The $r.m.s.$ speed of a certain gas is $v$ at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times,will be ...... $K$.

When pressure remains constant,at what temperature will the $r.m.s.$ speed of gas molecules increase by $10 \%$ of the $r.m.s.$ speed at $STP$?

$A$ container is divided into two equal halves by a diathermic partition. Two different ideal gases are filled in the left $(L)$ and right $(R)$ parts. The $rms$ speed of the molecules in the $L$ part is equal to the average speed of the molecules in the $R$ part. Find the ratio of the mass of a molecule in the $L$ part to the mass of a molecule in the $R$ part.

Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules is

The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

If the rms speed of the molecules of a diatomic gas at a temperature of $322 \ K$ is $2000 \ m \ s^{-1}$,then the gas is