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 $P V^{n} = c o n s t a n t$ , then $n$ is given by (Here $C_{P}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively)

\begin{matrix} n = \frac{C_{p}}{C_{v}} \end{matrix}

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\begin{matrix} n = \frac{C - C_{p}}{C - C_{v}} \end{matrix}

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\begin{matrix} n = \frac{C_{p} - C}{C - C_{v}} \end{matrix}

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\begin{matrix} n = \frac{C - C_{v}}{C - C_{p}} \end{matrix}

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Solution

The correct option is B $\begin{matrix} n = \frac{C - C_{p}}{C - C_{v}} \end{matrix}$
For a polytropic process given as $P V^{n}$ = constant.
The specific heat is given as,
$C = C_{v} + \frac{R}{1 - n}$
$⟹ 1 - n = \frac{R}{C - C_{v}}$
$n = 1 - \frac{R}{C - C_{v}}$

$= \frac{C - (C_{v} + R)}{C - C_{v}}$

$= \frac{C - C_{p}}{C - C_{v}}$

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Similar questions

Q. 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).

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):