The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31\,^oC$ is ........ $^oC$.

Let $\bar{v}$,${v_{rms}}$ and ${v_p}$ respectively denote the mean speed,root mean square speed,and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of a molecule is $m$. Then

If the molecular weights of two gases are $M_1$ and $M_2$,then at a constant temperature,the ratio of their root mean square velocities $v_1$ and $v_2$ will be:

The $rms$ speed of $n$ molecules in a gas having speeds $\upsilon_1, \upsilon_2, \upsilon_3, \dots, \upsilon_n$ is equal 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 $100 \ K$,then at $400 \ K$,the r.m.s. velocity becomes:

At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.