Problem 4-solution - h out,s = 581 kJ/kg, leading to η =...

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Problem 4 [20 points] Consider an air compressor that receives air at 100 kPa, 25 C . It compresses the air to a pressure of 1 MPa, where it exits at a temperature of 540 K. The compressor heat losses are 50 kJ for each kg of air flowing through the compressor. Find the following: a) Work of the compressor assuming variable specific heats. b) The efficiency of the compressor assuming variable specific heat. c) The amount of entropy generated. d) Draw the T - s diagram. Problem 4 Solution (a) From the thermodynamic tables, the inlet state is T in = 298 K, p in = 100 kPa, h in = 298 . 44 kJ/kg, p r,in = 1 . 38, s o in = 1 . 7 kJ/kg K. The outlet state T out = 540 K, p out = 1 MPa, h out = 550 . 12 kJ/kg, s o out = 2 . 299 kJ/kg K. Applying first law for a control volume consisting of the compressor, for steady state, 0 = ˙ Q + ˙ m ( h in - h out ) + ˙ W ˙ W ˙ m = ( h out - h in ) + ˙ Q ˙ m = 550 . 12 - 298 . 44 + 50 = 301 . 68kJ/kg (b) Assuming isentropic compression to p 2 = 1 MPa, s 2 = s 1 and p r, 2 /p r, 1 = p 2 /p 1 p r, 2 = 1 . 38 × 1000 / 100 = 13 . 8, for this value we get from the table
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Unformatted text preview: h out,s = 581 kJ/kg, leading to η = ˙ W ← isentropic ˙ W ← = h out,s-h in ˙ W ← / ˙ m = 581-298 . 44 301 . 68 = 0 . 937 (c) Noting that the compressor boundary temperature at which heat is transferred to the surrounding is unknown, we take both compressor plus surrounding as a control mass and apply the second law of thermodynamics, dS c dt + dS sur dt = ˙ S irr note that compressor is undergoing steady operation, then dS c /dt = 0. The surrounding is a thermal reservoir for which dS sur dT = ˙ S ← heat + ˙ m ( s in-s out ) sur ⇒ ˙ S irr = dS sur dT = ˙ Q ← T-˙ m ( s in-s out ) c ⇒ ˙ S irr ˙ m = ˙ Q ← ˙ mT-( s in-s out ) c = 0 . 156 kJ/kg K It is assumed that heat is transferred to the surrounding at the inlet temperature. In reality this temperature is higher. 5...
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This note was uploaded on 02/07/2011 for the course MECH 310 taught by Professor I.l during the Fall '08 term at American University of Beirut.

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