An ideal gas having molar mass '$$\mathrm{M}_0$$', has r.m.s. velocity 'V' at temperature 'T'. Then

An ideal gas at $$27^{\circ} \mathrm{C}$$ is compressed adiabatically to $$(8 / 27)$$ of its original volume. If ratio of specific heats, $$\gamma=5 / 3$$ then the rise in temperature of the gas is

What is the ratio of the velocity of sound in hydrogen $$\left(\gamma=\frac{7}{5}\right)$$ to that in helium $$\left(\gamma=\frac{5}{3}\right)$$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is