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

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.)

$A$ closed vessel contains $10 \ g$ of an ideal gas $X$ at $300 \ K$,which exerts $2 \ atm$ pressure. At the same temperature,$80 \ g$ of another ideal gas $Y$ is added to it and the pressure becomes $6 \ atm$. The ratio of root mean square velocities of $X$ and $Y$ at $300 \ K$ is

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures, and number densities are the same. The molecular size of $A$ is half of that of $B$ and the mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} /s$, then the collision frequency in gas $A$ is . . . . . . $/s$.

Select the $incorrect$ statement$(s)$.

An ideal gas filled in a cylinder occupies volume $V$. The gas is compressed isothermally to the volume $V/3$. Now,the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules should escape to bring the pressure in the cylinder back to its original value (in $\%$)?