Question

A gas undergoes a process in which its pressure P and volume V are related as $V{P}^n=constant$. The bulk modulus of the gas in the process is

• A. nP
• B. $P^{1/n}$
• C. P/n
• D. $P^n$

Answer 1

The correct option is C P/n

Bulk modulus $\beta =-\frac{△P}{△V/V}$

For this process = $V{P}^n=k$

$P{V}^{1/n}=k$

Differentiating this we get,

$P\frac{1}{n}{V}^{\frac{I}{n}-1}+V^{\frac{I}{n}}\frac{dP}{dV}=0$

$V.\frac{dP}{dV}\frac{-1}{n}P$

$|V.\frac{dP}{dV}|=\frac{P}{n}$

ANSWER : C.