[QUE/SM-03006] SM-PROBLEM

{A particular system obeys the fundamental equation, $$U=A\ \frac{N^3}{V^2}\exp\left( \frac{S}{Nk_B}\right), $$ where $A$ (joule metre$^2$) is a constant. Initially the system is at $T=317.48$ kelvin, and $P=2\times 10^5$ pascals. The system expands reversibly until the pressure drops to a value of $10^5$ pascals, by a process in which the entropy does not change. What is the final temperature\footnote{HINT: Take partial derivatives of $U$ with respect to $S$ and $V$ and get $T$ and $P$ respectively. Find a relation between $P$ and $T$ when entropy does not change.

KPN