Match List-I with List-II. List-I (Partial Derivatives): (A) $\left(\frac{\partial \mathrm{G}}{\partial \mathrm{T}}\right)_{\mathrm{P}}$ (B) $\left(\frac{\partial \mathrm{H}}{\partial \mathrm{T}}\right)_{\mathrm{P}}$ (C) $\left(\frac{\partial \mathrm{G}}{\partial \mathrm{P}}\right)_{\mathrm{T}}$ (D) $\left(\frac{\partial \mathrm{U}}{\partial \mathrm{T}}\right)_{\mathrm{V}}$ List-II (Thermodynamic Quantity): (I) $\mathrm{C}_{\mathrm{p}}$ (II) $-\mathrm{S}$ (III) $\mathrm{C}_{\mathrm{v}}$ (IV) $\mathrm{V}$ Choose the correct answer from the options given below :

Each match follows directly from the fundamental differential of the corresponding state function. (A) From , holding P constant kills the term, leaving . Match: (A)–(II). (B) At constant pressure, heat absorbed equals the enthalpy change, , so . Match: (B)–(I). (C) From the same Gibbs differential…

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Chemical Thermodynamics

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Match List-I with List-II.

List-I (Partial Derivatives):
(A)

(\frac{\partial G}{\partial T})_{P}

(B)

(\frac{\partial H}{\partial T})_{P}

(C)

(\frac{\partial G}{\partial P})_{T}

(D)

(\frac{\partial U}{\partial T})_{V}

List-II (Thermodynamic Quantity):
(I)

C_{p}

(II)

- S

(III)

C_{v}

(IV)

V

Choose the correct answer from the options given below :

Answer: A → II, B → I, C → IV, D → III

Solution

Each match follows directly from the fundamental differential of the corresponding state function.

(A) From

d G = V d P - S d T

, holding P constant kills the

V d P

term, leaving

(\frac{\partial G}{\partial T})_{P} = - S

. Match: (A)–(II).

(B) At constant pressure, heat absorbed equals the enthalpy change,

(d q)_{P} = d H = n C_{P} d T

, so

(\frac{\partial H}{\partial T})_{P} = C_{P}

. Match: (B)–(I).

(C) From the same Gibbs differential, holding T constant kills the

- S d T

term, leaving

(\frac{\partial G}{\partial P})_{T} = V

. Match: (C)–(IV).

(D) At constant volume, heat absorbed equals the change in internal energy,

(d q)_{V} = d U = n C_{V} d T

, so

(\frac{\partial U}{\partial T})_{V} = C_{V}

. Match: (D)–(III).

The correct matching is (A)–(II), (B)–(I), (C)–(IV), (D)–(III).

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Match the columns

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JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Chemical Thermodynamics

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