Internal energy of $$n_1$$ moles of hydrogen at temperature '$$T$$' is equal to internal energy of '$$n_2$$' moles of helium at temperature $$2 T$$, then the ratio $$\mathrm{n}_1: \mathrm{n}_2$$ is

[Degree of freedom of $$\mathrm{He}=3$$, Degree of freedom of $$\mathrm{H}_2=5$$]

For an ideal gas, $$R=\frac{2}{3} C_v$$. This suggests that the gas consists of molecules, which are [$$\mathrm{R}=$$ universal gas constant]

The rms speed of a gas molecule is '$$\mathrm{V}$$' at pressure '$$\mathrm{P}$$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

Equal volumes of two gases, having their densíties in the ratio of $$1: 16$$ exert equal pressures on the walls of two containers. The ratio of their rms speads ($$\mathrm{C}_1: \mathrm{C}_2)$$ is