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July 1

BTUs and air conditioning

We are getting a new 3.5-ton air conditioner for a 1946-square foot house with 8-foot ceilings. Is this reasoning right:

(1) 3.5 tons of A/C, 1 ton = 12,000 BTU per hour. So 3.5 tons of A/C cools 42,000 pounds of water 1 degree Farenheit in 1 hour.

(2) 1946 square feet x 8 feet = 15,568 cubit feet of air in the house.

(3) Water has 4.23 times more specific heat capacity of air.

(4) A cubic foot of air weighs 0.08 lbs.

(5) So there are 1,245 pounds of air in the house. Air's specific heat is 4.23x less than that of water, so that is equivalent to 294 pounds of water.

(6) If the A/C can cool 42,000 pounds of water 1 degree F in 1 hour, it can cool 294 pounds of water (or all of the air in the house) 1 degree F in 25 seconds. Bubba73 ^{You talkin' to me?} 16:33, 1 July 2022 (UTC)[reply]

I'm not familiar with those units, but that appears to be correct (haven't checked the first line). However, the heat capacity of your house is much larger than the heat capacity of the air in your house. All those solids and liquids matter: walls, floors, ceilings, furniture, jars of peanut butter, whatever. Then, a change in temperature will affect the rate at which heat is produced in the house and the rate at which it leaks in or out. PiusImpavidus (talk) 18:18, 1 July 2022 (UTC)[reply]

British thermal unit: The amount of joules it takes to warm a pound of water by 1° Fahrenheit.

Ton: A ton is the cooling power of ice melting at a steady pace of 1 ton per day. Sagittarian Milky Way (talk) 04:45, 3 July 2022 (UTC)[reply]

I think that is right too. I got the 12,000 BTU per hour figure from Ton of refrigeration. Bubba73 ^{You talkin' to me?} 02:30, 4 July 2022 (UTC)[reply]

The cooling is not instantaneous. The temperature will not go down from 90°F to 32°F in (90 − 32) × 25 seconds = 24 minutes and 10 seconds. The cool air that is blown in is probably warmer than 32°F anyway, and it does not simply replace the hot air but mixes until equilibrium is reached. This may take a long time. The equilibrium temperature also depends critically on the outside temperature and the isolation. --Lambiam 21:10, 1 July 2022 (UTC)[reply]

Oh, yes, I see. Bubba73 ^{You talkin' to me?} 19:06, 2 July 2022 (UTC)[reply]