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Kinetic Theory of Gases

The root mean...

Question

The root mean square velocity of one mole of a monatomic gas having molar mass M is $u_{r m s}$ . The relation between the average kinetic energy $E$ per mole of the gas and $u_{r m s}$ is.

u_{r m s} = {(\frac{2 E}{m})}^{\frac{1}{2}}

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u_{r m s} = {(\frac{3 E}{2 m})}^{\frac{1}{2}}

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u_{r m s} = {(\frac{E}{2 m})}^{\frac{1}{2}}

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u_{r m s} = {(\frac{E}{3 m})}^{\frac{1}{2}}

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Solution

The correct option is A $u_{r m s} = {(\frac{2 E}{m})}^{\frac{1}{2}}$
Kinetic energy $(E) = \frac{3}{2} k T$ .......(i)
RMS speed $(u_{r m s}) = \sqrt{\frac{3 k T}{M}}$ .......(ii)
Multiply and divide 2 in equation (ii)
RMS speed $(u_{r m s}) = \sqrt{\frac{3 k T \times 2}{M \times 2}} . . . . (i i i)$
Substituting equation (ii) in (iii) we get,
$\Rightarrow u_{r m s} = \sqrt{\frac{2 E}{M}}$

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Kinetic Theory of Gases

Standard XIII Chemistry

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The root mean square velocity of one mole of a monatomic gas having molar mass M is urms. The relation between the average kinetic energy E per mole of the gas and urms is.

The correct option is A urms=(2Em)12Kinetic energy (E)=32kT.......(i) RMS speed (urms)=√3kTM.......(ii) Multiply and divide 2 in equation (ii) RMS speed (urms)=√3kT×2M×2....(iii) Substituting equation (ii) in (iii) we get, ⇒urms=√2EM

The root mean square velocity of one mole of a monatomic gas having molar mass M is $u_{r m s}$ . The relation between the average kinetic energy $E$ per mole of the gas and $u_{r m s}$ is.