The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the $R$.$M$.$S$. velocity of its molecules at $100 \ K$,what does it become at $400 \ K$?

The rms speed of an oxygen molecule at a certain temperature is $600 \,ms^{-1}$. If the temperature is doubled and the oxygen molecule dissociates into atomic oxygen atoms,the new rms speed is (in $\,ms^{-1}$)

The $v_{rms}$ of gas molecules in a container is $400 \ ms^{-1}$. If half of the gas leaks out of the container at a constant temperature,the $v_{rms}$ of the remaining gas molecules will be . . . . . . $ms^{-1}$.

$A$ perfect gas of volume $10 \ L$ is compressed isothermally to a volume of $1 \ L$. The $rms$ speed of the molecules will

If the temperature of an ideal gas is increased from $27^{\circ}C$ to $927^{\circ}C$,what happens to its $r.m.s.$ velocity?

Derive the equation of $v_{rms}$ in terms of the mass of a molecule.