Solution:
\begin{parts}
\part [5] Please write down the fundamental property relation for $dA$ for a closed system.
\part [12] In a closed system, based on one mole of a homogeneous fluid of constant composition, please derive to obtain $\displaystyle \left[ \frac{\partial \left( A / RT \right)}{\partial V} \right]_T = – \frac{P}{RT}$ and $\displaystyle \left[ \frac{\partial \left( A / RT \right)}{\partial T} \right]_V = – \frac{1}{T} \left( \frac{U}{RT} \right)$.
\end{parts}
\vspace*{0.5em}\textbf{[Note]} $A \equiv U – TS$ where $A$ is the Helmholtz energy.
