Question

The adiabatic Bulk modulus of a perfect gas at pressure $P$ is given by

• A. $P$
• B. $2P$
• C. $P/2$
• D. $\gamma P$

Answer 1

The correct option is D $\gamma P$

Bulk modulus,
$B=-\frac{dP}{\frac{dV}{V}}=-V\frac{dP}{dV}$

$P{V}^{\gamma }=$ constant
$P\gamma V^{\gamma -1}dV+V^{\gamma }dP=0$
$⟹P\gamma =-V\frac{dP}{dV}=-V\frac{dP}{dV}=B=P\gamma$