Solution:
One mole of an {\bf ideal diatomic gas} is compressed adiabatically in a piston–cylinder device from $2\ bar$ and $25^\circ C$ to $7\ bar$. The process is irreversible and requires $35\%$ more work than a reversible, adiabatic compression from the same initial state to the same final pressure.
\begin{parts}
\part [3] What is the constant–volume heat capacity of this ideal gas?
\part [12] What is the entropy change of the gas, in unit of $J/(mol \cdot K)$?
\end{parts}
