First slide

Kinetic theory of ideal gases

Question

At what absolute temperature T is the root mean square speed of a hydrogen molecule equal to its escape velocity from the surface of the moon? Radius of moon is R, g is acceleration due to gravity on moon’s surface, m is mass of hydrogen molecule and k is Boltzmann constant.

Moderate

A

$\frac{m g R}{2 k}$
B

$\frac{2 m g R}{k}$
C

$\frac{3 m g R}{2 k}$
D

$\frac{2 m g R}{3 k}$

Solution

$V_{r m s} = V_{e} \Rightarrow \sqrt{\frac{3 k T}{m}} = \sqrt{2 g R} \Rightarrow T = \frac{2 m g R}{3 k}$

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