Given below are two statements:Statement I: T | vedclass

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(D) Statement $I$: In an ideal gas,molecules move in random directions. For every molecule with momentum $\vec{p}$,there is a statistically equal prob

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Statement $I$ is false but Statement $II$ is true.

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(D) Statement $I$: In an ideal gas,molecules move in random directions. For every molecule with momentum $\vec{p}$,there is a statistically equal probability of finding a molecule with momentum $-\vec{p}$. Thus,the average momentum $\vec{p}_{avg} = 0$,which is independent of temperature.Statement $II$: The rms speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initially,$v = \sqrt{\frac{3RT}{M_{O_2}}}$.When temperature is doubled $(T' = 2T)$ and $O_2$ dissociates into $O$ atoms,the molar mass becomes $M' = \frac{M_{O_2}}{2}$.The new rms speed $v' = \sqrt{\frac{3R(2T)}{M_{O_2}/2}} = \sqrt{4 \cdot \frac{3RT}{M_{O_2}}} = 2v$.Therefore,Statement $I$ is false and Statement $II$ is true.

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