Kinetic Theory Of Gases Question 12
Question: The relation between internal energy $ U $ , pressure $ P $ and volume $ V $ of a gas in an adiabatic process is $ U=a+bPV $ where a and b are constants. What is the effective value of adiabatic constant $ \gamma $ ?
Options:
A) $ \frac{a}{b} $
B) $ \frac{b+1}{b} $
C) $ \frac{a+1}{a} $
D) $ \frac{b}{a} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] For an adiabatic process, $ 0=dU+PdV $ Or $ d(a+bPV)+PdV=0 $ Or $ (b+1)\frac{dV}{V}+b\frac{dP}{P=0} $ Or $ (b+1)logV+blogP=constant $ Or $ {{V}^{b+1}}P^{b}=cons\tan t $ Or $ P{{V}^{\frac{b+1}{b}}}=cons\tan t $
$ \
Therefore \gamma =\frac{b+1}{b} $
BETA
