The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at $27^{\circ} C$ is (in $^{\circ} C$)

$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The rms speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

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 $K$)

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

If $V_H, V_N$,and $V_O$ represent the $rms$ speeds of hydrogen,nitrogen,and oxygen molecules at a given temperature,respectively,then which of the following is correct?

When the temperature of a gas is raised from $27^o C$ to $90^o C$,the percentage increase in the $r.m.s.$ velocity of the molecules will be ..... $\%$