The rms velocity of molecules of a gas at `-73^(@)C` and 1 atmospheric pressure is `100 m//s`. The temp. of the gas is increased to `527^(@)C` and pressure is doubled. The rms velocity becomes K times. What is the value of K ?

Answer

2

Explanation

Here, `T_(1)=-73^(@)C = (-73+273)K = 200K`
`P_(1) = 1 atmospheric , C_(1) = 100m//s`
`T_(2) = 527^(@)C = (527+273) K = 800K, C_(2)=?`
`P_(2) = 2 atmosphere`
As rms velocity is not affected by change in pressure, and
`(C_(2)^(2))/(C_(1)^(2)) = (T_2)/(T_1) :. sqrt((T_2)/(T_1)) = sqrt((800)/(200)) = 2`
or, `C_(2) = 2 C_(1) = KC_(1)`, where `K=2`.