A rigid container and a piston contains 1L of diatomic nitrogen at 500 K and 300 kPa. In an isothermal process, the gas expands to 2L. The control volume has a uniform cross section 0.5 m2 and the piston can only move up and down. Ignore friction for simplicity.

(a) In the context of reduced temperature and reduced pressure, explain why ideal gas law a reasonable approximation throughout this entire process. [1 Pt]

(b) What is the work done by the gas? [3 Pts]

(c) How much work do you have to do on the piston to reduce the volume of the gas from 2 L to 1 L in an isobaric (constant pressure) quasi-equilibrium process? [2 Pts]

(d) If the location of the piston is fixed after (c), how much heat from (c) do you have to add/remove from the gas to go back to the initial state? [2 Pts]

(e) Draw the trajectories of this cycle [(b)->(c)->(d)] in a P-T diagram. [2 Pts] ?