# Homework Help: How much power to heat up air?

1. Aug 27, 2013

### sromag

Hello,

Technically, this is not homework but I thought it might be more appropriate here as it is a homework type question but it is for practical use. If the moderator thinks it should go somewhere else, then please move it to wherever you think is more appropriate.

I've not found the answer on the internet. Maybe because I'm not asking my search engine the right question but I'm trying to work out how calculate what power would be required to heat up an enclosed space such as an oven up to a temperature of 50 degrees C.

What equations do I need? Can this be done with linear equations?
-I assume the volume to be heated. (How much does the shape of the space being heated matter?)
-Perhaps the humidity of the air (as a %)
-Air density ρ
-Air pressure P.

But then I start getting lost.

The best I found with my search is that it takes about 0.005 watts to heat up a cubic foot of air by 1 degree F.
However I'm not sure if that power increases linearly - i.e. 0.01 watts to increase it by 2 degrees F. 0.015 watts for 3 degrees etc - as it would translate to just 0.25 watts to heat up 1 cubic foot of air by 50 degrees F (not C).

If that's the case, I could work it all out without too many difficulties but I've seen answers to questions posed on the internet before and prefer things to be backed up by several sources before I believe it... especially if I'm going to make practical use of it.

Many thanks and if my question is a bit open ended, please let me know.

2. Aug 27, 2013

### haruspex

That doesn't make dimensional sense. Watts measure power. To heat a given volume of air by a given amount requires energy. It would make sense if you specified a period of time for that level of power.

3. Aug 27, 2013

### sromag

Thanks for the reply.

As for time period, say 10 minutes - 600 seconds.
And as I say, I'm not sure about the 0.005 watts answer. You're right, it seems a little incomplete.

4. Aug 27, 2013

### sromag

And quite coincidentally Haruspex, I'm very much into renewable energy too. :)

5. Aug 27, 2013

### haruspex

According to http://www.engineeringtoolbox.com/spesific-heat-capacity-gases-d_159.html, the constant pressure specific heat for air at 1 atm. is about 1000 J/kgoK. It doesn't say, but I would guess that's dry air. For steam it's nearer 2000, so if you know the absolute humidity you can adjust for that.
I'll leave you to do all the conversions.

6. Aug 27, 2013

### sromag

Thanks for that. I'm away for a couple of days now. I'll take a proper look when I get back. Apt a glance, I didn't notice anything about working out the power in watts, but I'll take a better look when I get back.

Appreciated :)

7. Aug 27, 2013

### haruspex

Just plug in how quickly you want the heating to happen. If it takes j Joules and you want it to happen in t seconds then the power is j/t Watts.

8. Aug 27, 2013

### Chopin

Actually there are two parts to this: the energy required to get the air heated up to the desired temperature, and the energy required to keep it there.

The first can probably be modeled for the most part using the specific heat calculations that have already been described. But once the air is the right temperature, it's going to tend to cool down due to heat being dissipated through the oven walls. In order to compute how much heat is required to keep it at the desired temperature, you'll need to work out how quickly heat is diffusing (which is dependent on the temperature difference between the inside and outside, as well as how good an insulator the walls are). From that, you can work out how much additional energy per unit time is required to keep the oven at the desired temperature.

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