= Solution
Use the <enthalpy> $H=U+pV$. The <equation of state> gives $pV=RT+pb$, so
$$
H=C_VT+U_*+RT+pb.
$$
At fixed <pressure>, $pb$ is constant. Therefore
$$
\boxed{C_p=\left(\frac{\partial H}{\partial T}\right)_p=C_V+R,
\qquad \gamma=\frac{C_p}{C_V}=1+\frac R{C_V}.}
$$
Since $C_V$ and $R$ are constants, this ratio is independent of both <temperature> and <pressure>. Although the <gas> is not mechanically ideal when $b\ne0$, its constant-pressure/constant-volume heat-capacity difference remains $R$ in this model.
Back to article page
