Q3 / 160 · WBJEE 2010 · Chemistry
Which of the following thermodynamic relation is correct?
- Correct answerA$\mathrm{dG}=\mathrm{VdP}-\mathrm{SdT}$
- B$\mathrm{dE}=\mathrm{PdV}+\mathrm{TdS}$
- C$\mathrm{dH}=-\mathrm{VdP}+\mathrm{TdS}$
- D$\mathrm{dG}=\mathrm{VdP}+\mathrm{SdT}$
Solution
$$
\text { Hints: } \begin{gathered}
\mathrm{dG}=\mathrm{dH}-\mathrm{TdS}-\mathrm{SdT}(\text { as } \mathrm{G}=\mathrm{H}-\mathrm{TS} \text { ) } \\
\text { again, } \mathrm{H}=\mathrm{U}+\mathrm{PV} \\
\therefore \mathrm{dH}=\mathrm{dU}+\mathrm{PdV}+\mathrm{VdP} \\
\& \mathrm{dU}=\mathrm{TdS}-\mathrm{PdV}
\end{gathered}
$$
Thus $d G=(T d S-P d V)+P d V+V d P-T d S-S d T$
$$
=\mathrm{VdP}-\mathrm{SdT}
$$
Hence, the correct answer is option: 'A'.