The root mean square speed of hydrogen molecules at a temperature of $27^{\circ }C27^\backslash circ\; C$ is

The temperature at which the oxygen molecules would have the same rms speed as of hydrogen molecule at 300 K is

One mole of an ideal monoatomic gas is at temperature of 300 $K_{0}K\_0$. Its volume is doubled keeping its pressure constant. The change in internal energy is

The root mean square speed of molecules of gas whose density is 1.4 kg/$m^{3}m^3$ at a pressure 76 cm of Hg (specific gravity of mercury 13.6 and g = 9.81 $m{s}^{-2}ms^\{-2\}$) will be

The temperature at which the root mean square speed of molecules of a gas is double of its value at $0^{\circ }C0^\backslash circ\; C$ is

A vessel of volume $8.0\times 10^{-3}{m}^{3}8.0\; \backslash times\; 10^\{-3\}m^3$ contains an ideal gas at 300 K and 200 kPa. The gas is allowed to leak till the Pressure falls to 125 kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.

The average translational kinetic energy of air molecules is 0.040 eV. The temperature of the air is (Given Boltzmann’s constant $k=1.38\times 10^{-23}J\mathrm{/}K,1eV=1.6\times 10^{-19}Jk\; =\; 1.38\; \backslash times\; 10^\{-23\}\; J/K,\; 1\; eV\; =\; 1.6\; \backslash times\; 10^\{-19\}J$)

The temperature at which the rms speed of hydrogen molecules becomes double the rms speed at 300 K, is

The average time taken by the oxygen molecule to travel a distance equal to the diameter of the earth with a constant speed equal to the average speed of oxygen molecule at 300 K will be (Radius of Earth = 6400 km)

The mean speed of the molecules of hydrogen equals the mean speed of molecules of the helium. The ratio of temperature of hydrogen and helium will be