A closed cylinder of 0.25 m diameter is fitted with a light friction-less piston.The piston is retained in position by a catch in the cylinder wall and the volume on one side of the piston contains air at a pressure of 750 kN/m2. The volume on the other side of the piston is evacuated. A helical spring is mounted coaxially with the cylinder in this evacuated space to give a force of 120 N on the piston in this position. The catch is released and the piston travels along the cylinder until it comes to rest after a stroke of 1.2 m. The piston is then held in its position of maximum travel by ratchet mechanism. The spring force increases linearly with the piston displacement to a final value of 5kN. Calculate the work done by the compressed air on the piston.
##W=\int p.dV ##
W- work done
L- piston displacement length = spring compression length
The Attempt at a Solution
Total work done by compressed air = workdone against the spring + workdone by expansion right ?
work done against the spring = ##\int F.L dF ## integrated between 120N and 5kN ??
i got this as 14991360 joules ,this is way more than the final answer i was given.
work done by expansion = ##\int pdV## = 750x103( (pi/4)0.252x1.2) = 44178.64 joules ??
The final answer i was given is 3.07 kJ ,my answer is nowhere close to this ,any help will be appreciated.