Consider an 5.00 moles of an ideal gas undergoing isothermal expansion along the multiple paths outlined below. path a: reversible expansion from p; = 40. atm and v; -2.25 l to p,- 10. atm. path b: a three-step irreversible expansion against subsequent external pressures 30. atm, 20. atm, and 10. atm, where each step is held until p = pext: path c: a six-step irreversible expansion against subsequent external pressures 35. atm, 30. atm, 25. atm, 20. atm, 15. atm, and 10. atm, where each step is held until p = pet. a. for each of the paths, calculate the total work done. b. for each of the irreversible paths, compare the magnitude of work to the reversible path. c. consider the magnitude in work as you increased the number of steps and predict, qualitatively, how much work would be done if the process was broken up into 10, 20, and 50 steps. (i'm just looking for a general trend here.) d. how much work would you expect to be done as the number of steps approaches infinity?