The r.m.s. velocity of hydrogen at $S.T.P.$ is $u \ m/s$. If the gas is heated at constant pressure until its volume becomes three times,then the final temperature of the gas and the r.m.s. speed are respectively:

$A$ flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

The oxygen molecule has a mass of $5.30 \times 10^{-26} \; kg$ and a moment of inertia of $1.94 \times 10^{-46} \; kg \cdot m^{2}$ about an axis through its centre perpendicular to the line joining the two atoms. Suppose the mean speed of such a molecule in a gas is $500 \; m/s$ and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

The internal energy of $10 \, g$ of nitrogen at $S.T.P.$ is about ......... $J$.

$A$ box of $1 \ m^{3}$ is filled with nitrogen at $1.5 \ atm$ at $300 \ K$. The box has a hole of an area $0.010 \ mm^{2}$. How much time is required for the pressure to reduce by $0.10 \ atm$,if the pressure outside is $1 \ atm$?

Fill in the blanks:
$(i)$ At absolute zero,the volume of an ideal gas is ...... .
$(ii)$ With an increase in temperature,the pressure of a gas ...... .
$(iii)$ All molecular motion will stop at ...... .
$(iv)$ Due to ...... at higher altitudes from the surface of the Earth,the air becomes cooler.