Match List-I with List-II.

Choose the correct answer from the options given below :

The first law of thermodynamics gives the relation $$\Delta Q = \Delta U + \Delta W$$ where:
  • $$\Delta Q$$ is the heat supplied to the system,
  • $$\Delta U$$ is the change in internal energy,
  • $$\Delta W$$ is the work done by the system.

For each thermodynamic process we check which of these three quantities is zero or non-zero.

Case A: Isothermal process

Definition: Temperature remains constant.
For an ideal gas, internal energy depends only on temperature, so when temperature is constant $$\Delta U = 0$$.
Heat supplied equals work done, but both are generally non-zero.
Hence the correct description is $$\Delta U = 0$$, i.e. List-II item (IV).

Case B: Adiabatic process

Definition: No heat is exchanged with the surroundings.
Therefore $$\Delta Q = 0$$.
Neither $$\Delta U$$ nor $$\Delta W$$ is automatically zero; they are related by $$\Delta U = -\Delta W$$.
Thus the matching statement is $$\Delta Q = 0$$, i.e. List-II item (II).

Case C: Isobaric process

Definition: Pressure remains constant.
At constant pressure, the gas expands or compresses, so work is done: $$\Delta W \ne 0$$.
Temperature usually changes, so internal energy changes: $$\Delta U \ne 0$$.
Only $$\Delta U \ne 0$$ is listed among the four given statements, therefore we match with List-II item (III).

Case D: Isochoric process

Definition: Volume remains constant.
Work done for a volume change is $$\Delta W = P\,\Delta V$$. With $$\Delta V = 0$$ we get $$\Delta W = 0$$.
Heat added goes entirely into changing internal energy: $$\Delta Q = \Delta U$$, so neither of them is necessarily zero.
Thus the matching statement is $$\Delta W = 0$$, i.e. List-II item (I).

Collecting the matches:
(A) Isothermal → (IV) $$\Delta U = 0$$
(B) Adiabatic → (II) $$\Delta Q = 0$$
(C) Isobaric → (III) $$\Delta U \ne 0$$
(D) Isochoric → (I) $$\Delta W = 0$$

This corresponds to Option C.

Final Answer: Option C   [ (A)-(IV), (B)-(II), (C)-(III), (D)-(I) ]