JEE Chemistry 2023 Question with Solution

Given: Four thermodynamic relations are listed.

Find: Which relations are correct and hence identify the correct option.

Check each statement using standard definitions and sign conventions.

• (A)

$$\Delta U = q + w$$

For pressure-volume work,

$$w = -p\Delta V$$

Therefore,

$$\Delta U = q - p\Delta V$$

So, $\Delta U = q + p\Delta V$ is incorrect.

• (B)

$$G = H - TS$$

This is the definition of Gibbs free energy, so statement (B) is correct.

• (C)

$$\Delta S = \frac{q_{\text{rev}}}{T}$$

This is the entropy change for a reversible process at temperature $T$, so statement (C) is correct.

• (D) For an ideal gas,

$$\Delta H = \Delta U + nRT$$

Hence, $\Delta H = \Delta U - nRT$ is incorrect.

Therefore, the correct relations are B and C, so the correct option is C.

The solution states directly that (B) and (C) are correct, while (A) and (D) are incorrect.

This matches the grouped answer choice:

$$\text{(2) B and C only}$$

and the page concludes: The Correct Option is C.