A horizontal cylinder, area $150$ cm$2$

$,$ is fitted with a freely floating, frictionless leak proof piston i$.$e$.$ there is

no piston rod. The left end of the cylinder, which contains $0\mathrm{.}0045$m$3$ of air at atmospheric pressure $(100103$

N$/$m$2$

$),$ is connected to a light inextensible balloon; the balloon is flat initially. The right$-$hand end of the cylinder

is connected, via a valve to a rigid vessel containing nitrogen at high pressure.The balloon is inflated by slowly admitting nitrogen to the right$-$hand end of the cylinder. During the inflating

process the piston moves a distance $250$ mm and when fully inflated the volume of the balloon is $0\mathrm{.}003$ m$3$

$.$ Any

changes in the air pressure P are related to the corresponding air volume V by PV$=$constant.

$($a$)$ Sketch the trace that would be obtained on an indicator connected to the left$-$hand end of the cylinder. $($b$)$

Evaluate the work done by each of the following system: $($i$)$ the atmosphere $($ii$)$ the balloon $($ii$)$ the air $($iv$)$ the

piston $($v$)$ the nitrogen