Match List-I with List-II. List-I (Partial Derivatives) List-II (Thermodynamic Quantity) --- --- --- --- (A) ( frac partial G partial T ) P (I) C P (B) ( frac partial H partial T ) P (II) -S (C) ( frac partial G partial P ) T (III) C V (D) ( frac partial U partial T ) V (IV) V Choose the correct answer from the options given below:

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

(A)-(I), (B)-(II), (C)-(IV), (D)-(III)

(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Chemistry · Thermodynamics & Thermochemistry

JEE Main 2025 — 22 January, Evening Shift — Question 32

Match List-I with List-II.

	List-I (Partial Derivatives)		List-II (Thermodynamic Quantity)
(A)	${{\left( \frac{\partial \text{G}}{\partial \text{T}} \right)}_{\text{P}}}$	(I)	${{\text{C}}_{\text{P}}}$
(B)	${{\left( \frac{\partial \text{H}}{\partial \text{T}} \right)}_{\text{P}}}$	(II)	-S
(C)	${{\left( \frac{\partial \text{G}}{\partial \text{P}} \right)}_{\text{T}}}$	(III)	${{\text{C}}_{\text{V}}}$
(D)	${{\left( \frac{\partial \text{U}}{\partial \text{T}} \right)}_{\text{V}}}$	(IV)	V

Choose the correct answer from the options given below:

(A) $\mathrm{dG}=\mathrm{VdP}-\mathrm{SdT}$

Constant pressure

$\mathrm{dG}=-\mathrm{SdT}$

$\left(\frac{\partial \mathrm{G}}{\partial \mathrm{~T}}\right)_{\mathrm{P}}=-\mathrm{S}$

(B) $\mathrm{dH}=(\mathrm{dq})_{\mathrm{P}}=\mathrm{nCpdT}$

$\left(\frac{\partial \mathrm{H}}{\partial \mathrm{~T}}\right)_{\mathrm{P}}=\mathrm{C}_{\mathrm{P}}$

At constant temperature

$\mathrm{dG}=\mathrm{VdP}$

$\left(\frac{\partial \mathrm{G}}{\partial \mathrm{P}}\right)_{\mathrm{T}}=\mathrm{V}$

(D) $\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}=(\mathrm{q})_{\mathrm{v}}$

\left(\frac{\partial \mathrm{U}}{\partial \mathrm{~T}}\right)_{\mathrm{V}}=\mathrm{C}_{\mathrm{V}}

Answer key and solution verified before publishing.

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