Consider a reversed Stirling cycle applied as a refrigerator. Assume each proces

Question

Consider a reversed Stirling cycle applied as a refrigerator. Assume each process is frictionless and internally reversible with Helium Gas as the working fluid. The refrigeration cycle has a cooling capacity of 30 J/s from a chilled region at 70 K. The outdoor environmental temperature is 290 K. The external heat exchangers are sized to reach a 10 K difference from of limiting temperatures (cycle Tmin < TC ? 10 K = 60 K, cycle Tmax > TH + 10 K = 300 K). Assume that internal heat transfer in the cycle is perfectly reversible. The minimum pressure in the cycle is 50 kPa and the compression ratio Vmax/Vmin = 4. The cycle executes in a piston-cylinder device operating at 60 cycles/s. There are no significant changes in potential and kinetic energy. This is a small device ( J/s not kJ/s ). CAREFULLY SKETCH p-v & T-s cycle diagrams and organize a state table showing (p,v,T) for each state. a) Find the reversed Stirling cycle COP = _______ (the maximum reversible cycle COP = TC/(TH ? TC) = 0.318) b) Find the specific heat transfer for each process, 1q 2, 2q 3, 3q 4 & 4q 1 = ________________ kJ/kg. c) Find the mass of Helium in the cylinder, m = _________kg and the max. cylinder volume, Vmax = ______ cc d) Find the entropy production for each process, 1?2, 2?3, 3?4 & 4?1 = ________________ J/K

Explanation / Answer

reversed Stirling cycle COP = 0.126 specific heat transfer for each process 1q 2 = 230KJ/Kg 2q 3 = 160KJ/Kg 3q 4 = 311KJ/Kg 4q 1 = 98.01 kJ/kg. mass of Helium in the cylinder, m =26.6 Kg max. cylinder volume, Vmax = 135 cc entropy production for each process 1s2 = 66 2s3 = 23 3s4 19 4s1 = 08 J/K

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