Calculate the thermal efficiency or coefficient of performance of following cycl

Question

Calculate the thermal efficiency or coefficient of performance of following cycles, and determine if the cycles are reversible, irreversible, or impossible. A steam power cycle that receives heat input 1000kJ while producing a net work output 600 kJ, when interacting with two thermal reservoirs at temperatures of 600 degree C and 20 degree C. A refrigeration cycle that needs 10 kJ work input to remove heat of 120 kJ to cool a room when interacting with two the inside and outside temperatures are at 15 degree C and 40 degree C.

Explanation / Answer

a)

Thermal eff = W / Qin

= 600 / 1000

= 0.6

Carnot eff = 1 - T_low / T_high

= 1 - (20+273)/(20+600)

= 0.527

Since thermal eff is greater than Carnot eff, cycle is impossible.

b)

COP = Heat rejected / Win

= 120 / 10

= 12

Carnot COP = T_low / (T_high - T_low)

= (15+273) / (40-15)

= 11.52

Since COP > Carnot COP, cycle is impossible.

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