Behold, our secret weapon in the furnace wars. (This photo will look familiar to those who read Blog Action Day: Walking My Watershed. I hope you read it; it's one of the most popular posts on this blog.)
Our bathroom sink and one of the twin sinks in our kitchen hold about 10 liters of water. Suppose we fill it with the tap water at 50C (122F). That's 10 kg of water with a heat capacity of 4.2 kJ/(kg-K). One liter of water will release 4.2 kiloJoules of energy for every degree C it cools. Suppose the water cools to a comfortable 25C (77F), then it releases10 liters * 25 degrees * 4.2 kJ/(kg-K) = 1050 kJoules.
Our kitchen is roughly 12x12 feet with 8 feet ceilings. Convert that into meters and we get an air volume of 32621 liters. The molecular mass of air is about 0.029 kg/mole. (Air is a mixture of gases so this is the weighted mass of it's constituent gases.)
One mole of gas at standard temperature and pressure (STP), a comfortable temperature for humans at sea level pressure, fills up 22.14 liters. So the air in our kitchen weighs
32621 liters * 0.029 kg/mole / 22.14 liters/mole = 42.7 kg.
The heat capacity of air at STP is 1.00 kj/(kg-K), so the 1050 kiloJoules of energy released by the cooling sink water can heat the air in the kitchen
1050 kJ / (42.7 kg * 1.00 kJ/(kg-K)) = 24.6 C
If the air in the kitchen started at 20 C, and is warmed another 24.6 C, then it would be a toasty 112 F.
The kitchen does not get that warm because some of that heat is transferred to the porcelain sink, heat capacity 1.07 kJ/(kg-K), furnishings, etc. But, you get the general idea. You used an awful lot of energy to heat that hot water, so you might as well get as much of that energy back before you send it down the drain.
Fancy new houses might have an expensive heat exchanger system*, using waste heat from the water leaving the house to heat up the water coming into the house. But, we have an older and simpler house; we use the same cheap and effective technology our grandparents used, our brains.
Now calculate the equilibrium temperature when 10 kg of water at 50 C meets 42 kg of air at 20 C. Assume that it is a closed system (no heat loss to the sink or furnishings). Leave your answer in the comments.
* Actually, heat exchanger systems are not that high tech or new. They just run tubes of hot and cold water around each other. I first read about that in the 1970s. But, they did not gain traction in mass-market housing. They were recently resurrected in expensive and huge LEED homes.
Addendum:
Alison makes a good point in her comment. You do get much bang for your energy buck if you let the bathwater cool before you send it down the drain. When we used to take baths, that's what we did in the winter time. We take showers now--with a very low flow shower head. If you don't mind rinsing the soap off your feet in the faucet before you exit the tub, you can recoup a great deal of heat from your shower water, too.
We turned our furnace on for the first time this week, too. So far, we're just having to run it once in the morning to take the chill off. The reason? We finally got insulation added to our walls. Our house dates from the 50s, and didn't have ANY insulation in the walls. Insulation has made a big difference!
ReplyDeleteSo you’re saying you reduce your heating requirements by letting the dishwater cool off in the sink before you drain it? I don’t think our dishwater is 50°C by the time the dishes are done.
ReplyDeleteLetting bathwater cool before draining it would contribute more, I think. Maybe put a stopper in the tub during showers. If you can’t let the water drain, everyone will need to keep to very short showers — or share them — so that the tub doesn’t overflow by the time everyone’s clean. Combined water conservation and heating efficiency!
We pay about $600/year to heat 2400 ft^2 in Montreal. We don’t heat until the temp drops below about 17°C in the day or 15°C at night (63°F or 59°F); my beloved starts complaining about the heat at 67°F. We’ve thought about switching to a greener, more modern heating method like geothermal, but it makes no sense because we pay so little in heat compared to what it would cost to retrofit.
Secrets:
We live in an old-fashioned, poorly-insulated house built in 1929. It’s what we Montrealers call a triplex — like a row house, only better. We have neighbours on either side and on top of us. For the 20,000 ft^3 of living space and basement, we have a total of 500 ft^2 of surface area (walls, windows and doors) exposed to the cold winter air.
Also: Old-fashioned layout. Vestibules act as airlocks. Lots of doors that stay shut so only the desired space is heated. Important because my beloved works from a home office.
Related: dogs, not cats. Heat-giving dogs accept being confined in a warm room with you. We keep thinking about getting a kitty and keep rejecting the thought because kitties do not tolerate closed doors.
Sharon Astyk considers dogs to be inefficient but very useful and targeted engines for burning grass [once it has been converted to denser fuel by feeding it to rabbits]. I should calculate how much my dogs’ heat costs based on the price of the expensive kibble I buy them.
Finally did the calculation. The calories in dog kibble cost me about 25x as much as the calories in heating oil. The dogs are much more than 25x as much fun to hang out with so I’m satisfied.
ReplyDeleteIn other news, we are no longer using heating oil but have switched to all electric. That means we do localized heating only, room by room, and each room has its own thermostat. All electricity, general use and heating combined, cost me $150 for two months. That’s $75/month (about 34 kWh/day in electricity, not counting another 4 kWh/day or so in body heat) to run and heat a two-person, two-dog household occupying a 20,000 ft^3 dwelling.
Mean temperatures for December and January were -3.4C and -11.9C respectively.
Is that 25x after taking into account that food calories are actually kcals?
Deletehttp://www.nutrition.gov/whats-food/commonly-asked-questions-faqs
Yep! My calculations were all in kcals but ‘calories’ flows better in a sentence and since it’s relative it doesn’t matter.
DeleteThose are expensive kibbles. I hope your dogs appreciate how good they have it! ;-)
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