I'm working on a project about electricity pricing, and need to understand the following: to keep the room at confortable temperature (70 degree, for example), does the amount of energy consumed by the AC grow linearly as the outside air temperature rises over the same length of time (a day, say)?


  • \$\begingroup\$ A/Cs switch on and off, so the energy usage is intermittent. What period of time are you averaging over? \$\endgroup\$
    – endolith
    Apr 14 '11 at 1:49

The short answer is no. It's not linear.

Here's the long answer.

There are three kinds of heat transfer: conduction, convection, and radiation.

Conduction means heat transfer due to physical contact. In the case of a building, the conduction is linear-- the amount of energy that leaks into a building is linearly proportional to the difference between the temperature outside and the temperature inside. The constant of proportionality is called the thermal conductivity of the material the heat is passing through. For well-insulated buildings, a great deal of the heat comes in through the windows, as glass is a poor insulator.

Convection means heat transfer due to bulk fluid flow, like wind. Unfortunately, this is hard to model accurately for buildings. It's safe to say that in most places on Earth, for most buildings, convection heats up your building, but not as much as conduction. Still, it screws up your model. It's particularly a problem with cold winds in the winter, where the temperature difference can be higher than in the summer.

For buildings, radiation means the sun. The effects of radiation are roughly proportional to the projected area of your windows over the course of the day. Unfortunately, the contribution to heating from radiation can be greater than that from conduction, especially for a well-insulated house with a lot of windows facing toward the equator. This is where the real nonlinearity comes in-- total irradiance is difficult to measure without considering the geometry of the windows and modeling cloud cover as a function of time.

To add a few numbers-- on a hot night (say, 80 F), you can cool a two-car garage with 1000 W air conditioner (which is actually providing you around 3000 W of cooling, see heat pumps). At noon, the sun averages around 1000 W per square meter, so if your garage has some large windows pointed toward the sun (say, skylights on a roof angled toward the equator), your AC unit can easily be overwhelmed by radiation alone.


I am not an expert on this at all, but my assumption would be that it is not linear at all. There are many factors that are going to determine a relation between outside air and energy consumption. Here are a few items to think about:

  • There is a large amount of energy required to start up AC units. Ideally you would start up less often, but this means either running longer resulting in larger temperature swings or running the motor at a slower speed.
  • The energy efficiently for the motor for the fans is non-linear. (Like if you were to run it at a slower speed)
  • The energy passed through the walls may be non-linear, and different per material. Like sheetrock, plaster, brick, wood, insulation, etc.
  • Psychological aspects. What I mean by this is people tend to allow the temperature in the house to be higher when it is warmer outside. This is due to the act of the air blowing (which it will be doing more often when its hot outside) makes people more comfortable regardless of temperature. This causes the "comfortable" temperature to change.

I go with linear for first order. Cooling must make up the heat gain, for conduction heat is like current and temperature difference like voltage. And there is a ohm's law.

The efficiency of air conditioners depends on temperature difference because it is a heat engine and this falls as the temperature difference increases, since this is on top of the linear demand above it is a diviation from linear.

I think that the effect of start up currents, overall, is small.

Just my opinion with out running any calculations.


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