A Room Air Conditioner Operates As A Carnot Cycle Refrigerator

A room air conditioner operates as a Carnot cycle refrigerator between an outside temperature Th and a room at a lower temperature T1. The room gains heat the outdoors at a rate A (Th – Tl); this heat is removed by the air conditioner. The power supplied to the cooling unit is P.
(a) Show that the steady state temperature of the room is
Tl = (Th + P/2A) – [(Th + P/2A)2 – Th2]1/2.
(b) If the outdoors is at 37oC and the room is maintained at 17oC by a cooling power of 2kW, find the heat loss coefficient A of the room in WK-1. A good discussion of room air conditioners is given by H.S left and W.D. In a realistic unit the cooling coils may be at 282 K and the outdoor heat exchanger at 378 K.

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