A 700 kg piston is initially held in place by a removable latch above a vertical cylinder. The cylinder has an area of 0.1 m2; the volume of the gas within the cylinder initially is 0.1 m3 at a pressure of 10 bar. The working fluid may be assumed to obey the ideal gas equation of state. The cylinder has a total volume of 0.25 m3, and the top end is open to the surrounding atmosphere at 1 bar.
(a) Assume that the frictionless piston rises in the cylinder when the latches are removed and the gas within the cylinder is always kept at the same temperature. This may seem like an odd assumption, but it provides an approximate result that is relatively easy to obtain. What will be the velocity of the piston as it leaves the cylinder?
(b) What will be the maximum height to which the piston will rise?
(c) What is the pressure behind the piston just before it leaves the cylinder?
(d) Now suppose the cylinder was increased in length such that its new total volume is 0.588 m3. What is the new height reached by the piston?
(e) What is the maximum height we could make the piston reach by making the cylinder longer?
