV / RT) for a gas obeying the truncated virial equation of state: PV = RT + A2P, where A2 is a function of temperature.

(B) The fugacity f may be evaluated according to the following integral: In (f/P) = ∫p0 (Z-1/P)dP
Determine the expression of the fugacity for a gas obeying the truncated virial equation of state.

(C) Evaluate the fugacity for a gas of Ar at 100 bar and 298K (for Ar, A2 = -15.8 cm3/mol).

Summary

The question belongs to Chemical Engineering and it is about explaining expression the compressibility factor of a gas obeying truncated virial equation of state for function of temperature and determining the expression of the frugacity of a gas obeying the truncated virial equation state.

Note: The solution is in handwritten format.