Heat and Thermodynamics 4 Question 28
30. Three closed vessels $A, B$ and $C$ at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only $O _2, B$ only $N _2$ and $C$ a mixture of equal quantities of $O _2$ and $N _2$. If the average speed of the $O _2$ molecules in vessel $A$ is $v _1$, that of the $N _2$ molecules in vessel $B$ is $v _2$, the average speed of the $O _2$ molecules in vessel $C$ is
(1992, 2M)
(a) $\left(v _1+v _2\right) / 2$
(b) $v _1$
(c) $\left(v _1 v _2\right)^{1 / 2}$
(d) $\sqrt{3 k T / M}$
where, $M$ is the mass of an oxygen molecule.
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Answer:
Correct Answer: 30. (b)
Solution:
- The average speed of molecules of an ideal gas is given by
$$ \langle v\rangle=\sqrt{\frac{8 R T}{\pi M}} $$
i.e. $\langle v\rangle \propto \sqrt{T}$ for same gas.
Since, temperatures of $A$ and $C$ are same, average speed of $O _2$ molecules will be equal in $A$ and $C$ i.e. $v _1$.
