“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

## Monday, September 07, 2009

### Cooling

I made a post in which I estimated the total energy use in my family. It was disturbing, in that we use a LOT of energy and there aren't a lot of places where cuts are easy (hypermiling my 3 ton SUV notwithstanding). Over 18 months have gone by since I wrote that article, and I've learned a few things. None would change the overall thrust of the article though; the main modification would be in the energy content of purchased items (the so-called "embedded energy"). I estimated one third of the cost of the average purchased item went for the total energy used in producing it, I now think that's probably too high.

But the last couple of weeks have been quite hot (around 100 degrees F for a daytime peak) and I've had the air conditioner on quite a bit. Our air conditioning system was manufactured in 1995 by Goodman Manufacturing and is a model CK60-18. As best I can tell, this means it's rated at a little under 60,000 BTU/hour (about 56,000) cooling capability at a Seasonal Energy Efficiency Ratio ("SEER") of about 10.5. This is typically found by adjusting the Energy Efficiency Ratio ("EER") which is defined as the cooling capacity over a period (e.g., BTU/hour) divided by the power used during that period in kilowatts at a particular outdoor temperature. Thus, EER is a mixed unit, BTU/hour/kilowatt. In dimensional terms, it's unitless but it's expressing how much energy it takes to move any particular amount of heat from inside to outside in a particular amount of time. Residential central air conditioners installed in the United States after 2006 are required to have a SEER of at least 13.

Air conditioner cooling capacity can also be rated in "tons," equivalent to the ability to move 12,000 BTU/hour from inside to outside in an hour. This unit hearkens back to the days when ice was used for cooling and the melting of a (short) ton of ice removes about 288,000 BTU from the environment, so doing so in a day uses 12,000 BTU per hour. My air conditioner thus provides the equivalent cooling capacity of about 5 tons of melting ice and hence is a five ton unit. Furlongs per fortnight anyone?

Now interestingly, working it out, my air conditioner will move 56,000 BTU of thermal energy from the inside my house to the outdoors in an hour. 56,000 BTU/hour is energy divided by time or power and is equivalent to about 16,400 watts. But the EER is about 9.5 so, since EER=(btu/hour)/watts, the electrical energy input is (BTU/hour)/EER or 5,890 watts. That's nice, my air conditioner produces about 2.8 times as much heat output as electrical energy input. Has Goodman Manufacturing succeeded in defying the law of conservation of energy and the first and second laws of thermodynamics? And by specifying a SEER no less than 13 is the U.S. government requiring changing the laws of physics?

No. The electrical input is used to compress a fluid and pump it around a circuit (absorbing heat from room air by changing from a liquid to a gas in the evaporator coil, then releasing it by changing back to a liquid) and to power a fan to blow the air cooled by the coil into the rooms of the house. Thus, the work being done is the movement and compression of fluids. The entropy of the air inside the house is decreased, that of the air outside is increased more in strict accordance to the second law.

The functioning of an air conditioning system is the same as that of a refrigerator and the most wonderful television series of all time, "The Secret Life of Machines," covers the refrigerator (among many other fascinating topics), here. A series of three YouTube videos comprising that episode are embedded below, but all episodes can be downloaded in their entirety. I heartily recommend doing so.

If my air conditioner is operating at a SEER of 9 (it's 14 years old after all), and I replace it with a new one with an SEER of 14, what can be saved? Well, I'll use 9/14 as much electrical energy, and I estimate that I'm using 560 hours per air conditioning season at about 5 kilowatts costing about $0.125/kilowatt hour. This will cost me about$350. If I buy the new unit, I'll spend (9/14)*$350 or$225, saving \$125. It will take a very, very long time to pay for the new unit at that rate.