Problem 2, 20 marks - derivative manipulations In this problem assume that you do not know the equation of state. In other words, do not assume the substance is an ideal gas. a) Using the relationship between the constant pressure heat capacity and state functions, CP=(TH)P and the definition of the enthalpy, HU+PV, show that CP=(TU)P+P(TV)P b) Using the relationship between the constant volume heat capacity and state functions, CV=(TU)V and using a "non-natural derivative" manipulation from the course web page https://personal . utdallas. edu/ son051000/chem3321/Chem3321math1.pdf show that CPCV=(VU)T(TV)P+P(TV)P