1. Tardigrade
  2. Question
  3. Physics
  4. 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 PVn = constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) :

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Q. 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) :

JEE MainJEE Main 2016Thermodynamics

Solution:

$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}} $