Prove that for an ideal gas. U and ii 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 .A for a process in which an ideal gas goes from (T₁, P₁) to (T₂ ∙ P₂) equals ii 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 b 50°C, resulting in a specific internal energy change ΔU = 3500 cal/mol.