# How much power does it take to heat up air?

#### 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.

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#### haruspex

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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.
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.

#### sromag

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.

#### sromag

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

#### haruspex

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Gold Member
2018 Award
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.

#### 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 :)

#### haruspex

Homework Helper
Gold Member
2018 Award
I didn't notice anything about working out the power in watts
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.

#### 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.

#### khrizthian

Hello good people of PF I am also in need of an answer to the poster's question. I am currently designing an oven with carbon fiber threaded heat tubes and I have to heat it to 240C and want to know how many watts are necessary. The total CBM is about 77. 6cbm. Any ideas on how to calculate the past link is dead so I could not find out much from it. Thanks in advance.

#### Chestermiller

Mentor
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.
That's the heat capacity at constant pressure. For a constant volume oven, it is more like 720 J/kg K.

Also, the thermal inertia of the oven metal needs to be considered. It is not only the air that is being heated.

#### khrizthian

Hey Chester thanks so much for your response. I am still lost as to how I would be able to calculate this. I am in diré need of this info since I am building this oven in the next few days. An equation would be great and any info needed I can provide. A big big beer or coffee would be given as well so you don't think you lose time helping me out. Thanks

My oven is a curing oven for a paint factory that I have. It consists of a rolling chain and the products would be transported inside for a certain amount of time 30min to 42min..

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#### Chestermiller

Mentor
If you include the mass and heat capacity of the oven in the calculation, then the amount of energy you need to add is $$Q=(m_oC_o+m_aC_a)\Delta T$$ where m is mass and C is heat capacity. This neglect heat losses to the room during the heating time.

#### khrizthian

If you include the mass and heat capacity of the oven in the calculation, then the amount of energy you need to add is $$Q=(m_oC_o+m_aC_a)\Delta T$$ where m is mass and C is heat capacity. This neglect heat losses to the room during the heating time.
Hey Chester thanks a lot but for Delta I am not sure what to write and the mass you mean the area inside the oven with the heat capacity being the difference between the outer temperature and the temperature inside the oven I need??

#### ZapperZ

Staff Emeritus
2018 Award
Hey Chester thanks a lot but for Delta I am not sure what to write and the mass you mean the area inside the oven with the heat capacity being the difference between the outer temperature and the temperature inside the oven I need??
This is what happens when you neglect to clearly reveal what you know and what you don't know. Most of us, when we look at your question, assumes that you know how to calculate heat using a substance's heat capacity (this is covered in first year General Physics courses). It appears that you don't, and this should have been something you inform us way in the beginning.

So, let's start from the beginning. Do you know what this equation below means, and if you do, do you know how to use it?

Q = mcΔT

Without properly establishing that, there is no way one can tackle your question.

Zz.

#### khrizthian

This is what happens when you neglect to clearly reveal what you know and what you don't know. Most of us, when we look at your question, assumes that you know how to calculate heat using a substance's heat capacity (this is covered in first year General Physics courses). It appears that you don't, and this should have been something you inform us way in the beginning.

So, let's start from the beginning. Do you know what this equation below means, and if you do, do you know how to use it?

Q = mcΔT

Without properly establishing that, there is no way one can tackle your question.

Zz.
Hey zz how are you thanks a lot for the time you took to take a look at my question. Yes, indeed I am not very knowledgeable when it comes to physics. I know this equation is the heat transfer equation and this is heat in joules mass obviously and the change in temp I assume. Other than that I have not used this in any practical scenario this would be my first time..... Be gentle... I thought there was just a simple heat area power equation. I guess I was wrong. Thanks for looking at the question tho! I feel lucky you guys are helping me out.

#### khrizthian

Hello guys any help? I am in diré need of this info. Any help would be greatly rewarded and appreciated. Please it's urgent. Can pm if necessary as well. Thanks a lot.

#### russ_watters

Mentor
Hello good people of PF I am also in need of an answer to the poster's question. I am currently designing an oven with carbon fiber threaded heat tubes and I have to heat it to 240C and want to know how many watts are necessary. The total CBM is about 77. 6cbm. Any ideas on how to calculate the past link is dead so I could not find out much from it. Thanks in advance.
This question is totally different from the OP's question and I disagree with the main answer given so far*. This is entirely an insulation problem because time to heat up an oven is generally not a significant issue; power to keep the temperature is what matters. So tell us how well insulated it is.

#### khrizthian

Hey guys we figured out an easy way to calculate the oven with a really simple equation. It's more than 300m rolling chain and using 550W tubes. Thanks anyways!

"How much power does it take to heat up air?"

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