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  4. If P represents the pressure exerted by an ideal gas and E represents the translational kinetic energy per unit volume of the gas, then

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Q. If $P$ represents the pressure exerted by an ideal gas and $E$ represents the translational kinetic energy per unit volume of the gas, then

Kinetic Theory

Solution:

$P=\frac{1}{3} \frac{m N v_{ ms }^{2}}{V}$
$=\frac{2}{3}\left(\frac{1}{2}(m N) v_{ ms }^{2}\right) \cdot \frac{1}{V}=\frac{2}{3}\left(\frac{K E}{V}\right)$
$\Rightarrow \,P=\frac{2 E}{3}$