Two vessels $A$ and $B$ are of the same size and are at the same temperature. Vessel $A$ contains $1 \ g$ of hydrogen and vessel $B$ contains $1 \ g$ of oxygen. If $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively,then the ratio $\frac{P_{A}}{P_{B}}$ is:

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.

$A$ vessel containing $5 \, L$ of a gas at $0.8 \, Pa$ pressure is connected to an evacuated vessel of volume $3 \, L$. The resultant pressure inside will be ...... $Pa$ (assuming the whole system to be isolated).

$28\, g$ of $N_2$ gas is contained in a flask at a pressure of $10\, atm$ and at a temperature of $57^\circ C$. It is found that due to leakage in the flask,the pressure is reduced to half and the temperature is reduced to $27^\circ C$. The quantity of $N_2$ gas that leaked out is

State Avogadro's law for matter.

$A$ gas is filled in a vessel at a pressure given by $P = (6.02 \times 10^{23})kT$,where $k$ is the Boltzmann constant and $T$ is the absolute temperature. The number of molecules per unit volume of the gas is: