Problem — Air conditioner and open window

Problem

An air conditioner with the window open in summer never cools the room. Explain why, in terms of heat flows between indoors, outdoors, and the compressor.

Solution

How an air conditioner works. It’s a refrigerator: it extracts heat $Q_f$ from the indoor air and, with the help of the compressor’s electrical work $L$, discharges it outdoors as $Q_c = Q_f + L$. It only works if the room to be cooled is closed, i.e. thermally isolated from outside.

Why the open window ruins everything. With the window open:

• convective return: the warmer outdoor air (at higher temperature) continuously flows back in, bringing back in exactly the heat just expelled. The air conditioner is cooling a volume that is effectively in direct contact with the entire outdoor atmosphere — a practically infinite reservoir.
• the compressor heats things up: the electrical work $L$ doesn’t disappear. By the first law it all ends up as heat. If part of that heat stays in the shared volume, the net balance on the room can even be a warming.

Conclusion.

$\ev{\text{open system} \Rightarrow Q_c \text{ flows back} + L \text{ heats} \Rightarrow \text{no net cooling}}$

An air conditioner only cools a confined space: by separating the two areas (cold indoors, hot outdoors) it can move heat from one to the other. If the two areas communicate, it moves heat in a circle and on top of that adds the heat from its own motor.

Collegamenti

Argomenti: Macchine termiche Concetti: Frigorifero e pompa di calore · Primo principio della termodinamica Competenze: Analisi di casi limite e fantafisica Oggetti: Frigorifero