For 1 mol of a gas,the average kinetic energ | vedclass

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Question

(A) The average kinetic energy $(E)$ for $1 \ mol$ of an ideal gas is given by $E = \frac{3}{2}RT$.From this,we can express $RT$ as $RT = \frac{2E}{3}

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$(\frac{2E}{M})^{1/2}$

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(A) The average kinetic energy $(E)$ for $1 \ mol$ of an ideal gas is given by $E = \frac{3}{2}RT$.From this,we can express $RT$ as $RT = \frac{2E}{3}$.The formula for root mean square velocity $(U_{rms})$ is $U_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass.Substituting the value of $RT$ into the $U_{rms}$ formula:$U_{rms} = \sqrt{\frac{3}{M} 	imes \frac{2E}{3}}$$U_{rms} = \sqrt{\frac{2E}{M}}$$U_{rms} = (\frac{2E}{M})^{1/2}$.

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

For $1 \ mol$ of a gas,the average kinetic energy is $E$. Then the root mean square velocity $U_{rms}$ of the gas is:

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