Thermodynamics Question 324
Question: A gas expands adiabatically at constant pressure such that its temperature $ T\propto a/\sqrt{V}. $ The value of $ \gamma =(C _{p}/C _{V}) $ of the gas is
Options:
A) 1.30
B) 1.50
C) 1.67
D) 2.00
Show Answer
Answer:
Correct Answer: B
Solution:
[b] In adiabatic expansion,
$ p{{V}^{\gamma }}= $ constant put $ p=\frac{RT}{V} $
$ ( \frac{RT}{V} ){{V}^{\gamma }}=\text{constant} $
$ T{{V}^{\gamma -1}}= $ constant or $ T\propto {{V}^{1-\gamma }} $
$ \because $ $ T\propto \frac{1}{\sqrt{V}} $
$ \therefore $ $ 1-\gamma =-\frac{1}{2} $
or $ \gamma =1+\frac{1}{2}=\frac{3}{2}=1.5 $
