The ratio of the velocity of sound in hydrogen gas $\left(\gamma=\frac{7}{5}\right)$ to that in helium gas $\left(\gamma=\frac{5}{3}\right)$ at the same temperature is

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio $T_1: T_2$ is

Two gases A and B having same initial state ( $\mathrm{P}, \mathrm{V}, \mathrm{n}, \mathrm{T}$ ). Now gas A is compressed to $\frac{\mathrm{V}}{8}$ by isothermal process and other gas B is compressed to $\frac{\mathrm{V}}{8}$ by adiabatic process. The ratio of final pressure of gas $A$ and $B$ is (Both gases are monoatomic, $\gamma=5 / 3$)

Two vessels separately contain two ideal gases A and B at the same temperature, pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of $B$. The ratio of molecular weights of $A$ and $B$ is