Kinetic Theory Of Gases Question 168
Question: A container has $ n _{1} $ moles of a monoatomic gas and $ n _{2} $ moles of a diatomic gas. The molar specific heat capacity at constant volume $ (C _{v}) $ of the mixture is found to be 2R. Then the ratio $ n _{1}/n _{2} $ is
Options:
A) 3/5
B) 5/3
C) 1
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c]: Average number of degree of freedom per molecule
$ f=\frac{\text{Total number of degree of freedom}}{\text{Total number of molecule}} $
$ =\frac{n _{1}N _{A}f _{1}+n _{2}N _{A}f _{2}}{n _{1}N _{A}+n _{2}N _{A}}=\frac{n _{1}f _{1}+n _{2}f _{2}}{n _{1}+n _{2}} $
Here, $ f _{1}=3,,f _{2}=5 $ and $ \gamma =1+1/f $
Also, $ \gamma =\frac{C _{p}}{C _{v}}=\frac{3R}{2R}=1.5=1+1,/f,\Rightarrow f=4 $
Hence, $ \frac{3n _{1}+5n _{2}}{n _{1}+n _{2}}=4 $ which gives $ n _{1}/n _{2}=1 $
BETA
