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At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at – 20 °C ?

Q13.9 At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20^{0}C ? (atomic mass of Ar=39.9\mu, of He=4.0\mu).

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S Sayak

As we know root mean square velocity is given as v_{rms}=\sqrt{\frac{3RT}{M}}

Let at temperature T the root mean square speed of an atom in an argon cylinder equal to the rms speed of a helium gas atom at -20^{0}C

\\\sqrt{\frac{3R\times T}{39.9}}=\sqrt{\frac{3R\times 253}{4}}\\ T=2523.7\ K

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