Match List - I with List - II. Given V_1 and V_2 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 V_2 V_1 C. Irreversible Compression III. w = -p_ ext (V_1 - V_2) D. Cyclic reversible IV. q_ rev T = 0 Choose the correct answer from the options given below :
C. A-II, B-I, C-III, D-IV
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 ( V_2 V_1 ), which gives q = nRT ( V_2 V_1 ). 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 corresponds to the expression in III. Thus, C matches III. For a cyclic reversible process, the initial and final states are the same, so the change in entropy S = 0. Since S = q_ rev T , we get q_ rev T = 0. Thus, D matches IV. The correct matching is A-II, B-I, C-III, D-IV. Answer: A-II, B-I, C-III, D-IV
Related: Chemistry — Thermodynamics (C) · All PYQ Banks