Two vessels $A$ and $B$ contain oxygen. The volume of $B$ is twice that of $A$,the pressure of $B$ is thrice that of $A$ and the temperature of $B$ is half of that of $A$. Then,find the ratio of number of molecules of oxygen in vessels $A$ and $B$.

Explain Avogadro's hypothesis by relating pressure,temperature,and volume of a gas.

$A$ large flask contains air at $27 \, ^{\circ}C$. In order to expel half the mass of air from the flask, the flask should be heated up to what temperature in $^{\circ}C$?

The $SI$ unit of universal gas constant is

The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

$A$ 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 $cm$)