Question

a) Assume that the total cost of operation of a heat pump is four times the theoretical power cost for perfect efficiency, whereas the cost of direct electrical heating is just the power cost. If it is required to maintain room temperature at 27 °C, what limitations on the outside temperature will be required to economically justify the use of heat pump?

(b) A Carnot heat engine with an efficiency of 75% receives heat from a source at a rate of 4,000 kJ/min, and rejects the waste heat to a medium at 300 K.

Determine, the power that is generated by the engine.

Answer 1

1n a) Consider inside heat pump vroom temperature is to be maintained at 270 ie 3ook Let the outside temperature = - 23c je 250k 3ook HP 250k Let the energy required to maintain 27' t room Heat kump ic electricity temperature is 300J And work done on consumed is 50J 3ook IT 13005 ИР 505 2505 250k'a If if take temperature values, cop= Ti T-T2 300 300-250

COP=300 50 COP = 6 19 take energy values, cop= Qi 300 50 6 Now, ac In both cases, cop= same according to question, actual power cost = 4x therritical power cest = 4x50 2200 J 3ook 13005 HPK 2005 A looJ Tz In this condition, for heat fump to be masumum efficient, a T, w T-T2 300 200 300 300 - Tz Ta = look = -173°c

b) Carnot heat Engine, efficiency, 2 = 75% 2-75 TI 44000 kJ/min Heat Engine) 3ook h = w ai • 75 4ooo we 75X4000 w = 3000 kJ/min Power Generated, w = 300dx tub Kols 250kW