Question

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?

• A. $\frac{5 p_0}{6 \alpha}$
• B. $\frac{p_0}{2 \alpha}$
• C. $\frac{p_0}{4 \alpha}$
• D. $\frac{5 p_0}{8 \alpha}$

Answer 1

Answer: (D)

$d s=n C_v d T+P d V=0$
$n R \frac{d T}{d V}+\left(p_0-\alpha V\right)=0$
$p_V=n R T$
$p_0 V-\alpha V^2=n R T$
$p_0-2 a V=n R \frac{d T}{d V} $
$-\left(p_0-\alpha V\right)(\gamma-1)=p_0-2 a V $
$-p_0(\gamma-1)+a(\gamma-1) V=P_0-2 a V $
$p_0 V=\alpha V(\gamma+1)$
$V=\frac{P_0 \gamma}{a(\gamma+1)}$
$V=\frac{P_0 \times \frac{5}{3}}{a\left(\frac{5}{3}+1\right)} =\frac{5P_0}{P_0}$