Problem 4: 200mol of an ideal gas, with Constant Pressure Molar Heat Capacity CPTH(T,P)(J/(molK))=(5/2)R(J/(molK)),R=8.314(J/(molK)) that is constant throughout the (P,V) state-space, undergoes the following paths in (P,Vt) state-space, starting at P1=1 bar and V1t=8.314m3, and ending at P2=8.314 bar and V2t=1m3 : a. Isothermal compression. b. Adiabatic, reversible compression followed by cooling at constant pressure. c. Adiabatic, reversible compression followed by cooling at constant volume. d. Heating at constant volume followed by cooling at constant pressure. e. Cooling at constant pressure followed by heating at constant volume. Calculate Q,W,UU(P2,V2)U(P1,V1),HH(P2,V2)H(P1,V1), and SS(P2,V2)S(P1,V1) for each of these processes, and sketch the paths of each process on a single (P,V) diagram. (similar to Problem 3.10 Smith, Van Ness, Abbott)