Kinetic Theory Of Gases Question 114
Question: A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of $ \gamma $ (ratio of specific heats) for this mixture is
Options:
A) 3/2
B) 4/3
C) 5/3
D) 7/5
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Below 100 K only translational degree of freedom is considered. Hence $ {\gamma _{mixture}}=\frac{\frac{{\mu _{1}}{\gamma _{1}}}{{\gamma _{1}}-1}+\frac{{\mu _{2}}{\gamma _{2}}}{{\gamma _{2}}-1}}{\frac{{\mu _{1}}}{{\gamma _{1}}-1}+\frac{{\mu _{2}}}{{\gamma _{2}}-1}} $ according to question, $ {\mu _{1}}={\mu _{2}} $ and $ {\gamma _{1}}={\gamma _{2}} $
$ =1+\frac{2}{3}=\frac{5}{3} $
$ \Rightarrow {\gamma _{mix}}={\gamma _{1}}=\frac{5}{3} $
BETA
