A small, un-insulated closed cylinder with a freely moving piston contains air and is accidentally dropped into a lake and falls slowly to the bottom at 100 m below the surface. Initially, the air in the cylinder is at atmospheric pressure of 100 kPa with a volume of 0.1 m^3and a temperature of 20°C. The lake is also at a uniform and constant temperature of 20C. As the cylinder falls, the air is compressed and there is a heat transfer for the air so that its temperature remains nearly constant at 20°C. Since air can be treated as an ideal gas this implies that the product of pressure and volume is constant (PV = constant) during the process. Neglect the mass of the piston, friction, air leakage from the cylinder, potential energy and kinetic energy effects for the air and determine the following:

a. Final pressure (kPa) of the air at the lake bottom.
b. Final volume (m) of the air at the lake bottom.
c. Work done (kJ) by the air in the device for entire process.