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Question 44

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Solution

For an ideal gas,

rms speed is

$$v_{rms}=\sqrt{\frac{3kT}{m}}$$

where
k = Boltzmann constant,
m = mass of one molecule.

Squaring,

$$v_{rms}^2=\frac{3k}{m}T$$

But mean squared velocity is

$$\overline{v^2}=v_{rms}^2$$

So

$$\overline{v^2}\propto T$$

This means mean squared velocity varies linearly with absolute temperature.

So the graph is a straight line through origin.

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