Question

A polytropic process for an ideal gas is represented by equation $P V^{n}=$ constant. If $g$ is ratio of specific heats $\left(\frac{C_{p}}{C_{v}}\right)$, then value of $n$ for which molar heat capacity of the process is negative, is given as:

• A. $\gamma > n$
• B. $\gamma > n > 1$
• C. $n > \gamma$
• D. none, as it is not possible

Answer 1

Answer: (B)

$C=\frac{R}{\gamma-1}-\frac{R}{n-1}$
$=\frac{R(n-\gamma)}{(n-1)(\gamma-1)}$
$C$ is negative if $\gamma>n>1$