When the temperature of a gas is increased to $3$ times,what will be the change in $v_{rms}$?

The temperature of an ideal gas is increased from $140 \,K$ to $560 \,K$. If the r.m.s. speed of gas molecules is $v$ at $140 \,K$, then at $560 \,K$, the r.m.s. speed becomes:

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 . . . . . . $ms^{-1}$.

The root mean square speed of molecules of a given mass of a gas at $27^{\circ} C$ and $1$ atmosphere pressure is $200\, ms^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}\, ms^{-1}$. The value of $x$ will be ......$ms^{-1}$.

In a sample of chlorine gas at $300 \ K$,the average kinetic energy per molecule is $6.21 \times 10^{-21} \ J$ and the root mean square speed $\nu_{rms}$ is $325 \ m/s$. What will be the values of these quantities at $600 \ K$?

The temperature at which the root mean square velocity of a molecule will be doubled than its value at $100^{\circ}C$ is: