Question 1 (25 points) Part A (15 points) An Otto cycle engine comprises the following processes: A-B - an adiabatic com

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Question 1 25 Points Part A 15 Points An Otto Cycle Engine Comprises The Following Processes A B An Adiabatic Com 1 (98.67 KiB) Viewed 28 times

Question 1 (25 points) Part A (15 points) An Otto cycle engine comprises the following processes: A-B - an adiabatic compression from volume Vh to VL B-C - an isochoric pressurization at volume, VL •C-D an adiabatic expansion from volume VI to V D-A - an isochoric depressurization at volume, VH Assume that the working fluid for an ideal Otto engine is an ideal gas. (i) (2 points) Sketch the Otto cycle on a P-V diagram. On your diagram indicate: the direction of the cycle; processes where heat enters and leaves the cycle; and the total work done by the cycle. (ii) (2 points) Derive an expression for the total work done by one cycle of the Otto engine in terms of VH, VL, PA, PB, Pc, Pp and 7. (iii) (2 points) Derive an expression for the heat input into one cycle of the Otto engine in terms of VH, VL, PA, PB, Pc, Pp and 7. (iv) (2 points) Derive an expression for the entropy change in each leg of the Otto cycle in terms of VH, VL, PA, PB, Pc, Pp and y. (v) (2 points) Prove that the entropy change for one complete cycle is equal to zero. (vi) (3 points) Show that the efficiency of the Otto cycle can be expressed as: TA n=1 TB' where TĄ and Tg are the temperatures at points A and B. (vii) (2 points) Comment on the similarity between this expression and that for the Carnot cycle efficiency. Are they related or is the similarity in form just a coincidence?