For an ideal gas with constant pressure,the root mean square velocity $v_{rms}$ is proportional to . . . . . . .

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 $400 \ K$?

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T \ K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

At room temperature,a diatomic gas is found to have an $r.m.s.$ speed of $1930 \, m/s$. The gas is

The r.m.s. speed of oxygen molecules at $47^{\circ} C$ is equal to that of the hydrogen molecules kept at . . . . . . ${ }^{\circ} C$. (Mass of oxygen molecule/mass of hydrogen molecule $= 32 / 2$)

The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?