Prove that for an ideal gas, U^ and H^ are related as H^ U^ RT, where R is the gas constant. Then: (a) Taking as given that the specific internal energy of an ideal gas is independent of the gas pressure, justify the claim that ΔH^ for a process in which an ideal gas goes from (T1, P1) to (T2, P2) equals ΔH^ for the same gas going from T1 to T2 at a constant pressure of P1. (b) Calculate ΔH(cal) for a process in which the temperature of 2.5 mol of an ideal gas is raised by 50°C, resulting in a specific internal energy change ΔU^ 3500 cal/mol.