JEE Main · 2023 · Shift-IIeasyTHERMO-018

Which of the following relations are correct? (A) U = q + p V (B) G = H - T S (C) S = qrevT (D) H = U - nRT

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

Which of the following relations are correct? (A) $\Delta U = q + p\Delta V$ (B) $\Delta G = \Delta H - T\Delta S$ (C) $\Delta S = \frac{q_{\text{rev}}}{T}$ (D) $\Delta H = \Delta U - \Delta nRT$

Options

a
C and D only
b
B and C only
✓
c
A and B only
d
B and D only

Correct Answerb

B and C only

Detailed Solution

🧠 Two relations have wrong signs — spot them Check each against the standard thermodynamic identities.

(A) $\Delta U = q + p\Delta V$ — Wrong. First Law at constant pressure: $\Delta U = q_p - p\Delta V$ (work done by system carries a minus sign). (A) has the sign flipped.

(B) $\Delta G = \Delta H - T\Delta S$ — Correct. ✓

(D) $\Delta H = \Delta U - \Delta nRT$ — Wrong. Correct form is $\Delta H = \Delta U + \Delta nRT$ . (D) has a minus where it should be plus.

Only B and C are correct → option (b).

⚠️ Relation (D) has a sign flip that many students miss — it's $+\Delta nRT$ , not $-\Delta nRT$ .

$\boxed{\text{Answer: (b)}}$

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