The enthalpy of a simple (and not particularly realistic) modelsystem is given by
H = c1 TP + c2T2 /2
where c1 and c2 are constants.
1. Evaluate the partial derivatives (∂H/∂T)p and (∂H/ ∂P)t . Demonstrate thatthese partial derivatives satisfy the appropriate Maxwell relationsand also determine cP.
2. Construct the inexact differentials (dH)T,(dH)P, and the exact differential, dH .
3. Integrate these three differential quantities along thefollowing two paths that connect the same two equilibrium states:(T1, P1) to (T2, P2).
Path 1: The temperature is first increased to T2 at constantpressure, P1. The pressure is then increased to P2 at constanttemperature, T2.
Path 2: The pressure is first increased to P2 at constanttemperature, T1. The temperature is then increased to T2 atconstant pressure, P2.
Compare the integrated values for (ΔH)T,(ΔH)P, and ΔH obtained along the two paths.
