Kinetic Theory Of Gases Question 35
Question: Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of $ V _{rms} $ of molecules and speed of sound in mixture?
Options:
A) $ \sqrt{3/2} $
B) $ \sqrt{2} $
C) $ \sqrt{2/3} $
D) $ \sqrt{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] From graph, $ T^{2}V=\text{const}\text{.} $ ….(i) As we know that $ T{{V}^{\gamma -1}}=\text{const}\text{.} $
$ \Rightarrow V{{T}^{\frac{1}{\gamma -1}}}=\text{const}\text{.} $ …(ii) On comparing (1) and (2), we get
$ \Rightarrow \gamma =3/2 $ Also $ v _{rms}=\sqrt{\frac{3P}{\rho }} $ and $ v _{sound}=\sqrt{\frac{{P _{\gamma }}}{\rho }} $
$ \Rightarrow \frac{v _{rms}}{v _{sound}}=\sqrt{\frac{3}{\gamma }}=\sqrt{2} $
BETA
