Question

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity Cremains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n =$ 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

Answer: (B)

$n = \frac{C - C_P}{C - C_V}$

Answer 2

$C = C_{V} + \frac{R}{1 - \eta}$
$\Rightarrow 1 - n = \frac{R}{C -C_{V}}$
$n = 1 - \frac{R}{ C - C_{V}} = \frac{C - \left(C_{V} + R\right)}{C - C_{V}} = \frac{C-C_{P}}{C - C_{V}}$