$A$ jar contains a gas and a few drops of water at $T \, K.$ The pressure in the jar is $830 \, mm$ of mercury. The temperature of the jar is reduced by $1\%.$ The saturated vapour pressure of water at the two temperatures are $30 \, mm$ and $25 \, mm$ of mercury. Then the new pressure in the jar will be ..... $mm$ of $Hg$.

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 $\rho/2$.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion $A$: If the average kinetic energy of $H_2$ and $O_2$ molecules, kept in two different sized containers are same, then their temperatures will be same. Reason $R$: The r.m.s. speed of $H_2$ and $O_2$ molecules are same at same temperature. Choose the correct answer from the options given below.

The ratio of the speed of sound in a monatomic gas at $27^{\circ} C$ and the root-mean-square (rms) speed of the molecules of the same gas at a temperature of $127^{\circ} C$ is

The average translational kinetic energy and the $r.m.s.$ speed of molecules in a sample of oxygen gas at $300 \, K$ are $6.21 \times 10^{-21} \, J$ and $484 \, m/s$ respectively. The corresponding values at $600 \, K$ are nearly (assuming ideal gas behaviour):

According to the kinetic theory of gases,which of the following statements are correct?
$A$. The motion of the gas molecules freezes at $0^{\circ} C$.
$B$. The mean free path of gas molecules decreases if the density of molecules is increased.
$C$. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
$D$. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2} k_{B} T$ (for monoatomic gases).
Choose the most appropriate answer from the options given below: