$A$ gas in container $A$ is in thermal equilibrium with another gas in container $B$. Both contain equal masses of the two gases in the respective containers. Which of the following can be true?

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$ if gravity is assumed to be constant throughout the container.

If a closed container containing gas is in motion and is suddenly stopped,the random motion of the gas molecules will .......

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = C_p/C_v, T_i = $ initial temperature, $T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.

Two gases of equal mass are in thermal equilibrium. If $P_a, P_b$ and $V_a, V_b$ are their respective pressures and volumes,then which relation is true?

Moon has no atmosphere because