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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 :

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

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

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

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

answer is B.

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Detailed Solution

(A) dG = VdP – SdT
Constant pressure
dG = – SdT

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

$(B) dH = (dq)_{P} = nCpdT {(\frac{\partial H}{\partial T})}_{P} = C_{P} (C) dG = VdP - SdT$

At constant temperature
dG = VdP

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

$\begin{array}{l} (D) dU = {nC}_{V} dT = (q)_{v} \\ {(\frac{\partial U}{\partial T})}_{V} = C_{v} \end{array}$

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