Kinetic Theory Of Gases Question 150
An adiabatic vessel contains $ n _{1}=3 $ moles of a diatomic gas. The moment of inertia of each molecule is $ I=2.56\times {{10}^{-46}},kgm^{2} $ and root mean square angular velocity is $ {\omega _{0}}=5\times 10^{12},rad/s $ . The temperature of the gas in the vessel is
Options:
A) 250 K
B) 500 K
C) 1000 K
D) 1500 K
Show Answer
Answer:
Correct Answer: A
Solution:
[a]: Degree of freedom associated with rotational motion of diatomic gas molecules = 2 Average rotational energy per molecule
$\langle \omega^2 \rangle_{rms}=2\times \frac{1}{2}kT=kT$
Hence initial temperature $ T_1 $ of diatomic gas
$ =\frac{1}{2}l\omega _{0}^{2}=kT $
which give $ T _{1}=250,\text{K} $
BETA
