When the pressure on a gas is decreased to $1/4$ and the absolute temperature is increased four-fold the volume of the gas

• As number of moles are constant , therefore we can apply the formula given below :

                  $\mathrm{PV}=\mathrm{nRT}$

                $\mathrm{PV}=\mathrm{T}$

                  $\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2}$

By solving we get,

$\frac{{\mathrm{P}}_1{ \mathrm{V}}_1}{{\mathrm{P}}_2{ \mathrm{V}}_2}=\frac{{\mathrm{T}}_1}{{ \mathrm{T}}_2}$

$\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}$=$\frac{{\mathrm{P}}_1{\mathrm{V}}_2}{4\times 4{\mathrm{T}}_1}$ (as pressure is decreased to 1/4 and temperature is increased 4 times.)

 ${\mathrm{V}}_1=\frac{{\mathrm{V}}_2}{16}$

$16{\mathrm{V}}_1={\mathrm{V}}_2$

Therefore, the new volume is equal to 16 times of old one.