State Avogadro's law (Hypothesis).

Hydrogen gas is filled in a balloon at $20^\circ C$. If the temperature is increased to $40^\circ C$ while the pressure remains constant,what fraction of the original Hydrogen gas will escape from the balloon?

$A$ balloon contains $1500 \, m^3$ of helium at $27^\circ C$ and $4 \, atm$ pressure. The volume of helium at $-3^\circ C$ temperature and $2 \, atm$ pressure will be ...... $m^3$.

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of cross-section $8.0 \times 10^{-3} \, m^2$. Initially,the gas is at $300 \, K$ and occupies a volume of $2.4 \times 10^{-3} \, m^3$,and the spring is in its relaxed state as shown in the figure. The gas is heated by a small heater until the piston moves out slowly by $0.1 \, m$. The force constant of the spring is $8000 \, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless,and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible.) (in $, K$)

The equation for an ideal gas is $PV = RT,$ where $V$ represents the volume of