According to the kinetic theory of gases,the $r.m.s.$ velocity of gas molecules is directly proportional to:

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by what factor?

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 molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is

For a gas,the $r.m.s.$ speed at $800 \, K$ is