Kinetic Theory Of Gases Question 160
Question: Certain perfect gas is found to obey $ P{{V}^{3/2}}= $ constant during adiabatic process. If such a gas at initial temperature T is adiabatically compressed to half the initial volume, its final temperature will be
Options:
A) $ \sqrt{2},\cdot T $
B) 2T
C) $ 2\sqrt{2},\cdot T $
D) 4T
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ P{{V}^{3/2}}= $ Constant, $ PV=RT $ or $ P=\frac{RT}{V}; $ $ ( \frac{RT}{V} )\times {{V}^{3/2}}= $ Constant or $ T{{V}^{1/2}}= $ Constant.
$ \
Therefore $ Thus V changes to V/2, the temp. becomes $ \sqrt{2T} $ .
BETA
