A Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C.How much energy does it need to remove 2000 J of heat from the interior of the house?
A) 105 J
B) 130 J
C) 780 J
D) 520 J
E) 340 J

Question

Quizplus · Accepted Answer

The efficiency of a Carnot air conditioner is given by the formula: COP = T_c / (T_h - T_c), where T_c and T_h are the absolute temperatures (in Kelvin) of the cold and hot reservoirs, respectively. Converting the temperatures to Kelvin, T_c = 293 K and T_h = 312 K. The COP is 293 / (312 - 293) = 15.42. The work done (energy needed) is Q_c / COP = 2000 J / 15.42 ≈ 130 J.

A Carnot Air Conditioner Operates Between an Indoor Temperature of 20°C