A monatomic gas is contained in a long, vertical cylinder of inner radius r = 14.0 cm. A movable piston of negligible mass is inserted in the cylinder at a height h = 1.20 m. Initially, the gas inside the piston is at ambient temperature (23.5 °C) and standard pressure (1 atm). You place a 250.0 kg mass on the top of the piston and allow it to isothermally compress the gas below it.

(a) What is the final pressure of the gas?

(b) How far is the piston displaced from the equilibrium position?

(c) Assuming an isobaric expansion, to what temperature should the gas inside the cylinder be heated in order to lift the mass 15.0 cm above the original position of the cylinder (i.e., to a height of 1.35 m)?