The ideal gas equation of state can be written using the compressibility factor as Z = PV RT = 1 Many improvements of this equation focus on adding dimensionless volumetric or density correction terms to the unity value. For example, an improvement of this equation could be of the form Z = PV RT = 1+ B V , where B is a function of temperature. A common form for B is B = exp T , where , , and are component dependent constants. Assume that carbon dioxide can be described with this equation with = 137.6, = 87.7, and = 325.7 (all constants), T is in Kelvin, and B is in cm3 /mol. The ideal gas mean constant volume heat capacity for carbon dioxide can be assumed as 34.2 J/mol lK.

(a) Set up a thermodynamic solution path to calculate the change in internal energy for carbon dioxide undergoing the changes in thermodynamics conditions described in part (b). Derive any expressions needed to evaluate the changes in internal energy.

(b) Evaluate the changes in internal energy, using the solution path developed in part (a), for the following changes in thermodynamic conditions: Specific volume change from 0.033 m3 /mol to 0.0006 m3 /mol at a constant temperature of 400 K. Pressure change from 50 bar to 60 bar at a constant temperature of 400 K. From (400 K, 0.003 m3 /mol) to (500 K, 0.001 m3 /mol)