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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 rms speed of a helium gas atom at `-20^(@)C`? (atomic mass of `Ar = 39.9 u, of He = 4.0 u)`.

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Let C and C. be the r.m.s. velocities of argon and a helium gas atoms at temperature TK and T.K. respectivley.
Here, `M = 39.9 , M. = 4.0 , T = ?`
`T. = -20+273 = 253K`
Now, `C = sqrt((3RT)/(M)) = sqrt((3RT)/(39.9))` and
`C. = sqrt((3RT.)/(M.)) = sqrt((3R xx 253)/(4))`
Since, `C = C.`, therefore `sqrt((3 RT)/(39.9))`
`= sqrt((3 R xx 253)/(4)) or T = (39.9 xx 253)/(4) = 2523.7K`.
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