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Find out the temperature at which the mo...

Find out the temperature at which the molecular rms speed of a gas would be `1/3`rd its value at `100^@C`.

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Let the required temperature be `T_2K` molecular rms speed at this temperature be `c_2` and that at `100^@C` be `c_1`.
According to the question , `c_2=1/3c_1`
Here `T_1=100^@C=(100+273)K=373K`
As `c prop sqrt T` we have, `c_1/c_2=sqrt(T_1/T_2)`
or, `T_2=T_1(c_2/c_1)^2=373times(1/3)^2=373/9=41.44K`
`=(41.44-273)^@C=-231.56^@C`.
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