(a) The partition function for a two-dimensional monatomic gas at temperature T with particle mass m that can move around freely within a plane with an area A is given by Z= 2AmmkT h² Use this partition function Z to derive the heat capacity Cy and entropy S of the system. (b) Assume you define a property of a system as which is given by e-s= U + PV T T (2) T Show that the volume of the system can be written as V = -T