Problems#$2$

A $5-$kg piston in a cylinder with a diameter of $100$ mm is loaded with a linear spring and

the outside atmospheric pressure is $100$ kPa $,$ as show in the figure below. The spring exerts

no force on the piston when it is at the bottom of the cylinder. For the state shown in the figure,

the air pressure inside the cylinder is $400$ kPa with volume $0\mathrm{.}4$ litre. The valve is opened to let

some air in$,$ causing the piston to rise $2$ cm from the present position in the figure. Find the new

air pressure in the cylinder, in kPa $.$