An ideal monatomic gas, initially at state O(P0,V0), is taken through the following four reversible steps that form a closed cycle:
Step 1: Isothermal expansion to volume 2V0.
Step 2: Adiabatic expansion to volume 3V0.
Step 3: Isothermal compression until the pressure becomes 3P0.
Step 4: Adiabatic compression back to the initial state O.
(i) Draw a neat, qualitative sketch of the entire cycle on a P–V diagram, clearly indicating each step and its direction.
(ii) At the junction point between Steps 1 and 2, compare the slopes of the adjoining isothermal and adiabatic segments. Which one is steeper? Give your reasoning without detailed calculus.
(iii) Rank the magnitudes of the work done by the gas in the four individual steps (largest to smallest). Base your answer solely on the relative areas under the respective curves in your sketch and any necessary qualitative arguments.
(iv) State whether the net work done over the complete cycle is positive, negative, or zero, and justify your answer in one or two sentences.