Question

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

Answer 1

Bulk modulus of the gas $B=-\frac{dP}{dV/V}$ (at constant temperature)

The given process is $V{P}^n=constant$

Differentiating, we get $V\times n{P}^{n-1}dP+P^{n}dV=0$

$\therefore$ $Vn{P}^{n-1}dP=-P^{n}dV$

$⟹$ $-\frac{dP}{dV/V}=\frac{P}{n}$

$⟹$ Bulk modulus of the gas $B=\frac{P}{n}$