Q. A gas undergoes a process in which its pressure $p$ and volume $V$ are related as $Vp^{n} =$constant. The bulk modulus for the gas in this process is
A) $np$
B) $p^{1/n}$
C) $\frac{p}{n}$
D) $p^{n}$
Explanation
(c) $Vp^{n} = constant$
$\therefore\ Vp^{n} = \left( V + \frac{\mathrm{\Delta}V}{V} \right)\left( 1 + n\frac{\mathrm{\Delta}p}{p} \right)$
$1 = 1 + \frac{\mathrm{\Delta}V}{V} + n\frac{\mathrm{\Delta}p}{p} + n\frac{\mathrm{\Delta}V}{V}\frac{\mathrm{\Delta}P}{p}$
Or $\frac{\mathrm{\Delta}V}{V} = - n\frac{\mathrm{\Delta}p}{p}$, (neglecting the product)
As $k = \frac{- \mathrm{\Delta}p}{\mathrm{\Delta}V/V} = \frac{p}{n}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.