A building is to be cooled by a Carnot engine operated in re

A building is to be cooled by a Carnot engine operated in reverse (a Carnot refrigerator). The outside temperature is 35°C (95°F) and the temperature inside the building is 20°C (68°F). (a) If the engine is driven by a 12x10³ watt electric motor, how much heat is removed from the building per hour? (b) The motor is supplied with electricity generated in a power plant which consists of a Carnot engine operating between reservoirs at temperatures of 500°C and 35°C. Electricity (transmitted over a 5 ohm line), is received at 220 volts. The motors which operate the refrigerator and the generator at the power plant each have an efficiency of 90%. Determine the number of units of refrigeration obtained per unit of heat supplied. (c) How much heat must be supplied per hour at the power plant? (d) How much heat is rejected per hour from the power plant?

Solution

(a) Effieciency of the engine = 1 - (TL/T_H )= 1 - [(273+ 20)/ (273 + 35)] = 15/308 = 0.0487

% efficiency =4.87

Now given that in 1 second, the energy given to engine = 12000 Joule

Total energy given in one hour =12000 x 3600 = 43.2 MJoule

heat removed in 1 hour = 43.2 x 10⁶ x 4.87 /100 = 2.10 MJoule