Question

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

• A. np
• B. p${}^{1/n}$
• C. $\frac{p}{n}$
• D. p${}^n$

Answer 1

The correct option is C $\frac{p}{n}$

$V{p}^n=$constant

$B=\frac{\Delta p}{\left(\frac{\Delta V}{V}\right)}$ where B is Bulk modulus

Differentiate on both sides w.r.t,

$p^n+n{p}^{n-1}\frac{\Delta p.V}{\Delta V}=0$

$p^{n-1}(p+\frac{n\Delta p}{\Delta V}.V)=0$

$p=0$

$p+n\frac{\Delta p}{\Delta V/V}=0$

$p-nB=0$

$B=\frac{p}{n}$