If a gas is compressed isothermally,then the r.m.s. velocity of its molecules

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

$A$ 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.

Two boxes are at the same temperature. The first box contains gas with molecular mass $m_1$ and rms speed $v_1$. The second box contains gas with molecular mass $m_2$ and average speed $v_2$. If $v_1 = 1.5 v_2$,then $\frac{m_1}{m_2}$ is

$A$ gas is allowed to expand isothermally. The root mean square velocity of the molecules

The temperature at which the $r.m.s.$ velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ} C$ is (Molecular weight of hydrogen and oxygen molecules are $2$ and $32$ respectively). (in $^{\circ} C$)