Cranking that air conditioner is more expensive than you think

We've had a heat and drought wave in southern Ontario for the last few weeks. The grass goes "crunch" underfoot, there's been virtually no rain for a month, and the thermometer's been consistently in the high 20s to low 30s- and, with humidity at 70+ percent, it feels a lot hotter.

It's obviously quite tempting to crank up the air conditioner and pretend that it's nice and cool. The energy (and financial) cost of running that air conditioner, though, escalates much faster than you might expect.

Let's look at some technical details, then see what conclusions we can draw about your thermostat and your power bill.

TL;DR: Air conditioner costs scale with the square of the temperature difference, so don't set the thing any colder than you really have to.

Some Introductory Thermodynamics

Heat flows into your house in three ways:

  • Conduction through the walls, windows, foundations and roof.
  • Radiation in the form of visible and infrared light, mainly affecting windows but also playing a role in wall cavities.
  • Convection as hot air leaks through the house's air barrier or circulates inside wall cavities.

The rate of heat transfer by conduction is linear with the temperature difference. If it is 10 degrees colder inside than outside, twice as much heat will be conducted into the house than if it were 5 degrees colder inside than outside. (The choice of Celsius, Fahrenheit or Kelvin doesn't matter, except that you must choose appropriate coefficients when you do the calculations.)

Radiative heat transfer depends on the difference between the 4th power of the temperatures. (Kelvin units are required here.) For typical summer weather- say 303 K (30 C) outdoors- this works out to be fairly close to linear with the difference in temperature. So, like before, chilling the house by 10 degrees means you'll have double (well, 1.95 times) the radiative heat transfer in your wall cavities, window cavities and such, compared to chilling the house by 5 degrees. The rate at which heat is carried into your house by visible and infrared sunlight shining through the windows is nearly independent of the temperature inside your house, so we can, for the present purposes, neglect it.

Let us assume that your house is well built and properly insulated, so that convection is a minor player (except between window panes, but we can ignore that for the moment).

To a first approximation, then, the rate at which heat flows into your house is a linear function of the difference in temperature. Double the temperature difference between inside and out, and you double the rate at which heat flows into the house.

Most household air conditioners are based on vapour-compression cycles. A detailed description of how they work is not necessary for the present purposes (although it is very interesting- do look it up, if you have time). For now, the main features we are interested in are:

  • Most of the electrical power used to run an air conditioner is consumed by the compressor, which compresses the refrigerant so that it can release its heat and return to a liquid state.
  • The power required to achieve a given rate of heat flow through the air conditioner is, to a first approximation, a linear function of the difference in temperature. If you double the temperature difference, you double the amount of energy the air conditioner must consume to move a given quantity of heat.

We now combine these observations:

  • Rate of heat flow into the house: Approximately linear in delta T.
  • Power needed to move heat out of the house: Approximately linear in delta T.

The energy demand (and therefore operating cost) of our air conditioner, then, scales with the square of the difference in temperature!

What does it mean to you?

Say it's 30 Celsius outside. You set your air conditioner to 26 C. Your neighbour, whose house is identical, sets his to 22 C.

Your neighbour's air conditioning bill will be four times as expensive as yours. We are talking, here, about a device that, in a typical house, can easily use 300 to 600 kWh per month (more, if your house is big). In financial terms, that would look like $50 to $100 a month. If you're a small business owner, setting your shop's A/C too cold can easily cost you hundreds, even thousands of dollars a month. And that power is being used during the hottest parts of the day, when electricity is at its most expensive and we have to fire up dirty fossil-fuel generating stations to meet the demand.

So if you want an extra $100 a month in your pocket, while reducing our dependence on dirty fossil-fuel power plants, try opening some windows. Turn on some fans. Dress (or undress) according to the  weather; humans are very well adapted to temperatures in the mid to high 20s as long as we don't bundle up as if it were wintertime. If it's still too hot, then by all means close the windows and fire up the air conditioner- just don't set it any colder than necessary. Try starting at 27-28 C, then turn it down half a degree every half-hour until you're comfortable. (Starting at winter temperature of 21 C and going up will almost certainly yield a lower, i.e. more expensive, temperature than you need.)  Your wallet, and local utilities commission, will thank you.

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Comments

great post

I have been scouring the internet for information on air conditioners, maintenance, and efficciency. There is a ton of information, but you took a scientific approach which I really appreciate. I have been building a site http://www.airconditionercorpuschristi.com and needed real information and advice to help grow the content to desired levels. We live in Corpus Christi, Texas so the AC demand here is huge. Almost no heating, very hot summers. There are a few other things you can do to your AC such as proper maintenance. Simply cleaning your coils can help increase efficiency dramatically as debri, dust, dirt, leaves and other unwanted sediments get stuck and restrict airflow. Also, do your suggested yearly maintenance with a technician. They can decrease your energy bill and extend the life of your unit by ensuring maintenance is done correctly. Stuff like if your base is not level you can lose significant efficiency. Also, clean out your ducts increasing airflow and decreasing the amount of dust and irritants that are circulated throughout your house. Finally, make sure you seal your windows and doors so that your AC does not constantly leak. Just a few tips that can save a bunch of money in the long run.

Maintenance is important!

Matthew's picture

Good point about maintenance, OTET. A filthy condenser coil will certainly make the unit run a lot more often than it needs to, and at reduced efficiency.

I am not convinced that AC units need professional annual maintenance in a temperate climate. In Texas, where you run the things full-tilt for ten months at a time, that may be different- you'd put as many hours on your AC in one year as we do in five. (Furnaces, on the other hand, can produce toxic carbon monoxide and other nasties if their innards start to corrode, and certainly do need annual safety inspections even if they aren't used very much.)

I agree!

You can do the maintenance by yourself. Not necessarily that you will be the one to do the whole cleaning process of your air conditioning system but you can do a little cleaning and keep your air con the way that it use to perform. You should follow the instructions given to you by the installers of your air con system. These are simple things that these save you money by just doing some little efforts.

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