The root mean square velocity of a gas molecule at 100 K and 0.5 atm pressure is 106.4 m s − 1 . If the temperature is raised to 400 K and the pressure is raised to 2 atm , the root mean square veloci

Question

The root mean square velocity of a gas molecule at 100 K and 0.5 atm pressure is 106.4 m s − 1 . If the temperature is raised to 400 K and the pressure is raised to 2 atm , the root mean square velocity becomes :

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Question Explanation:

Find the root mean square velocity.

Concept:

This question is based on the kinetic theory of gases.

Solution: The root mean square velocity, $u$ , is given by the formula:

$u = \frac{3 RT}{M}$ OR $\frac{u _{1}}{u _{2}} = \frac{T _{1}}{T _{2}}$

$\frac{106.4}{u _{2}} = \frac{100}{400}$ (Note that pressure does not come in use )

or $u_{2} = 212.8 m s^{- 1}$ .

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