A cylindrical container of initial volume V0 contains N atoms of a classical ideal gas at room temperature: T=300 K. One end of the container is movable, and so we can compress the gas slowly, reducing the volume by 2 percent while keeping the temperature the same (because the container's walls are in contact with the air in the room). Specifically, V0 = 0.01 m^3 and N = 3x10^22 atoms.

(a) What is the change in entropy of the confined gas? (Provide first an algebraic expression and then a complete numerical evaluation)

(b) How much work do we do in compressing the gas?

(c) How much energy was absorbed by the environment through heating?

(d) What was the entropy change of the environment?