The temperature of a gas at $-173^{\circ} C$ is $1 \text{ atm}$ at constant volume. Up to what temperature should the gas be heated so that the pressure becomes $2 \text{ atm}$ (in $^{\circ} C$)?

$A$ gas is contained in a $5 \, L$ vessel at a pressure of $0.8 \, m$. It is connected to another evacuated vessel of $3 \, L$ capacity. What will be the resultant pressure in $m$ (at constant temperature)?

$A$ thin tube sealed at both ends is $100 \ cm$ long. It lies horizontally, the middle $20 \ cm$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform) ........ $cm$

Air pressure in a car tyre increases during driving. Explain.

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 $bar$).

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 \,cm$, the total length of the hollow cylinder is: (in $\,cm$)