(a) Consider a reversed Carnot engine acting as a heat pump by delivering heat at a rate On to the hot bath having a tem

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A Consider A Reversed Carnot Engine Acting As A Heat Pump By Delivering Heat At A Rate On To The Hot Bath Having A Tem 1 (76.21 KiB) Viewed 21 times

(a) Consider a reversed Carnot engine acting as a heat pump by delivering heat at a rate On to the hot bath having a temperature Th, consuming power P, and taking heat at a rate 0from the cold bath having a temperature T. Heat also escapes from the hot bath directly into the cold bath at a rate g = (T)-T.) K, where K is a constant. (1) Sketch a labelled schematic of the system. (ii) Show that in equilibrium P (T) – T.)? K T [8 Marks] (b) On a day where the outside temperature is 10°C a house maintains 21 °C internally using a heat pump (1) Calculate the value of for the heat pump. (ii) If the power consumed by the heat pump is 15% of its maximum with the indicated temperatures, calculate if the heat pump is working at 100% of its capacity. [4 Marks) (c) At the beginning of March this year an unusual cold front associated with the breakup of the polar vortex brought a significant drop in temperature to Ireland. Householders needed to heat their houses more than normal to maintain the internal temperature of their houses. (1) What is the coldest temperature that the house in Q. B2 (b)(1) could maintain 21 °C with the heat pump working at 100% of its capacity? (ii) If the temperature outside is -10°C, what is the highest temperature that the heat pump can maintain inside the house? [8 Marks)