A) \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}\]
B) \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}\]
C) \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{V}}\]
D) \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{V}}\]
Correct Answer: B
Solution :
The Gibbs-Helmholtz equation is as: \[H+T{{\left( \frac{\delta G}{\delta T} \right)}_{P}}\] Dividing above equation by \[{{T}^{2}}\] \[\frac{G}{{{T}^{2}}}=\frac{H}{{{T}^{2}}}+\frac{1}{T}{{\left( \frac{\delta G}{\delta T} \right)}_{P}}\] This on rearrangement becomes \[{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}=-\frac{H}{{{T}^{2}}}\] \[H=-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}\] where H = enthalpy
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