## Very hot coffee ?

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Moose57
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### Very hot coffee ?

I have a temperature changing mug, which shows the ideal temperature for tea. However it also shows the temperature of the surface of the sun. If it was possible to have a cup of coffee (or tea) at 5,800K at sea level in an ambient of 20K how far away from me would it need to be in order for me not to burn my lips ?

Any replies appreciated.

Regards,

Moose

gmalivuk
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### Re: Very hot coffee ?

I assume you mean 20ºC ambient (293K), as your lip would be pretty uncomfortable at 20K regardless of the temperature of your tea.

I'm also not sure what you're asking. Are you drinking this tea through a long straw so it gets a chance to cool down on its way to you?
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DaBigCheez
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### Re: Very hot coffee ?

20K is a very cold ambient for sea level...

There's a few assumptions that would need to be made. How is the temperature of the coffee cup maintained - does it magically stay at 5800K indefinitely, or does the coffee start at 5800K and gradually cool, giving off its energy to its surroundings? Can we assume a standard air atmosphere at STP? If so, is the air perfectly motionless, or is there a breeze/convection from the hot cup? Is the cup sitting on something (which would potentially melt), or floating in midair?

My first thought is to ignore all the conduction/convection/heating of the air and just look at pure blackbody radiation, inverse-square laws and all that, but I don't have a good sense for the intensity of infrared radiation that would result in lip burns. Alternately, if the cup gradually gives up its energy, you could look at what volume of air it'd be able to heat up to what temperature, assume a hemisphere of air, and use that to get your safe distance. If the cup's magically held at 5800K, then I'd assume it'd just heat up the entire atmosphere over time, which would presumably steady-state at some point to radiative losses if we're not willing to take the atmosphere as a closed system that'd eventually turn into a planetwise conflagration due to the unbounded addition of energy...

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LaserGuy
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### Re: Very hot coffee ?

Well, at 5800K, the problem is that you aren't talking about coffee any more, nor are you talking about a coffee cup. Even if your cup was made of tungsten, it would be in gaseous form, as would, of course, the coffee. But at 5800K, the water in your coffee isn't water any more either, it's H+ and OH- radicals. So things get a bit weird.

Here's a really simple approach that might at least give a very vague order of magnitude estimate. A cup of coffee is 150 mL. If we assume it's basically water, then that's 150g. How much energy is required to heat it to 5800 from boiling (~374K to 5800K)? Turning it all to gas requires 339kJ of energy. Heating it up to temperature requires another 1600 kJ of energy, plus we need another 4100 kJ to break the chemical bonds as we go. So in total, we're looking at ~6000 kJ of energy. Which is about the equivalent of 1 kg of TNT. Safe distance from a 2 kg of TNT explosion is about 350 m, so if we're okay with the coffee being a bit warm/hot, then the safe distance in our case is probably of order 100m, I would guess.

Tub
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### Re: Very hot coffee ?

Well, if you picked a regular cup of coffee and instantly heated it to 5800K, then the sudden rise of pressure would be pretty explosive, and the comparison to the stick of dynamite might be valid.

But if you just have a 5800K cloud of coffee at air pressure, and you put it on a table, then you need a big table, but it's not going to be as dangerous. Most of it will just rise up and eventually cool off in the atmosphere. You could get quite close without convection affecting you (unless there's a sudden gust of wind), so we're back to calculating blackbody radiation as the dominating danger; and you only need to withstand the radiation for a short time before the cloud out of range. Results depend on the size of the coffee cloud at air pressure, on the rate of ascend of the cloud and of course your lip's color and reflectiveness.

Moose57
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### Re: Very hot coffee ?

Thank you very much for your replies.

I apologise for my mistake. Of course I meant an ambient temperature of 20 deg C (293K).

I also assumed that we are in normal sea level atmospheric conditions, with no wind. The "cup of coffee" would more realistically be a body (suspended in mid air) that could withstand a temperature of 5,800K, and maintain it for a minute or so. Then the question simply boils down to the distance away to avoid being burnt by the radiated heat.

gmalivuk
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### Re: Very hot coffee ?

This document says burning due to radiant heat can happen after 10 seconds of 3500W/m^2, so you'd need the area of a sphere at your distance to be about 570m^2 to avoid burns in that amount of time, or a radius of about 6.75 meters.
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Moose57
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### Re: Very hot coffee ?

Thank you very much for the information, Greg. I shall not be trying this experiment at home - even if it was possible to do so.

Regards,

Bruce

Eebster the Great
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### Re: Very hot coffee ?

But the air is going to conduct heat too. How does the conducted heat compare to the radiated heat?

gmalivuk
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### Re: Very hot coffee ?

I suspect the main thing the air is going to do is expand rapidly. If it could somehow be held in place but otherwise had all its normal properties, it probably wouldn't add much to the heat being transferred to your skin on account of being a poor conductor of heat when it isn't moving.

Adding realistic details to the scenario gets complicated, because one of the realistic thermal properties of air is the fact that it turns into plasma just like everything else at sufficient temperatures.
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morriswalters
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### Re: Very hot coffee ?

Like arc welders. The arc temperature can get near that temperature. UV coming off the arc can burn your skin(similar to a sunburn) at real world distances. Carbon arc lights are hotter.