For Boyle's law to hold, the gas should be:

When the volume of a system is increased two times and the temperature is decreased to half of its initial temperature,then the pressure becomes ...... times.

Which relation is correct for the given $P-V$ diagram?

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 $, K$)

An inverted bell lying at the bottom of a lake $47.6 \ m$ deep has $50 \ cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70 \ cm$ of $Hg$ and density of $Hg = 13.6 \ g/cm^3$)

On $0^{\circ}C$,the pressure measured by a barometer is $760 \, mm$. What will be the pressure at $100^{\circ}C$?