Find the approximate number of molecules contained in a vessel of volume $7 \text{ litres}$ at $0^{\circ}C$ and a pressure of $1.3 \times 10^{5} \text{ Pa}$.

$A$ 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 gas in a vessel is subjected to a pressure of $20 \ atm$ at a temperature of $27^{\circ}C$. If one-half of the gas is released from the vessel and the temperature of the remaining gas is raised by $50^{\circ}C$,the final pressure of the gas in the vessel is ....... $atm$.

State Boyle's Law and Charles's Law.

$A$ jar $P$ is filled with a gas having pressure,volume,and temperature $P, V, T$ respectively. Another gas jar $Q$ is filled with a gas having pressure $2P$,volume $\frac{V}{4}$,and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is:

$A$ gas at $27^\circ C$ temperature and $30$ atmospheric pressure is allowed to expand to atmospheric pressure. If the volume becomes $10$ times its initial volume,then the final temperature becomes ...... $^\circ C$.