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GATE 2023 MT – Question 36

Metallurgical Thermodynamics · Thermodynamic laws and functions · 2 marks · Multiple choice

Let $S,T,P,V$ denote entropy, temperature, pressure, and volume. Match Column I to the natural variables in Column II.

Column I:

A. Gibbs free energy

B. Helmholtz free energy

C. Enthalpy

D. Internal energy

Column II:

1. T, V, composition

2. T, P, composition

3. S, P, composition

4. S, V, composition

  1. A–2, B–1, C–3, D–4
  2. A–4, B–3, C–2, D–1
  3. A–3, B–1, C–4, D–2
  4. A–2, B–1, C–4, D–3

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Show answer and explanation

Correct answer: (A) A–2, B–1, C–3, D–4

Explanation

The thermodynamic differentials are $dG=-S\,dT+V\,dP$, $dA=-S\,dT-P\,dV$, $dH=T\,dS+V\,dP$, and $dU=T\,dS-P\,dV$, with composition terms when amounts vary.

Thus the natural variables are respectively T/P, T/V, S/P, S/V. Match: **A–2, B–1, C–3, D–4; option A**.