Why coefficient of performance of a refrigerator is greater than 1?

Answer 1

The coefficient of performance (see Wikipedia article on "coefficient of performance") is a measure of merit for a refrigerator. To understand what it is telling us, we need to understand what a refrigerator does. Heat flows naturally from a hot region to a cold region. Even though your kitchen refrigerator is insulated to minimize the heat flow, without the machinery, the inside would gradually warm up to the temperature of the room. To keep the inside cold, the refrigerator must counter the natural flow by moving heat from the colder region inside the refrigerator to the outside. We have to put energy (usually electrical work) into the refrigerator to accomplish this.

If the inside were warmer than the outside, it would take no work to remove heat from the inside. The warmer inside would pass heat to the colder outside naturally. If the inside is just a little colder than the outside, it would take just a little work to move heat from inside to outside. As the temperature difference you wish to maintain increases, so does the work needed. But when we deal with thermodynamics, we must use absolute temperatures. If the temperature of the room is 68 degrees Fahrenheit, that is 20 degrees Celcius, or 293 degrees Kelvin. (The Kelvin temperature scale starts at absolute zero) If the temperature inside the freezer compartment is -5 degrees Celcius, that would be 268 Kelvin. The difference of 25 degrees is less than a tenth the lower absolute temperature. So in essence, this is the case of a small temperature difference.

The coefficient of performance is the ratio of the heat removed at the colder temperature to the work required to do it. Like many other figures of merit (the efficiency of an engine, the miles per gallon your car gets, ) the coefficient of performance measures the ratio of what you get (heat moved out of the box) to what you have to pay for (work from the electric company). But unlike the efficiency of an engine, the number can be greater than one. Because the temperature difference is small compared to the absolute temperature of the box, the energy expended to run the refrigerator is less than the energy moved from the inside to the outside.

Answer 2

The coefficient of performance (COP) of a refrigerator is greater than 1 because it is a ratio of the heat removed from the cooled space to the work input required to remove that heat. The COP indicates how much heat energy is moved relative to the amount of work put in. Since refrigerators move more heat energy than the work input required, the COP ends up being greater than 1.