When the temperature of an ideal gas is increased from $27^{\circ} C$ to $127^{\circ} C$,calculate the percentage increase in its $v_{\text{rms}}$. (in $\%$)

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

At what temperature will the $rms$ speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere $?$ (Given: Mass of oxygen molecule $(m) = 2.76 \times 10^{-26} \, kg$,Boltzmann's constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$)

$A$ gas is at a temperature of $0^{\circ}C$. To what temperature in $^{\circ}C$ must the gas be heated so that the $rms$ speed of its molecules becomes double?

The root mean square $(r.m.s.)$ velocity of a gas particle is $v$ at pressure $P$. If the pressure is increased to $2P$ while keeping the temperature constant,the $r.m.s.$ velocity becomes:

At what temperature $T$ (in $K$) will the $rms$ speed of $H_2$ be equal to the $rms$ speed of $O_2$ at $47^{\circ}C$?