Question

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $P{V}^n=$constant, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively).

• A. $n=\frac{C_P}{C_V}$
• B. $n=\frac{C-C_P}{C-C_V}$
• C. $n=\frac{C_P-C}{C-C_V}$
• D. $n=\frac{C-C_V}{C-C_P}$

Answer 1

The correct option is B $n=\frac{C-C_P}{C-C_V}$

For a polytropic process given as $P{V}^n=constant$

The specific heat is given as,

$C=\frac{R}{\gamma -1}+\frac{R}{1-n}$

$C=C_v\frac{\gamma -n}{1-n}$

$C=\frac{C_p-C_{v}n}{1-n}$

$\therefore n=\frac{C-C_p}{C-C_v}$