Problem 1 A heat engine is proposed using a monatomic ideal gas as its working substance. The heat engine has 4 steps in order a, b, c, (1: Step 3: isothermal compression from V; and P1 to V2 and P2. Step b: isobaric expansion from V2 and P2 to V3 and P3 Step c: isothermal expansion from P3 and V3 to P4 and V4 Step (1: isobaric compression from V4 and P4 to Vi and P1 In completing parts (A) and (C) consider the following reduced variables: W1 2 P1V1 (A) Calculate the work done in each step a-d in terms of the reduced variables W1 , [3 and 6 (and any mathematical operations) and the total work done in one full cycle. Simplify as possible ( 5 points 1 (B) Calculate the heat added to the system in each step ad in terms of the reduced variables W1 , ,8 and 6 (5 points) (C) Determine an expression for the maximum theoretical efficiency of the heat engine. Then calculate the theoretical efficiency if the following pressures and volumes are achieved in the device: P1 : 1 bar P2 = 10 bar V: = V3 =lm3 (5 points) (D) Plot P versus V for the entire cycle using a computer and the pressures and volumes from part (C). Label points 144 corresponding to the endpoints of transformations (steps ad) on each diagram {5 points)