N molecules, each of mass m of gas A, and $$2N$$ molecules, each of mass $$2m$$ of gas B, are contained in the same vessel which is maintained at a temperature T. The mean square of the velocity of the molecules of B type is denoted by $$vB2$$ and the mean square of the $$x-component$$ of the velocity of A type is denoted by $$vA2$$ . The ratio $$vB2vA2=N3$$ . Find N.

Question

N molecules, each of mass m of gas A, and $$2N$$ molecules, each of mass $$2m$$ of gas  B, are contained in the same vessel which is maintained at a temperature T. The  mean square of the velocity of the molecules of B type is denoted by $$vB2$$  and the  mean square of the $$x-component$$ of the velocity of A type is denoted by $$vA2$$ . The  ratio  $$vB2vA2=N3$$ . Find N.

Infinity Learn · Accepted Answer

$$vB2=3kT2mvA2=v23=133kTm$$   (where$$ $$v2$$ is RMS velocity of molecules of A $$type).$$vA2vB2=133kTm3kT2m=23$$

Kinetic theory of ideal gases

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$v_{B}^{2} = \frac{3 k T}{2 m}$
$v_{A}^{2} = \frac{v^{2}}{3} = \frac{1}{3} \frac{3 k T}{m}$ (where $v^{2}$ is RMS velocity of molecules of A type).
$\frac{v_{A}^{2}}{v_{B}^{2}} = \frac{\frac{1}{3} \frac{3 k T}{m}}{\frac{3 k T}{2 m}} = \frac{2}{3}$

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Kinetic theory of ideal gases

Remember concepts with our Masterclasses.

vB2=3kT2mvA2=v23=133kTm (where v2 is RMS velocity of molecules of A type).vA2vB2=133kTm3kT2m=23

Ready to Test Your Skills?

free study material

$v_{B}^{2} = \frac{3 k T}{2 m}$
$v_{A}^{2} = \frac{v^{2}}{3} = \frac{1}{3} \frac{3 k T}{m}$ (where $v^{2}$ is RMS velocity of molecules of A type).
$\frac{v_{A}^{2}}{v_{B}^{2}} = \frac{\frac{1}{3} \frac{3 k T}{m}}{\frac{3 k T}{2 m}} = \frac{2}{3}$