$A$ closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass of $A$ is $16$ times that of $B$ $(M_A = 16 M_B)$ and mass of gas $A$ contained in the vessel is $2$ times that of $B$ $(m_A = 2 m_B)$. Which of the following statements are true?
$(i)$ Average kinetic energy per molecule of $A$ is equal to that of $B$.
$(ii)$ Root mean square value of translational velocity of $B$ is four times that of $A$.
$(iii)$ Pressure exerted by $B$ is eight times that exerted by $A$.
$(iv)$ Number of molecules of $B$ in the cylinder is eight times that of $A$.

Two boxes containing different ideal gases are placed on a table. Box $A$ contains $1 \text{ mole}$ of nitrogen gas at temperature $T_o$,and box $B$ contains $1 \text{ mole}$ of helium gas at temperature $(7/3) T_o$. If they are brought into thermal contact such that both gases reach a final common temperature $T_f$,what is the final temperature $T_f$ in terms of $T_o$? (Neglect the heat capacity of the boxes.)

The average translational kinetic energy of ${N}_{2}$ gas molecules at $... {}^{\circ} {C}$ becomes equal to the ${K.E.}$ of an electron accelerated from rest through a potential difference of $0.1 \ V$. (Given ${k}_{B} = 1.38 \times 10^{-23} \ J/K$). (Fill the nearest integer).

Select the correct statement.

When the gas is heated,in which direction will the piston move?

$A$ thermally isolated cylindrical closed vessel of height $8 \ m$ is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass $8.3 \ kg$. Thus,the partition is held initially at a distance of $4 \ m$ from the top. Each of the two parts of the vessel contains $0.1 \ mol$ of an ideal gas at temperature $300 \ K$. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached,the distance of the partition from the top (in $m$) will be. . . . . . (take the acceleration due to gravity $g = 10 \ m/s^2$ and the universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$).