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

ΔS = C_v ln(T2/T1) for a constant volume process

ΔS = Cp 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, rigid container to a temperature of 368 K. Take the specific heat at constant volume to be 1.42 KJ/Kg.K

c. Calculate 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 stays 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  = 29.3 KJ/(kmol K)