The adjoining figure shows graphs of pressure and volume of a gas at two temperatures $T_1$ and $T_2$. Which of the following is correct?

We have a jar filled with gas characterized by parameters $P, V, T$ and another jar $B$ filled with gas having parameters $2P, V/4, 2T$,where symbols have their usual meaning. The ratio of the number of molecules in jar $A$ to those in jar $B$ is

$A$ cylinder containing gas at $27\,^{\circ}C$ is divided into two parts of equal volume,each $100\,cm^3$,and at equal pressure by a piston of cross-sectional area $10.85\,cm^2$. The gas in one part is raised in temperature to $100\,^{\circ}C$ while the other is maintained at the original temperature. The piston and walls are perfect insulators. How far will the piston move during the change in temperature? (in $cm$)

The figure shows graphs of pressure $(P)$ versus density $(\rho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.

On which does the value of $\alpha_V$ depend for an ideal gas?

$A$ vessel of volume $8\, L$ contains an ideal gas at $300\, K$ and $2\, atm$ pressure. The gas is allowed to leak until the pressure becomes $125\, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.