If the pressure of a gas increases by $2 \%$ at constant volume,then its temperature

$A$ sample of $O_2$ gas has a volume of $100 \ ml$ at a pressure of $1 \ atm$ and a temperature of $27^{\circ}C$. If the pressure is increased to $2 \ atm$ while the volume remains $100 \ ml$,the new temperature will be .... $^{\circ}C$.

When the pressure of a gas is increased by $0.4\%$,its temperature increases by $1\,^{\circ}\text{C}$. What is the initial temperature of the gas?

At $0^{\circ}C$,the density of a fixed mass of a gas divided by pressure is $x$. At $100^{\circ}C$,the ratio will be

$A$ 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 $\,cm$)

Explain Avogadro's hypothesis by relating pressure,temperature,and volume of a gas.