A gas in a cylinder occupies a volume of 3.0 m^3, and supports a piston of mass 1.0 kg and diameter 20.0 cm. The external pressure is 1.0 atm. What is the final pressure and work necessary to compress the gas to a volume of 0.05 m^3 for the following cases.
a. Compress is fast, so that no heat is released during compression
b. Compression is slow, so that the temperature of the gas remains constant and the same as outside.