A Carnot engine/cycle consists of the following reversible process steps between states 1, 2, 3, and 4: 1 - 2: adiabatic compression 2 - 3: isothermal expansion at TH 3 - 4: adiabatic expansion 4 - 1: isothermal compression at TC Assume that the working fluid is an ideal monatomic gas with cV = (3/2)kB and cP = (5/2)kB. Prove that the Carnot cycle achieves the maximum efficiency allowed by the second law for a heat engine, max = 1 - TC/TH