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(D) The formula for the average velocity $(V_{av})$ of a gaseous molecule is given by $V_{av} = \sqrt{\frac{8RT}{\pi M}}$.From this expression,it is c

Vedclass · Accepted Answer

$1.4$

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(D) The formula for the average velocity $(V_{av})$ of a gaseous molecule is given by $V_{av} = \sqrt{\frac{8RT}{\pi M}}$.From this expression,it is clear that $V_{av} \propto \sqrt{T}$.When the temperature is doubled,the new temperature $T' = 2T$.Therefore,the ratio of the new average velocity to the initial average velocity is $\frac{V_{av}'}{V_{av}} = \sqrt{\frac{T'}{T}} = \sqrt{\frac{2T}{T}} = \sqrt{2} \approx 1.414$.Thus,the average velocity increases by a factor of approximately $1.4$.

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

By what factor does the average velocity of a gaseous molecule increase when the temperature (in Kelvin) is doubled?

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