A while ago I wrote about keeping the house cool by blowing a lot of cool outside air through it at night. At the time I was talking about my dad's house, since we were out of our house most of that summer, but now we're in our own house. I've put in a whole-house fan, and we've been following this approach.

One thing I've been thinking about is how much to avoid heat and humidity generating activities during the time the house is closed up, and how much it's worth trying to move them to the early morning or evening. Things like showers (especially long hot ones), dishwasher, dryer [1], oven, stove, and toaster. If there was no downside to delaying them then might as well, but it would be useful to figure out whether they're actually worth avoiding.

Taking the toaster as an example, it uses 135W when running, and all of that is turning into heat. If it runs for 10min that's 81kJ. Specific heat of air is about 1kJ per kg per degree C, and air is about 1 kg per m^3. The kitchen is ~12x12x8 which is 32 m^3. So I see:

temperature_rise =
  81kJ *
  (1 kg * delta_C) / kJ *
  (1 m^3 / 1 kg) *
  (1/32 m^3) =
  2.5C =
  4.5F

But this ignores that the structure also holds heat. Which is one of the reasons we want to run the whole-house fan overnight instead of just when it's coolest outside: we're not just trying to replace the warm inside air with cool outside air we're trying to cool the walls and floor.

That calculation was based on a mass of air of 32kg, but compared to the structure of the house that's not that much. The house itself probably weighs 1000x that, with a specific heat a bit higher than air (drywall is ~1, wood is ~2).

But we can't just predict that running the toaster will heat the whole house by 0.0045F because the heat isn't distributed evenly (that's why I used the air in the kitchen instead of the air in the whole house). If the house was perfectly insulated and you left it long enough, then yes, that's the long term effect, but what we really care about is how warm the room gets during the ~14hr when the house is shut up. Which depends on how quickly heat moves between the air and the structure, which depends on constants I don't know and also how much air movement there is.

This does suggest that if you're running the toaster and it's getting hot you should run a fan as well. Not only will the fan cool you off via evaporative cooling it will accelerate the process of transferring the heat from the air to the structure.

(The opposite holds true as well: don't run fans in rooms where there aren't any people, since the fan will accelerate the mixing of the heat from the outside walls and windows into the rest of the building. Plus the fan itself gives off 25-50% of the heat of a toaster and you run it for much longer.)

[1] If you had an in-unit dryer; ours is in the basement so I'm not so worried.