An ideal Brayton cycle refrigeration cycle has a compressor pressure ratio of 6. At the compressor inlet, the pressure and temperature of the entering air are 20 lbf/in2 and 460 R. The temperature at the inlet of the turbine is 700 R. For a refrigerating capacity of 15 tons, determine (a) the mass flow rate in lbm/min. (b) the net power input, in Btu/lbm. (c) the coefficient of performance."

(a) 185.1002 lbm/min

(b) 7125.12 Btu/min

(c) 0.42

Explanation:

Here we have;

= 6

γ = 1.4 for air

T₁ = 460 R = 255.56 K

T₃ = 700 R = 388.89 K

1 ton of refrigeration capacity = 3.52 kWh = 0.98 W

∴ 15 ton = 15×3.52 = 52.8 kW/h

= 189910.0534716 kJ/h = 3165.1676 kJ/min  

T₂ = 1.669 × 460 = 767.515 R = 426.4 K

Refrigeration effect per kg = 1 × × (T₃ - T₂) = 1.005 × (700 - 767.515) = 67.85 = 37.7 kJ/kg

83.96 kg/min = 185.1002 lbm/min

(b)

T₄ = T₃×1.669 = 700×1.669 = 1167.96 °R = 648.9 K

= 21925.83 kJ/min

= 14408.4 kJ/min

= 21925.83 - 14408.4  = 7517.43 kJ/min

1 kW = 56.87 Btu/min

Therefore;

125.29 kW = 7125.12 Btu/min

(c) The coefficient of performance (COP), is given by the relation;

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explanation:

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Explanation: