A gas has volume V and pressure P. The total | vedclass

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(D) The translational kinetic energy of a gas molecule depends only on its translational degrees of freedom,which is $3$ for any gas molecule (monoato

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$\frac{3}{2} PV$ in all cases

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(D) The translational kinetic energy of a gas molecule depends only on its translational degrees of freedom,which is $3$ for any gas molecule (monoatomic,diatomic,or polyatomic).From the kinetic theory of gases,the pressure $P$ of an ideal gas is given by $P = \frac{1}{3} \frac{N}{V} m v_{rms}^2$.This can be rewritten as $PV = \frac{1}{3} N m v_{rms}^2 = \frac{2}{3} (\frac{1}{2} N m v_{rms}^2)$.Since the total translational kinetic energy $K_{trans} = \frac{1}{2} N m v_{rms}^2$,we have $PV = \frac{2}{3} K_{trans}$.Therefore,$K_{trans} = \frac{3}{2} PV$.This relationship is independent of the atomicity of the gas because it only considers the translational motion.

$A$ gas has volume $V$ and pressure $P$. The total translational kinetic energy of all the molecules of the gas is :-

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