Finally Some Answers

Two questions have come up lately:  1)  Does cold air pulled in to the house by the wood stove “matter”, temperature-wise?  2)  Is the volume of air pulled into the house by the wood stove enough to make a difference in ventilation and air quality?

The short answers before the data:  1)  It barely matters, if at all.  2)  It replaces about 28% of our room air per day.

The tortured road to these conclusions, starting with the first question:

To begin, we need to know how much heat is delivered per unit of fuel.  We’ll call “unit of fuel” one mole of cellulose.  The combustion reaction is:  C6H10O5 + 6O2 –> 6CO2 + 5H2O.  Calculating the heat of this reaction requires the heat of formation (∆Hf) of all components; finding the ∆Hf of cellulose proved difficult (most sources simplify by using glucose instead, since cellulose is basically a chain of glucoses).  But this professor at MIT used a value of -961 kJ/mol, which seems pretty close.  I modified his calculations to wind up with water vapor instead of liquid water (since that’s how the stove works), and come up with: one mole of cellulose burns to produce 2,613 kJ.  Supposing the stove is 75% efficient, we find that 1,960 kJ of heat winds up in the room.

Now, how much cold air comes in to burn the mole of cellulose?  The formula shows we need 6 moles of oxygen.  Since air is 21% oxygen, we need a total of 28.6 moles of air (too bad we have to pull all that useless nitrogen into the house just to get a little O2).  Now, let’s assume that the room is 20ºC (68F) and outside is a chilly -10ºC (14F).  How much heat is lost to heat 28.6 moles by 30ºC?  Air actually requires very little energy to heat: .029 kJ heats one mole of air by 1ºC.  So we need (28.6 moles)*(30º)*(.029 kJ) = 25 kJ.

So:  burning one mole of fuel gives us 1,960 kJ of heat, and (on this imagined cold day) “costs” us 25 kJ in warming cold air pulled in to the house.  This difference, 1.3%, is rather trivial, and becomes even more trivial if the house is colder, or the outside is less frigid.  Beyond all this, there is still (IMHO) no thermal benefit to drawing cold air directly into the stove, bypassing the house: the air still has to be warmed by the fire, whether it happens in the room or inside the stove.

[One note of oversimplification:  I’m assuming the wood is bone-dry.  Some energy of the fire goes to evaporating the water in the wood, rather than into heating the house.  The wetter the wood, the less energy back per unit of cellulose.]

On to Question 2:  How much air (volume) does the stove pull in to the house?  We’ve already found that 1 mole of cellulose draws 28.6 moles of air, which is roughly 640 liters of air.  If we again assume the wood is very dry, and ignore the very small mass of non-combustible minerals in the wood (ash), then we can simplify and say that the wood is all cellulose, or similarly-burning hydrocarbons.  The molecular weight of cellulose is 162 g/mol.  On average, here at the Cold House, we burn about 9kg of wood per day.  Thus our daily burn is (9kg)*(1000g/kg)*(162 g/mol) = 55.5 moles of cellulose.

Continuing on, 55.5 moles of cellulose requires (55.5)*(640) = 35,520 liters, or 35.5 cu. meters, of air to burn.  For the imperially-minded, that is about 1,250 cu. ft.   A bit of measuring shows our downstairs living space to be about 4,500 cu. ft. Thus, an average daily stove run replaces about 28% of our room air.  Which, in fact, isn’t much.  I read on the web, for example, that classrooms in Britain are required to have 2.5 complete air changes per hour. Brrr.

A final note:  one thing which hadn’t occurred to me previously is that the volume of gasses coming out the chimney is much greater than the volume going into the stove.  I’ll spare you the calculations, but I estimated that it’s about 2.7 times the volume.  Largely this is due to the incoming gas being +/- room temperature, and the outgoing being +/- 400ºF.  But, also, it’s partly due to the fact that you’re putting in 28.6 moles of gas, but after combustion, releasing 33.6 moles.  Fascinating.

[Addendum: friend Leif has pointed out that my assumption that all air is drawn into the stove only to be used for combustion is probably faulty.  He notes that once a draft gets going, most likely a lot of extra air gets whisked up the chimney.  He’s probably right, though it’s difficult to know how much.  I did find one knowledgeable-sounding website which claims that “the average air consumption of a modern wood heater is in the range of 10 – 25 cfm [cubic feet per minute]”, which would be about 1.5-3x what I’d estimated.  Still, even at these rates, it would take 6-15 hours of steady burning to replace the air in our house just once.  For comparison, most clothes dryers seem to suck in the range of 100-150 cfm– and so could probably empty the house in a bit over an hour.]

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8 Responses to “Finally Some Answers”

  1. Jane Says:

    Wow! Bravo, and thank you for doing this. Nice to have one’s preconceptions confirmed, I must say.

  2. John Says:

    Don’t forget though that your stove doesn’t heat peripheral rooms very well, while the cold air comes in there to chill them off. So the rest of house gets much colder than it would be if the draught weren’t there. That’s the usual observation about homes with fireplaces: the room with the fireplace is toasty, but the rest of the house gets cold.

    • coldhousejournal Says:

      “the room with the fireplace is toasty, but the rest of the house gets cold”
      Actually, at our house, that’s pretty much exactly what we’re trying to achieve! In fact I much prefer it to the opposite possibility: warm air getting sucked out of the living room / kitchen and into the little-used peripheral rooms!

  3. John Says:

    You got the right answer, but showed the wrong calculation:

    “55.5 moles of cellulose requires (55.5)*(28.6) = 35,420 liters”

    but 55.5*28.6 = 1587.3 and those units would be weird. Instead:

    55.5 moles of cellulose requires (55.5mol cell)*(641 l air/mol cell)

    Otherwise you’ll get letters. 🙂

    Don’t forget too that you are likely a fairly frugal user of wood, so a more typical household is going to get a lot more air sucked into their house.

    PS Part of the way stoves get more efficient, I assume, is to use what is otherwise waste heat going up the chimney to heat intake air. It doesn’t look like that adds much but perhaps other design changes that result from that make the stove significantly more efficient.

  4. coldhousejournal Says:

    “You got the right answer, but showed the wrong calculation”
    Oops– quite right, I copied the wrong number. Think I’ve fixed it. Thanks!

    “Part of the way stoves get more efficient, I assume, is to use what is otherwise waste heat going up the chimney to heat intake air.”

    My understanding is that the main way stoves have gotten more efficient is by improving the percentage of carbon in the wood that gets fully combusted (i.e., reducing the result of smoke and burnable gasses.) I think there have also been efforts to circulate the hot exhaust through longer channels in the stove before it hits the chimney. Are there actually stoves that pre-heat intake air using chimney waste-heat?? It’s not something I’ve seen. There would be limits to this, anyway, as the chimney does have to be somewhat hot in order to prevent creosote, etc.

  5. John Says:

    I’ve been wondered about the consequences of an open fireplace or other chimney in which there is a constant draught up the chimney. Think Mary Poppins.

  6. Hannah Says:

    Our house is fairly tight and has a tall chimney, so the draw is palpable. A fire will suck the doors open. Even w/out a fire, if you take out the stovepipe and place a piece of paper against the hole of the chimney, it will stay there by suction. When we first started using our wood stove without a dedicated cold air pipe, we were drawing air from every available opening, including through our propane furnace/hot water system, which had the unfortunate and expensive effect of shorting out three mother boards before we figured out the problem. M. ran a pipe through an old dryer vent directly to the wood stove, and that seems to have solved it. (Your solution may have been to take out the whole propane backup system, but we aren’t there yet…;-)

    • coldhousejournal Says:

      Ha– yes, the moral of the story may be “Cut a hole in the wall”, or it may be “Don’t have backup heating systems containing motherboards” : ) Evidently, our house isn’t tight enough to have this problem.

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