$A$ gas at the temperature $250\,K$ is contained in a closed vessel. If the gas is heated through $1\,K,$ then the percentage increase in its pressure will be ...... $\%$

State Gay-Lussac's Law of Gaseous Volumes.

An ideal gas initially at pressure $1 \, bar$ is being compressed from $30 \, m^{3}$ to $10 \, m^{3}$ volume and its temperature decreases from $320 \, K$ to $280 \, K$. Find the final pressure of the gas (in $bar$).

The tyre of a motor car contains air at $15^{\circ} C$. If the temperature increases to $35^{\circ} C$, the approximate percentage increase in pressure is (ignore the expansion of the tyre).

$A$ cylinder of $5 \ L$ capacity,filled with air at $N.T.P.$,is connected to another evacuated cylinder of $30 \ L$ capacity. The resultant air pressure in both the cylinders will be ...... $cm$ of $Hg$. (in $.85$)

$A$ 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 $cm$)