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Question

A refrigerating unit working on Bell Coleman cycle takes air from cold chamber at 10c and compressed it from 1 bar to 6.5 bar with index of compression being 1.2. The compressed air is cooled to a temperature of 30C before it is expanded in the expander, where the index of expansion is 1.35. What is the refrigerating effect?

A
28.14 kJ/kg
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B
36.72 kJ/kg
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C
41.84 kJ/kg
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D
48.76 kJ/kg
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Solution

The correct option is B 36.72 kJ/kg
Wnet/kg=Work done on compressor-Work done by expander

=n1n11R(T2T1)n2n21R(T3T4)

=n1n11RT1[(P2P1)n11/n11]n2n21RT4[(P3P1)n21/n21]

where n1=1.2R=0.287 kJ/kgK

T1=263 K,n2=1.35,T3=273+30=303 K

T4=T5(P2P1)1.5511.55=303(6.5)0.33/1.35=186.5K

Wnet/kg=(1.21.21×0.287×263×((5.5)0.2/1.21))

=165.75129.03=36.72 kJ/kg

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