Kinetic Theory Of Gases Question 87
Question: The molar specific heats of an ideal gas at constant pressure and volume are denoted by $ C _{p} $ and $ C _{v} $ , respectively. If $ \gamma =\frac{C _{p}}{C _{v}} $ and R is the universal gas constant, then $C _v$ is equal to
Options:
A) $ \frac{R}{( \gamma -1 )} $
B) $ \frac{( \gamma -1 )}{R} $
C) $ \gamma R $
D) $ \frac{1+\gamma }{1-\gamma } $
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Answer:
Correct Answer: A
Solution:
[a] $ C _{p}-C _{v}=R\Rightarrow C _{p}=C _{v}+R $
$ \because \gamma =\frac{C _{p}}{C _{v}}=\frac{C _{v}+R}{C _{p}}=\frac{C _{v}}{C _{v}}+\frac{R}{C _{v}} $
$ \Rightarrow \gamma =1+\frac{R}{C _{v}}\Rightarrow \frac{R}{C _{v}}=\gamma -1\Rightarrow C _{v} $
$ =\frac{R}{\gamma -1} $
BETA
