Three closed vessels $$A,B$$ and $$C$$ are at the same temperature $$T$$ and contain gases which obey the Max wellian distribution of velocities. Vessel $$A$$ contain 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
A.
$$\frac{{{v_1} + {v_2}}}{2}$$
B.
$${{v_1}}$$
C.
$${\left( {{v_1} \cdot {v_2}} \right)^{\frac{1}{2}}}$$
D.
$$\sqrt {\frac{{3kT}}{M}} $$
Answer :
$${{v_1}}$$
Solution :
All three vessels are at same temperature. According to Maxwell's distribution of speed, average speed of molecules of a gas $$v \propto \sqrt T .$$
∴ The velocity of oxygen molecules will be same in $$A$$ as well as $$C$$ where $$M$$ is the mass of an oxygen molecule.
Releted MCQ Question on Heat and Thermodynamics >> Kinetic Theory of Gases
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