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Match the partial differential terms given in column-I with the thermodynamic quantities given in column-II
Column-I
(Partial derivative) Column-II
(Thermodynamic variable)
A ${(\frac{\partial U}{\partial T})}_{V}$ P $C_{P}$
B ${(\frac{\partial H}{\partial T})}_{P}$ Q $C_{V}$
C ${(\frac{\partial G}{\partial T})}_{P}$ R $- S$
D ${(\frac{\partial G}{\partial P})}_{T}$ S $V$

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$A - P; B - S; C - R; D - Q$

$A - S; B - P; C - Q; D - R$

$A - Q; B - R; C - S; D - P$

$A - Q; B - P; C - R; D - S$

answer is D.

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Detailed Solution

a) $U = n C_{v} T \Rightarrow {(\frac{\partial G}{\partial T})}_{V} = C_{V}$

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

c) $d G = V d P - S d T, {(\frac{\partial G}{\partial T})}_{P} = - S$

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

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