A cylinder is equipped with a frictionless piston with an inner diameter of 5 cm and a mass of 3 kg. A 27 kg weight rests on the piston. One mole of helium at 25^o C fills the cylinder. (30 pts)

a.  If the system is in equilibrium, find the absolute pressure and volume of the gas in the cylinder.

b. The piston reaches a new equilibrium when the weight is abruptly lifted. The first step is rapid so that negligible heat is exchanged with the surroundings. Then the slow step where the temperature returns to 25^o C.  What are the energy balances for these two steps? How about the overall process? What happens to the temperature during step one and why?

c.  What is the work done by the gas? What is the heat transferred during the entire process?