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(D) The pressure $P$ exerted by an ideal gas is given by the kinetic theory of gases as $P = \frac{1}{3} \rho v_{rms}^2$,where $\rho$ is the density o

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$P = \frac{2}{3}E$

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(D) The pressure $P$ exerted by an ideal gas is given by the kinetic theory of gases as $P = \frac{1}{3} \rho v_{rms}^2$,where $\rho$ is the density of the gas and $v_{rms}$ is the root mean square velocity.We know that the average kinetic energy per unit volume $E$ is given by $E = \frac{1}{2} \rho v_{rms}^2$.From this,we can write $\rho v_{rms}^2 = 2E$.Substituting this into the pressure equation: $P = \frac{1}{3} (2E) = \frac{2}{3}E$.Therefore,the correct relation is $P = \frac{2}{3}E$.

The relation between the gas pressure $P$ and average kinetic energy per unit volume $E$ is

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