Problem on reversible process

Question

a. For a reversible process involving ideal gases in a closed system, Illustrate that

ΔS = C_v ln(T₂/T₁) for a constant volume process
ΔS = C_p ln(T₂/T₁) for a constant pressure process
ΔS = R ln(V₂/V₁) = R ln(P₁/P₂) for an isothermal process

b. Determine the change in entropy when 2 kg of a gas at 277 K is heated in a closed vessel to a temperature of 368 K. Taking specific heat at constant volume to be 1.42 KJ/Kg.K

c. Compute the entropy change when 1 kmol of an ideal gas at 300 K and 10 bar expands to a pressure of 1 bar if the temperature remains constant.

d. What is the change in entropy when 1 kmol of an  ideal gas at 335 K and 10 bar is expanded irreversibly to 300 K and 1 bar? C_p = 29.3 KJ/(kmol K)