In the kinetic theory of gases,which of these | vedclass

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(D) Statement $(i)$ is false: Pressure $P = \frac{1}{3} \rho v_{rms}^2$. It is proportional to the square of the root mean square speed,not the mean s

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$(iii)$ and $(iv)$ only

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(D) Statement $(i)$ is false: Pressure $P = \frac{1}{3} \rho v_{rms}^2$. It is proportional to the square of the root mean square speed,not the mean speed.Statement $(ii)$ is false: $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $P \propto T$,$v_{rms} \propto \sqrt{P}$,not $P$.Statement $(iii)$ is true: The rate of diffusion is directly proportional to the average speed of the gas molecules.Statement $(iv)$ is true: The mean translational kinetic energy per molecule is given by $E = \frac{3}{2} k_B T$,which is directly proportional to the absolute temperature $T$.Therefore,statements $(iii)$ and $(iv)$ are correct. The correct option is $(D)$.

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