A monoatomic ideal gas goes through a process $p=p_{0}-\alpha V$ where $p_{0}$ and $\alpha$ are positive constants and $V$ is its volume. At what volume will the entropy of gas be maximum?

Question

Aicharya · Accepted Answer

$d s=n C_{v} d T+P d V=0$
$n R \frac{d T}{d V}+\left(p_{0}-\alpha Vight)=0$
$p V=n R T$
$p_{0} V-\alpha V^{2}=n R T$
$p_{0}-2 \alpha V=n R \frac{d T}{d V}$
$-\left(p_{0}-\alpha Vight)(\gamma-1)=p_{0}-2 \alpha V$
$-p_{0}(\gamma-1)+\alpha(\gamma-1) V=p_{0}-2 \alpha V$
$p_{0} V=\alpha V(\gamma+1)$
$V=\frac{p_{0} \gamma}{\alpha(\gamma+1)}$
$V=\frac{p_{0} \times \frac{5}{3}}{\alpha\left(\frac{5}{3}+1ight)}=\frac{5 p_{0}}{8 \alpha}$ ^

A monoatomic ideal gas goes through a process $p=p_{0}-\alpha V$ where $p_{0}$ and $\alpha$ are positive…

Solution