Calculate the thermal efficiency or coefficient of performan

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.

Solution

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.