Thermodynamics Question 310
Question: 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 the process is
Options:
A) np
B) $ {{p}^{1/n}} $
C) $ \frac{p}{n} $
D) $ p^{n} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c]$ Vp^{n}=\text{constant} $
$ Vp^{n}=(V+\Delta V){{(p+\Delta p)}^{n}} $
$ =Vp^{n}( 1+\frac{\Delta V}{V} )( 1+n\frac{\Delta p}{p} ) $
$ 1=1+\frac{\Delta V}{V}+n\frac{\Delta p}{p}+\frac{n\Delta V}{V}.\frac{\Delta p}{p} $
$ \frac{\Delta V}{V}=-n\frac{\Delta p}{p} $
$ \therefore $ $ k=\frac{-\Delta p}{\Delta V/V}=\frac{p}{n} $
