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Question

# A refrigerating unit working on Bell Coleman cycle takes air from cold chamber at −10∘c 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 30∘C 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/kgWnet/kg=Work done on compressor-Work done by expander =n1n1−1R(T−2−T1)−n2n2−1R(T3−T4) =n1n1−1RT1[(P2P1)n1−1/n1−1]n2n2−1RT4[(P3P1)n2−1/n2−1] where n1=1.2R=0.287 kJ/kgK T1=263 K,n2=1.35,T3=273+30=303 K T4=T5(P2P1)1.55−11.55=303(6.5)0.33/1.35=186.5K ∴Wnet/kg=(1.21.2−1×0.287×263×((5.5)0.2/1.2−1)) =165.75−129.03=36.72 kJ/kg

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