Search any question & find its solution
Question:
Answered & Verified by Expert
Adiabatic bulk modulus of a gas at a pressure ' $\mathrm{P}^{\prime}$ is ( $\gamma$-ratio of specific heat capacities of the gas)
Options:
Solution:
2807 Upvotes
Verified Answer
The correct answer is:
$\gamma \mathrm{P}$
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
$$
\mathrm{K}=-\left(\frac{-\gamma \mathrm{p}}{\mathrm{V}}\right) \mathrm{V}=\gamma \mathrm{P}
$$
$$
\mathrm{K}=-\frac{\Delta \mathrm{PV}}{\Delta \mathrm{V}}
$$
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
$$
\mathrm{K}=-\left(\frac{-\gamma \mathrm{p}}{\mathrm{V}}\right) \mathrm{V}=\gamma \mathrm{P}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.