JEE Chemistry 2025 Question with Solution

Given: An ideal gas undergoes a cyclic transformation in each of the three cases and returns to the initial point A.

Find: The correct relation among $\Delta U$ for Case-I, Case-II, and Case-III.

For an ideal gas, internal energy depends only on the thermodynamic state, so it is a state function. In a cyclic process, the system returns to its initial state. Therefore, the initial and final states are the same.

Using the first law of thermodynamics,

$$\Delta U = Q - W$$

but for a complete cycle, since the state returns to the starting point,

$$\Delta U_{\text{cycle}} = 0$$

Hence, in all three cases,

$$\Delta U(\text{Case-I}) = \Delta U(\text{Case-II}) = \Delta U(\text{Case-III}) = 0$$

Therefore, the correct option is B.

Given: Three different cyclic paths A→B→C→D→A are shown on the $PV$ diagram.

Find: Whether $\Delta U$ differs from one case to another.

Concept used: For an ideal gas, internal energy depends only on temperature. Since temperature is determined by the state of the system, internal energy is a state function.

In a cyclic process, the gas starts from a point and returns to the same point after completing the cycle. So the initial and final temperatures are equal.

Therefore,

$$\Delta U_{\text{cycle}} = 0$$

for each case separately.

Thus,

$$\Delta U(\text{Case-I}) = 0, \quad \Delta U(\text{Case-II}) = 0, \quad \Delta U(\text{Case-III}) = 0$$

So,

$$\Delta U(\text{Case-I}) = \Delta U(\text{Case-II}) = \Delta U(\text{Case-III})$$

Therefore, all three are equal and the correct option is B.