Physics

Physics

Problem

A room air conditioner is modelled as a heat engine run in reverse. An amount of heat QinQ_{in} is absorbed from the room at a temperature TLT_L by the cooling coils which contains a working gas; this gas is compressed adiabatically to a temperature THT_H; then the gas is compressed isothermally in a coil outside of the house, giving off an amount of heat QoutQ_{out}; the gas expands adiabatically back to a temperature TLT_L and the cycle is repeated. An amount of energy WW is input into the system in every cycle through an electric pump. This model describes the air conditioner with the best possible efficiency. ![Diagram of a room air conditioner modeled as a heat engine run in reverse. The system consists of a room (cold reservoir) and an external environment (hot reservoir). The working fluid circulates through a cooling coil inside the room, a pump, a heating coil outside the room, and a valve. The cooling coil absorbs heat Q_in from the room. The pump compresses the fluid. The heating coil rejects heat Q_out to the outside. The fluid expands back to the room temperature T_L.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260106T182719Z/eb7ee726cc254d35964a97b1f2b17df2/935eed7aa61f7777f62cfc032e11bee9_img.jpg) The outside air temperature is THT_H and the inside air temperature is TLT_L. The air conditioner unit consumes electric power PP. Assume that the air is dry sufficiently so that no condensation of water occurs in the cooling coils of the air conditioner. Which of the following can't be the rate at which heat is removed from the room? A. P2(TLTH−TL)\frac{P}{2} \left( \frac{T_L}{T_H - T_L} \right) B. 3P4(TLTH−TL)\frac{3P}{4} \left( \frac{T_L}{T_H - T_L} \right) C. P(TLTH−TL)P \left( \frac{T_L}{T_H - T_L} \right) D. 3P2(TLTH−TL)\frac{3P}{2} \left( \frac{T_L}{T_H - T_L} \right)

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