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

An insulated container contains a diatomic gas of molar mass ' m '. The container is moving with velocity ' $V$ ', if it is stopped suddenly, the change in temperature is ( $R=$ gas constant)

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. The gap to be kept between the two segments of railway track is

$$\left(\alpha_{\text {steel }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$$