Match List - I with List - II.
Choose the correct answer from the options given below :

The definitions of the various thermodynamic processes together with the first-law relation $$\Delta U = q + w$$ allow us to identify the characteristic quantity that becomes zero in each case.

Case A: Adiabatic process. By definition no heat is exchanged with the surroundings, therefore $$q = 0$$. This corresponds to List-II item (II).

Case B: Isochoric (constant-volume) process. Because the volume is fixed, $$\Delta V = 0$$ and the expansion work $$w = -P_{\text{ext}}\Delta V = 0$$. Hence it matches List-II item (I).

Case C: Isothermal (constant-temperature) process. The temperature does not change, so $$\Delta T = 0$$, which is List-II item (IV).

Case D: Free (Joule) expansion of an ideal gas into vacuum. The external pressure is zero, so $$w = 0$$. The vessel is insulated, so $$q = 0$$. Consequently, from the first law $$\Delta U = 0$$, giving List-II item (III).

Thus the correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Option C which is: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)