How Does a Thermos Bottle Work?

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bob012345
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Summary:

How does a Thermos bottle with a vacuum gap overcome the Stephan Boltzmann radiative law?
Given a standard thermos bottle containing a hot liquid, it is easy to see how the vacuum layer stops heat flow by conduction but what about heat radiating by the Stephan Boltzmann law? How does it mitigate that or is that a minor component of the overall heat loss? Is there a special surface coating that reflects heat radiation back inside the bottle? Thanks.

This question came up in a discussion of what would happen if someone removed their helmet in space. It was claimed that vacuum is a great insulator and would not conduct heat away (true for conduction) thus they would not lose heat very fast but I think the heat from ones head would radiate away by the Stephan Boltzmann law quicker than the heat flow from inside ones brain could replace it and the poor astronaut would quickly get frostbitten (among other problems).
 
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Vanadium 50
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You might work out the amount of heat lost to radiation by a thermos.
 
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russ_watters
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Given a standard thermos bottle containing a hot liquid, it is easy to see how the vacuum layer stops heat flow by conduction but what about heat radiating by the Stephan Boltzmann law? How does it mitigate that or is that a minor component of the overall heat loss? Is there a special surface coating that reflects heat radiation back inside the bottle? Thanks.
As you say, vacuum doesn't inhibit radiative heat transfer; reflective coatings do.
 
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bob012345
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As you say, vacuum doesn't inhibit radiative heat transfer; reflective coatings do.
Probably put on the outside of the inner glass bottle.
 
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russ_watters
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Probably put on the outside of the inner glass bottle.
I've never broken one open, but would think both.
 
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bob012345
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You might work out the amount of heat lost to radiation by a thermos.

Assuming only radiative heat loss, if a thermos contained 1 liter of water at 100C it would have a heat content of 4.128 x 10^5 Joules. Assuming an emissivity of 1, assuming a 10cm diameter by 20cm tall thermos, the surface of area 0.125 m^2 would radiate at 1x 5.67X10^-8 X (373)^4 = 1097.5 Watts/m^2 initially or a total of about 138 Watts. But given that it would stop when it got to room temp of 25C and that the total available energy that could radiate away is about 3.096X 10^5 Joules, the minimum time is 2243 seconds or about 37 minutes but it will be longer so I guess about 2-3 hours to get to within a degree of room temp. It demands integration of the Stephan Boltzmann law over the temperature as a function of time which I don't have.

I'm struggling right now with how to integrate the Stephan Boltzmann law for power to get the total heat loss assuming only radiative losses but the answer would have to end up being 'all of it'.

I once read a physicist say we have materials to keep a cup of coffee hot for 10,000 years although I wouldn't want to drink it especially if it was creamed.
 
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Vanadium 50
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assuming a 10cm diameter by 20cm tall thermos, the surface of area 0.125 m^2
1. Check your arithmetic & geometry
2. The net energy change is the energy radiated minus the energy absorbed.
3. I get a number closer to 800 hours - much longer than a real thermos is good for - even with an emissivity of 1.
4. "I once read" is not a suitable PF reference.
 
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jbriggs444
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This article states that humans can normally radiate around 1000 watts:
1000 watts sounds high. The figure I recall is more like 60 watts.

I suppose we can back into it by taking a 2000 calorie diet and dividing by 24 hours.

2 million gram calories times 4.2 Joules per calorie divided by 86400 seconds = 97 watts.

Edit: On further reading, the article is consistent with this:
the article said:
continuously radiates approximately 1000 watts. If people are indoors, surrounded by surfaces at 296 K, they receive back about 900 watts from the wall, ceiling, and other surroundings, so the net loss is only about 100 watts.
 
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bob012345
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1000 watts sounds high. The figure I recall is more like 60 watts.

I suppose we can back into it by taking a 2000 calorie diet and dividing by 24 hours.

2 million gram calories times 4.2 Joules per calorie divided by 86400 seconds = 97 watts.

Edit: On further reading, the article is consistent with this:
60 Watts is close to my thermodynamics professors claim that engineers figure 200 BTU's per person when designing public spaces such as arena's and stadiums ect. Of course, there's always a 'hothead' in any crowd.
 
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bob012345
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1. Check your arithmetic & geometry
2. The net energy change is the energy radiated minus the energy absorbed.
3. I get a number closer to 800 hours - much longer than a real thermos is good for - even with an emissivity of 1.
4. "I once read" is not a suitable PF reference.
1. Thanks. I was off by 2 in area.
2. It absorbs at a constant rate from a constant background which I accounted for.
3. Did you integrate or estimate?
4. How are you getting 800 hours?
 
  • #13
hutchphd
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2. It absorbs at a constant rate from a constant background which I accounted for.
3. Did you integrate or estimate?
4. How are you getting 800 hours?
The room radiates back at 273K so the process asymptotically approaches zero net radiation from the Dewar (thermos). You will never get to equilibrium. Specify a cutoff if your answer is to make sense.....
 
  • #14
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800 hours assumes a constant heat loss. Given that a real thermos is good for 12-24 hours, it doesn't matter if the radiation number is 80, 800 or 8000 hours, so there is no point in improving the calculation. We have our answer.
 
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  • #15
hutchphd
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Actually I somehow missed the original astronaut question!
Did someone mention that the method used to cool the EVA suits is the spontaneous evaporation of cooling water through a semi-porous membrane into space. It is this mechanism that would cause the rapid freezing (or freeze-drying perhaps) of the unlucky astronaut's head anyway...
 
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  • #16
sophiecentaur
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I've never broken one open, but would think both.
I think the silvering is pretty fragile so only the area between the skins would have the metabolised layer. Also, the vacuum environment keeps he metalising from getting oxidised. When a vacuum flask breaks, in real life, you are more concerned where the hot coffee has gone than what's on the inner and outer surfaces. I must remember to look, next time.
But these days, domestic flasks are steel and not glass. They are much tougher and work 'well enough'. Better than you'd expect. Good enough for storing and delivering liquid N2.
 
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hutchphd
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Pretty clearly the neck of the stainless flask is the culprit. The conductivity of steel is typically twenty times that of glass and the circumference of the neck looks bigger too.
On a lab Dewar the neck aperture is relatively small so probably not an issue. Is there any robust way to put a thermal "break" in the neck?
 
  • #19
bob012345
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Pretty clearly the neck of the stainless flask is the culprit. The conductivity of steel is typically twenty times that of glass and the circumference of the neck looks bigger too.
On a lab Dewar the neck aperture is relatively small so probably not an issue. Is there any robust way to put a thermal "break" in the neck?
The could but their marketing probably tells them it's not worth it. This is the 'wide mouth' version which is preferable for coffee and soup. They make a 'standard mouth' version also which has a smaller top.
 
  • #20
hutchphd
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Is there a good (and not prohibitively expensive) way to do it? Just wondering. The vacuum part for each seems roughly equivalent as one would expect.
 
  • #21
bob012345
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Is there a good (and not prohibitively expensive) way to do it? Just wondering. The vacuum part for each seems roughly equivalent as one would expect.
Maybe they are using an entirely plastic lid. Perhaps a smaller pancake shaped vacuum volume inside the lid would work. Or just a better insulator than plastic.
 
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This question came up in a discussion of what would happen if someone removed their helmet in space. It was claimed that vacuum is a great insulator and would not conduct heat away (true for conduction) thus they would not lose heat very fast but I think the heat from ones head would radiate away by the Stephan Boltzmann law quicker than the heat flow from inside ones brain could replace it and the poor astronaut would quickly get frostbitten (among other problems).
A human in space will boil away any surface liquid in moments, and boil away the rest over a short time. It will cool at a rate considerably faster than 1 kw a first, and eventually slow to equilibrium. This is cooling by convection of sorts and also by phase change. There must be a technical term for the latter, but I don't know it.
 
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I found some experiments done by retired physics teacher Rick Sorensen, with an older glass thermos and a newer metal flask here; Enjoy!

https://www.vernier.com/2020/03/10/the-thermodynamics-of-vacuum-insulated-bottles-an-investigation/
I wonder if he was comparing the 1980s thermos to a modern thermos that happens to be poorly made.

For a while I was brewing coffee in a Nissan stainless steel vacuum bottle and the temperature decline over half an hour was was about 3°C, on par with his vintage thermos. And that was with the lid slightly ajar.
 
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  • #25
hutchphd
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There must be a technical term for the latter, but I don't know it.
This is known as a "sublimation cooler" because the final external interface to cold vacuum is a perforated plate with holes plugged with ice except as applied lets water transpire.
 
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