Question

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. 340 J

B. 780 J
C. 105 J
D. 130 J
E. 520 J

Answer 1

D. 130 J

Step-by-step explanation:

The coefficient of performance for a machine that is being used to cool, is given by:

`COP=(Q_C)/(W)=(T_C)/(T_H-T_C)`

Here
`Q_C` is the heat removed from the cold reservoir, W is the work required, that is, the energy required to remove the heat from the interior of the house,
`T_C` is the cold temperature and
`T_H` is the hot temperature. Recall use absolutes temperatures(
`273.15+^\circ C`). Replacing and solving for W:

`W=Q_c(T_H-T_C)/(T_C)\\W=2000J(312.15K-293.15K)/(293.15K)\\W=129.63J`