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, $PV^{n}=$ constant, then $n$ is given by ( $C_{P}=$ molar specific heat at constant pressure, $C_{V}=$ molar specific heat at constant volume),

• A. $n=\frac{C_{P} - C_{V}}{C - C_{V}}$
• B. $n=\frac{C - C_{V}}{C - C_{P}}$
• C. $n=\frac{C_{P}}{C_{V}}$
• D. $n=\frac{C - C_{P}}{C - C_{V}}$

Answer 1

Answer: (D)

For a polytropic process,
$C=C_{V}+\frac{R}{1 - n}\Rightarrow C-C_{V}=\frac{C_{P} - C_{V}}{1 - n}$
$\Rightarrow 1-n=\frac{C_{P} - C_{V}}{C - C_{V}}$
$\Rightarrow n=1-\frac{C_{P} - C_{V}}{C - C_{V}}=\frac{C - C_{P}}{C - C_{V}}$ .