Problem — Room with the refrigerator door open

Problem

Why doesn’t a closed room cool down if we open the refrigerator door and leave it running? Discuss the overall energy balance of the room (refrigerator + ambient air).

Solution

Setup — closed system. Consider the closed room as a system isolated from outside: inside are the air and the refrigerator, powered by electrical work $L_\text{el}$. The refrigerator extracts heat $Q_C$ from inside the compartment and discharges it, together with the work spent, through the rear coil.

Refrigerator balance. Over a cycle $\Delta E_\text{int} = 0$, so by the first law the heat discharged by the coil is

$Q_H = Q_C + L_\text{el} > Q_C$

Room balance. Both the compartment and the coil are inside the room. The heat $Q_C$ extracted from the compartment is put back into the room by the coil, together with $L_\text{el}$. The net heat delivered to the room’s air is therefore

$Q_\text{net} = Q_H - Q_C = (Q_C + L_\text{el}) - Q_C = \ev{L_\text{el} > 0}$

Conclusion. The room heats up. Every cycle, the compressor’s electrical energy $L_\text{el}$ ends up, as heat, in the ambient air. The refrigerator moves heat from one point to another within the same room, but does not expel it: it would truly cool only if the hot coil were outside the room (as in air conditioners with an external condenser).

Links

Topics: Heat engines Concepts: Refrigerator and heat pump · First law of thermodynamics · Second law of thermodynamics Skills: Conservation of energy Objects: Refrigerator