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At what temperature will the rms speed o...

At what temperature will the rms speed of molecules of nitrogen gas be twice of that at `0^@C`?

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`T_1=0^@C=273 K`,rms speed at `0^@C=c_1`
At temperature `T_2`, rms speed `=c_2=2c_1`.
As `c=sqrt((3RT)/M),`
`thereforecpropsqrtT`, we have `c_1/c_2=sqrt(T_1/T_2)`
or,`T_2=T_1(c_2/c_1)^2=273times(2/1)^2=1092K`
`=(1092-273)^@C=819^@C`
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