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Question

# An air refrigeration system works on reversed Brayton cycle and used for 10 tones of refrigeration capacity. Air enters the compressor at −20oC and 1.4 bar and compressed to 4.2 bar. Compressed air is cooled in the cooler to 50oC with a loss in pressure of 0.2 bar. What is theoretical piston displacement ?

A
50m3/min
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B
1.01617m3/min
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C
79.1m3/min
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D
63.7m3/min
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Solution

## The correct option is C 79.1m3/min As loss an pressure is given in cooler, so, Ps=4.2−0.2=4 bar 3-4 is isentroic expansion process, T4T3=(P4P3)(γ−1)/γ T4=T4(41.4)(γ−1)/γ [T3=50+273=323K] T4=239.3K Let ˙m is the mass flow rate of air. So, Regirgeration capacity =˙m×cp(T1−T4) [T1=273−20=253K] 10×3.5=˙m×(1.005(253−239.3) ˙m=2.542kg/s Theoretical piston displacement =˙V1) P1V1=˙mRT1 ˙V1=2.542×0.287×253L4×102 ˙V1=13184m3/s=79.104m3/mm

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