The r.m.s. speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, -2, -4, -6) \, m/s$ is ...... $m/s$.

If the rms velocity of a perfect gas at $27^{\circ} C$ is $500 \,m \cdot s^{-1}$,the same at $927^{\circ} C$ will be

The respective speeds of five molecules are $2, 1.5, 1.6, 1.6$ and $1.2 \, km/s$. The most probable speed in $km/s$ is:

$A$ 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 r.m.s. speed of the molecules of a gas at $100^{\circ} C$ is $v$. The temperature at which the r.m.s. speed will be $\sqrt{3} v$ is: (in $^{\circ} C$)

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