Question

By how many times the absolute temperature of a gas would increase when $u_{rms}$ of a gas in a container of fixed volume is increased from $5\times {10}^{4}cmse{c}^{-1}$ to $10\times {10}^{4}cmse{c}^{-1}$?

Answer 1

Relation between root mean square velocity and temperature

$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

So $v_{\text{rms}}$ is directtly proportional to $\sqrt{T}$

Thus, $T$ is directly proportional to $(v_{\text{rms}}{)}^2$

$10\times {10}^4/5\times {10}^4=2$ So V becomes doubled

If v is doubled, T will be four times.