Question

The rms speed of the molecules of a gas in a vessel is $400m{s}^{-1}$. If temperature of the gas is reduced to half, the rms speed of the remaining molecules will be

Answer 1

Given,

R.M.S velocity of gas$V_{rms}=K\sqrt{T}=400m{s}^{-1}$

If temperature is reduced to half

$V{{}^{\prime }}_{rms}=K\sqrt{\frac{T}{2}}=\frac{1}{\sqrt{2}}k\sqrt{T}=\frac{400}{\sqrt{2}}=282.84m{s}^{-1}$

Hence, at half temperature, velocity reduce to $282.84m{s}^{-1}$