An ideal monatomic gas is taken from state 1 (P₁ = 2.0 atm, V₁ = 1.0 L) to state 2 (P₂ = 4.0 atm, V₂ = 2.0 L) by four different paths. In every path the gas receives exactly 200 J of energy by heating.
• Path A: first isochoric from 1.0 L to 1.0 L while the pressure rises from 2.0 atm to 4.0 atm, then isobaric expansion at 4.0 atm to 2.0 L.
• Path B: isobaric expansion at 2.0 atm from 1.0 L to 2.0 L, followed by an isochoric pressure rise to 4.0 atm.
• Path C: straight-line path on the PV diagram between the two states.
• Path D: first isobaric expansion at 3.0 atm from 1.0 L to 2.0 L, then isochoric pressure change to 4.0 atm.
Rank the final internal energy of the gas after the four paths from greatest to least. (Express your answer in the form B > D > C > A, etc.)