According to the kinetic theory of gases,when two molecules of a gas collide with each other,then:

Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.
Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.

As shown schematically in the figure,two vessels contain water solutions (at temperature $T$) of potassium permanganate $(KMnO_4)$ of different concentrations $n_1$ and $n_2$ $(n_1 > n_2)$ molecules per unit volume with $\Delta n = (n_1 - n_2) \ll n_1$. When they are connected by a tube of small length $\ell$ and cross-sectional area $S$,$KMnO_4$ starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed $v$ of the molecules is limited by the viscous force $-\beta v$ on each molecule,where $\beta$ is a constant. Neglecting all terms of the order $(\Delta n)^2$,which of the following is/are correct? ($k_B$ is the Boltzmann constant)
$(A)$ the force causing the molecules to move across the tube is $\Delta n k_B T S$
$(B)$ force balance implies $n_1 \beta v \ell = \Delta n k_B T$
$(C)$ total number of molecules going across the tube per sec is $\left(\frac{\Delta n}{\ell}\right)\left(\frac{k_B T}{\beta}\right) S$
$(D)$ rate of molecules getting transferred through the tube does not change with time

$CO_2$ $(O-C-O)$ is a triatomic gas. The mean kinetic energy of one gram of the gas will be (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molecular weight of $CO_2 = 44$).

An ideal gas is placed in a tank at $27^{\circ} C$. The pressure is initially $600 \ kPa$. One fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is $327^{\circ} C$ (in $kPa$)?

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.