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hw12_s13_sol - /ThermodynamicsI Spring2013 (Lectures125...

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Chemical Engineering 2300 / Thermodynamics I Spring 2013 Solution to Homework Assignment 12 (Lectures 1 25) Prof. Geof Silcox Due Tuesday, 2013 April 23, by 17:00 Problem 1 (10 points) An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kPa and 27 C, and 750 kJ/kg of heat is transferred to the air during the constant volume heat addition process. Assuming constant specific heats, determine (a) the pressure and temperature at the end of the heat addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. Approximate answers: (a) 4000 kPa, 2000 K: (b) 400 kJ/kg; (c) 60 percent; (d) 500 kPa. Solution From Table A 2 at 300 K, C v = 0.718 kJ/(kg K), k = 1.400. The process is sketched at below on a P v diagram. a) Find T 3 and P 3 . We start with the isentropic compression from 1 to 2:  K 2 . 689 8 300 v v T T or v v T T 4 . 0 1 k 2 1 1 2 1 k 2 1 1 2 From the ideal gas law, kPa 1746 300 2 . 689 95 8 T T rP P 1 2 1 2 . P v 2 1 3 4 w in w out q out q in TDC BDC
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For an ideal gas with constant C v , q in = C v (T 3 T 2 ). Then K 1734 2 . 689 718 . 0 750 T C q T 2 v 3 3 . From the ideal gas law,  kPa 4392 300 1734 95 8 T T rP P 1 3 1 3 . b) Find the net work leaving the engine (w net,out ). From an energy balance over the cycle, w net,out = q in q out . We start with the isentropic expansion from 3 to 4: K 7 . 754 8 1 1734 v v T T or v v T T 4 . 0 1 k 4 3 3 4 1 k 4 3 3 4 .
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