Match List - I with List - II. Given V₁ and V₂ are initial and final volumes respectively. List - I (Isothermal process) List - II (Expression) A. Reversible expansion I. q = 0 B. Free expansion II. q = nRT V₂ V₁ C. Irreversible Compression III. w = -p_ ext (V₁ - V₂) D. Cyclic reversible IV. q_ rev T = 0 Choose the correct answer from the options given below :

Step-by-step solution

For an isothermal reversible expansion, the change in internal energy U = 0 . From the first law of thermodynamics, q = -w . The work done is w = -nRT ( V₂ V₁ ) , which gives q = nRT ( V₂ V₁ ) . Thus, A matches II. For free expansion, the external pressure is zero ( p_ ext = 0 ), so the work done w = 0 . Since the process is isothermal, U = 0 . Therefore, the heat exchanged q = 0 . Thus, B matches I. For an irreversible compression, the work done against a constant external pressure is given by w = -p_ ext V . This