An ideal gas of molar mass $M$ is contained in a vertical tube of height $H$,closed at both ends. The tube is accelerating vertically upwards with acceleration $g$. Then,the ratio of pressure at the bottom $(P_B)$ and the midpoint $(P_m)$ of the tube will be:

During an experiment,an ideal gas is found to obey a condition $\frac{P^2}{\rho} = \text{constant}$ [$\rho = \text{density of the gas}$]. The gas is initially at temperature $T$,pressure $P$,and density $\rho$. The gas expands such that density changes to $\rho/2$.

For a diatomic gas,the change in internal energy for a unit change in temperature at constant pressure and constant volume is $U_1$ and $U_2$ respectively. The ratio $U_1 : U_2$ is

In saloons,there is always a characteristic smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \text{ molecules}/m^3$. Due to air ventilation,the number of molecules leaving in one minute is one-tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \text{ molecule}/m^3$?

$A$ box contains $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled while keeping the total kinetic energy of the gas the same as before. If the new pressure is ${P_2}$ and temperature is ${T_2}$,then:

The number of air molecules per $cm^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is $.........$