Adiabatic bulk modulus of a gas at a pressure ' $\mathrm{P}^{\prime}$ is ( $\gamma$-ratio of specific heat…
Adiabatic bulk modulus of a gas at a pressure ' $\mathrm{P}^{\prime}$ is ( $\gamma$-ratio of specific heat capacities of the gas)
$\gamma$
$\gamma \mathrm{P}$
P
$\frac{\gamma}{\mathrm{P}}$
Solution
Bolk modulus, $K=\frac{\text { Pressure }}{\text { Strain }}$
$
\mathrm{K}=-\frac{\Delta \mathrm{PV}}{\Delta \mathrm{V}}
$
For adiabatic process
$
\begin{aligned}
& P V^\gamma=K \\
& P \gamma V^{\gamma-1} d V+V^\gamma d P=0 \\
& \frac{P K d V}{V}+d P=0 \Rightarrow \frac{d P}{d V}=-\frac{\gamma P}{V}
\end{aligned}
$
Put this value in equation 1 , we have
$
\mathrm{K}=-\left(\frac{-\gamma \mathrm{p}}{\mathrm{V}}\right) \mathrm{V}=\gamma \mathrm{P}
$