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) ΔU=q+pΔV\Delta U = q + p\Delta V (B) ΔG=ΔHTΔS\Delta G = \Delta H - T\Delta S (C) ΔS=qrevT\Delta S = \frac{q_{\text{rev}}}{T} (D) ΔH=ΔUΔnRT\Delta H = \Delta U - \Delta nRT

Options
  1. a

    C and D only

  2. b

    B and C only

  3. c

    A and B only

  4. 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) ΔU=q+pΔV\Delta U = q + p\Delta VWrong. First Law at constant pressure: ΔU=qppΔV\Delta U = q_p - p\Delta V (work done by system carries a minus sign). (A) has the sign flipped.

(B) ΔG=ΔHTΔS\Delta G = \Delta H - T\Delta SCorrect.

(C) ΔS=qrev/T\Delta S = q_{\text{rev}}/TCorrect.

(D) ΔH=ΔUΔnRT\Delta H = \Delta U - \Delta nRTWrong. Correct form is ΔH=ΔU+ΔnRT\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 +ΔnRT+\Delta nRT, not ΔnRT-\Delta nRT.

Answer: (b)\boxed{\text{Answer: (b)}}

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