Consider the following engine cycle performed on an ideal gas of N monatornic atoms. Step 1-2 is performed at constant entropy1 step 2-3 is performed at constant temperature and step 31 is performed at constant volume. These steps are carried out by putting the gas in contact with appropriate heat reservoirs (at TL. TH) and insulator. V (a) (2 points) What are the temperatures at the three points in the above gure 7'1? 7'2} T3 in terms of TL and TH. Explain your reasoning. (h) (3 points) Find the total net work done by the gas during one cycle in terms of N, TL. TH. [Hint If you want to do an integral over dV that's OK, but you should note that VL / 1/; can be related to 7'1- / Tj so that your nal result is independent of V1 V2 V.;.] (c) (3 points) 'N hat are the heat input and heat output for the gas during one cycle in terms of N, TL and TH? ls energy conserved? (d) (2 points) Show that this cycle's efciency is less than that of a Carnot engine operating at the same of temperatures TL, TH