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At what temperature is the root mean squ...

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rmsspeed of a helium gas atom at `-20 ^@C` ? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

Text Solution

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We are given
Atomic mass of argon `M_1=39.9`
Atomic mass of helium `M_2=4`
Temperature of helium gas `T_2=-20^@C=273-20=253 K`
We are to calculate temperature of argon gas `T_1`
Using relation `v_(rms)=sqrt((3RT)/M) implies sqrt((3RT_1)/M_1)= sqrt((3RT_2)/M_2)`
`sqrt((3RT_1)/39.9) =sqrt((3R times 253)/4) or T_1=(39.9 times 253)/4=2523.7K`
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