Thermodynamics Question 270
Question: Certain perfect gas is found to obey $ P{{V}^{3/2}}= $ constant during an 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}T $
B) $ ~2T~~~ $
C) $ 2\sqrt{2}T $
D) $ 4T $
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Answer:
Correct Answer: A
Solution:
[a] $ P{{V}^{3/2}}=\text{constant} $
$ PV=nRT $
$ \Rightarrow {{V}^{1/2}}T=\text{const}\text{.} $
$ \Rightarrow {{( \frac{V}{2} )}^{1/2}}T’=\text{const}\text{.} $
$ \Rightarrow T’=T\sqrt{2} $
