Question

A certain ideal gas undergoes a polytropic process $P{V}^n=constant$ such that the molar specific heat during the process is negative. If the ratio of the specific heats of the gas be $\gamma$, then the range of values of n will be

• A. $0<n<\gamma$
• B. $1<n<\gamma$
• C. $n=\gamma$
• D. $n>\gamma$

Answer 1

Answer: (B)

$1<n<\gamma$

For polytropic process, $P{V}^n=constant$
Molar specific heat $C=\frac{R}{1-n}+\frac{R}{\gamma -1}$
Thus, $C<0\Rightarrow \frac{1}{n-1}>\frac{1}{\gamma -1}\Rightarrow 1<n<\gamma$