a) Draw an annotated schematic of the process described as well as a p vs. T state diagram.

b) Show that the expression for the real constant-pressure heat capacity is

C_p(T, P)/R = (7/2) + (3T/1000) + (aP/4T^0.5)

You have been tasked to design a heater to preheat a precursor gas upstream of a chemical reactor. Your feed stream is at about 27C and 50 bar and has a molar flow rate of nin=430mol/s. The specification is that the gas should enter the reactor at 227C and 50 bar. Suppose that you have the following information: - The equation of state is given by z=RTpv=1+T0.5apwitha=0.1K0.5/bar - The constant-volume heat capacity in the ideal-gas state is given by RcvIG=25+10003TwithTinKelvin - The ideal gas constant is R=8.3145J/(molK);1 bar =105N/m2=105J/m3 - The pricing on energy is $0.13/(kWhr);1kWhr=3.6106J