[Urza (OP)]

If 40 gigajoules of heat were emitted from a single point in an instant, what kind of temperature increase would occur in the air 1m, 5m, 10m, 50m, and 100m away? This is not a student's homework, simply hypothetical question from someone who doesn't understand the physics.

[Soul Surfer]

The question does not have an answer because it is not correctly worded.   I will answer the question based on what I think you mean and try to explain what is missing on the way.  

The temperature rise in the air would depend on in what form the energy was released and whether the air absorbed any of the energy.  

When you say heat a presume you mean is infra red radiation, the sort of heat you get from a flame or red hot metal.  This again depends on the frequency of the radiation and how wet the air is.  In general the air does not absorb much of the radiation and so does not warm up much.  

Next you are probably assuming that whatever is absorbing the heat is absorbing all of the radiation from the source that it receives.

The temperature rise depends on how much material is absorbing the heat.  A thin foil will get much hotter than a thick block.  

Finally the temperature rise depends on the thermal capacity of the material  to make things simple let us assume that our test absorber is a thin walled blackened box cube of side 1 cm containing water  i.e 1 cc of water picking up radiation from an area of 1sq cm  this needs about 4.2 joules to raise its temperature 1 degree C  

Let us start with the cube at 100m  i.e.  10,000 cm  the radiation of 40x10^9 joules.  The surface area of a 10^5 radius sphere is 4pi 10^10 so about pi joules per sq. cm so the temperature rise is a bit less than 1 degree c  

For half the distance 50 m this is for times greater  so this is about 3degrees rise.  4pi joules

10 m is 25 times greater at 100 pi joules  so this means that the temperature rise is about 75 degrees  

at 5 metres  the rise would in theory be four times  greater at 400pi joules so some of the water would boil.  It takes about 420 joules to get the water to boiling point and there are around  800 left

To evaporate 1gm of water at its boiling point needs 4.2x540 joules that is around 2200 joules so  about 40% is boiled away  

at 1m there is 25 times more energy it all boils away and some!

This shows the inverse square  law in operation

All these are quick approximate figures to give feeling for what could happen.

[Soul Surfer]

One thing I have forgotten is you say an instant.  If it really is a very brief period the heat absorbed does not have time to travel far and so absorbing surfaces can get very much hotter orders of magnitude hotter for brief impulses.

[Urza (OP)]

Because you're right, my terms were hard to work with, pretend it's a cube 1cm x 1cm x 1cm of a magical material with a heat capacity, temperature, and thermal conductivity that allows it to release 40gigajoules of heat energy into the surrounding air in the space of a second. (the air was 25oC prior to that one second of intense heat)

I was talking about heat as in energy transferred through mostly through conduction and convection. Sure I guess radiation would be there, but assume that for this heating element it would be negligible.

[Bored chemist]

I doubt that's remotely plausible.
To lose that much power from such a small object it would need to be very hot. If  it was that hot, it would radiate a lot of heat.

This
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

lets you calculate how much heat (and light etc) is radiated away.
your 1cm cube has an area of 0.0006 m^2 and is trying to loose 40GW so it's dissipating 6.6 E13 w/m^2
So, if I have got the maths right T^4 is 1.2E21 and so T is about 185000 Kelvin

That's quite hot.

Since the rate of loss by radiation goes up as T^4 but the loss by conduction goes up as (roughly) T the hotter the thing gets, the more important radiation is compared to conduction and convection.

You can also use this
http://en.wikipedia.org/wiki/Wien%27s_displacement_law
to calculate what sort of spectrum of radiation the thing will emit.
The peak turns out to have a wavelength of about 16nm which is well into the extreme UV or soft X ray region of the spectrum.

That sport of radiation is quite strongly absorbed by the air so the energy would be transferred to the surrounding air and would heat it up. That hot air would re radiate the energy  to the next layer of air out and so on.
Eventually the radiation would be long enough wavelengths not to be absorbed by the air. In any event you would get an explosion that would kill you if you were near it. It's roughly 10 tons of TNT equivalent energy.

[Soul Surfer]

The result is an explosion because that is basically what explosives do.  They create a lot of gas (air)at a high temperature and pressure that expands rapidly.  The one second for the energy release is relatively slow like old fashioned gunpowder.   High explosives would do this in microseconds. You would get a violent wind of very hot air that cooled down as it expanded. 

[Geezer]

You would get a violent wind of very hot air that cooled down as it expanded. 

Sounds a lot like what happened to me last night. We had curried chiken.

[Bored chemist]

If you choose to ignore the rules of physics and have the cube made of "magic" then what would happen would be that the air round it would heat up and behave exactly like a cube  made of air.
Since air is not magic the effect would be exactly the same.
The effect would be that the air would be heated to about 100000 K and explode.
Posting the same question elsewhere on this site is a breach of the rules and will not get a different answer. It might get you banned.

[Urza (OP)]

So next question; how long would it take for the air 1m around the cube to cool back down to 25oC?

And btw, I'm sorry that I'm talking about things that probably don't exist, it's a hypothetical. I guess it doesn't matter to me much if it transfers the heat through radiation or not as long as the spectrum doesn't allow the radiation to mostly bypass the air, because the air is what I'm interested in.

But yeah, a lot of what I want to know would be the thermodynamics of this. Would it mushroom or would this not be enough energy for that? How would the air currents affect the temperature at different distances away?

[Urza (OP)]

Also, sorry that the questions I'm asking are flawed, just consider that if I knew the right questions to ask, I probably wouldn't be asking here in the first place, I'd just calculate it on my own.

[Geezer]

Urza,

If you have another question, please start a new topic and ask it there.

Thanks.

G (Moderator)

[Urza (OP)]

Ok, well the Bored Chemist got mad at me for rephrasing this question in another topic, and the rephrasing included the additional question that I asked here so....

TIMELINE!!!

1.) I ask first question in Topic1.

2.) I don't get the kind of answer I'm looking for because of the phrasing of my question and Topic1 dies.

3.) I start Topic2 with a both a rephrasing of my original question + a couple related inqueries in for kicks.

4.) Topic1 is resurrected! Halleluiah! But in now in Topic1 I get reprimanded by Bored Chemist for starting Topic2.

5.) I decide to abandon Topic2 because of Bored Chemist and instead ask all the questions I'm curious about in Topic1.

6.) Geezer gets mad at me.

[Geezer]

Urza,

Geezer is not mad at you, but he will get mad at you if you post any more objections to his moderation in a thread.

Thanks,

G (Not mad moderator)