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At what temperature will the rms speed o...

At what temperature will the rms speed of a gas be half of its value at `0^@C` Pressure being constant.

Text Solution

Verified by Experts

We are given:
Temperature of gas `=0^@C=273K`
Velocity of gas at `0^@C=mu ms^-1`
We are to calculate the temperature at which velocity at `0^@C` or 273K.
Using relation `C=sqrt((3RT)/M)`
We have `C prop sqrt T implies T_2/T_1= (C_2/C_1)^2 or T_2=(C_2/C_1)^2 times T_1`
Substituting `C_1=u` and `C_2=u/2`
We get `T_2=(u/(2u))^2 times 273=273/4 =68.3 K or T=-205^@C`
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