At what temperature will oxygen molecules have the same K.E as ozone molecules at $30^{o} C$ ?

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Solution

The kinetic energy of a gas molecule is given by the equation,

$K E = \frac{3}{2} n R T$
For same mass of gas molecules,

$K E \propto \frac{T}{M}$

Hence for kinetic energy to be same,

$\frac{T_{1}}{M_{1}} = \frac{T_{2}}{M_{2}}$

$\frac{T_{1}}{32} = \frac{303}{48}$

$\Rightarrow T_{1} = 202 K$

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