First slide

Different type of processes

Question

A gas undergoes a process in which the pressure P and volume V are related as ${VP}^{2 n - 1} = constant .$ Find the bulk modulus for the gas.

Moderate

A

$\frac{p}{n}$
B

$\frac{p}{n - 1}$
C

$\frac{p}{2 n - 1}$
D

$\frac{p}{3 n - 1}$

Solution

$V P^{2 n - 1} = constant$
$\Rightarrow V (2 n - 1) P^{2 n - 2} dP + P^{2 n - 1} dV = 0$
$\Rightarrow V (2 n - 1) P^{2 n - 2} dP - P^{2 n - 1} dV$
$\Rightarrow - \frac{dP}{\frac{dV}{V}} = \frac{P^{2 n - 1}}{(2 n - 1) P^{2 n - 2}}$
$\Rightarrow = \frac{P^{2 n - 1 - 2 n + 2}}{(2 n - 1)} = (\frac{P}{2 n - 1})$

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