Carnot cycle of an engine is given below Total work done by the gas in one cycle is

Step-by-step solution

The Carnot cycle has two isothermal and two adiabatic processes. P Q : Isothermal expansion at T₁ ( T₁ = T₂ ): W_ PQ = RT₁ V₂ V₁ Q R : Adiabatic expansion: W_ QR = R(T₂ - T₃) - 1 R S : Isothermal compression at T₃ ( T₃ = T₄ ): W_ RS = - RT₃ V₃ V₄ S P : Adiabatic compression: W_ SP = R(T₄ - T₁) - 1 Since T₁ = T₂ and T₃ = T₄ , the adiabatic work terms cancel: W_ QR + W_ SP = 0 Total work: W = RT₁ V₂ V₁ - RT₃ V₃ V₄ = RT₁ V₂ V₁ - RT₂ V₃ V₄ Correct option: (2)