The temperature of an ideal gas is increased from $120 \,K$ to $480 \,K$. If at $120 \,K$, the root mean square speed of gas molecules is $v$, then at $480 \,K$ it will be

The temperature of an ideal gas is increased from $120 \ K$ to $480 \ K.$ If at $120 \ K,$ the root mean square velocity of the gas molecules is $v,$ at $480 \ K$ it becomes

The absolute temperature of a gas is determined by

Two gases $A$ and $B$ are contained in two separate, but otherwise identical containers. Gas $A$ consists of monatomic molecules, each with atomic mass of $4 \ u$, whereas Gas $B$ consists of rigid diatomic molecules, each with atomic mass of $20 \ u$. If gas $A$ is kept at $27^{\circ} C$, at what temperature should gas $B$ be kept so that both have the same rms speed (in $^{\circ} C$)?

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 $\pi=\frac{22}{7}$)

The $RMS$ velocity of oxygen molecules at $NTP$ is $0.5 \,km/s$. The $RMS$ velocity for the hydrogen molecule at $NTP$ is (in $\,km/s$)