/ Vacuum flasks - the physics of radiated heat loss

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TobyA on 25 Nov 2016
This might be a bit cheeky in the gear forum, but this is definitely an argument linked to gear and its use when climbing in the UK or ice climbing in the Nordic region!

We had a bit of a "discussion" last weekend about vacuum flasks and how they lose heat. A long time ago I got an A at GCSE physics so I hope I'm not totally incompetent on basic physics although I have done no other formal science studies since then. Also party to the discussion were two people with science PhDs (although not physics) one of who is a research scientist and has the white coat and everything and therefore is my go to guy on any question vaguely sciencecy. Finally the fourth party to the discussion is a man who sells many vacuum flasks as part of his business although I think only got to A level in his formal science studies. In other words we might have all been talking crap, but here goes.

Excluding conductive heat loss through the plastic stopper of the thermos flask, and also at the flask's neck where the two sides of the vacuum containing walls join, I presume that radiated heat loss is only way our hot coffee in the flask loses heat?

If this is true, does the temperature outside of the thermos have any effect on the speed of that heat loss via radiation? My feeling is that the answer is no - the two science PhDs reckoned it did, although they didn't explain why in a convincing way (which might show they know more about plant dna than about radiation). The man who sells vacuum flasks stayed reasonably neutral, although possibly slightly more favouring my position, and of course ready to sell us all flasks at reasonable rate should we want to conduct experiments.

I like to think its some vague recollection of GCSE physics that makes me think this, but actually it could be just as much that my 5 euro IKEA flask seemed to keep my coffee as warm when taking it out ice climbing in Finland at -20 as it does now taking my coffee up to Stanage on blowy, but otherwise moderate autumn day where lets say the temperature is 30 degrees warmer than in Finland.

We've got to quantum mechanics before when discussing the why grit friction is better in the cool, so surely this is an easy one for UKC's resident physicists?

maxticate - on 25 Nov 2016
In reply to TobyA:

The reflective layer within thermos flasks prevents loss of heat via radiation. The only heat sink is the tiny amount of conductive losses through the top of the thermos. There surface temperature will have an effect but it'll be down to someone else to calculate the rate of heat loss dependent on the outside temperature.
deepsoup - on 25 Nov 2016
In reply to TobyA:
> If this is true, does the temperature outside of the thermos have any effect on the speed of that heat loss via radiation?

Yes it does. The two walls either side of the vacuum are both radiating heat to the other side - at the same rate if they're at the same temperature, so there's no net transfer of heat from one side to the other. The greater the difference in their temperature, the greater the difference between what one side is radiating and what it's getting back from the other side.

In practice though I think the conductive losses around the stopper and neck are probably much more significant.
Post edited at 10:49
L BlueTotem on 25 Nov 2016
In reply to TobyA:
Yes it makes a difference. The radiation is happening in both directions.

(Edit - deepsoup beat me to it.)
Post edited at 10:50
Hardonicus - on 25 Nov 2016
In reply to maxticate:
Hmm. I would say the liquid heats up the the inner metal wall via conduction. Subsequently the inner wall radiates heat through the vacuum to the outer metal wall.

Now I'm no expert, but radiative heat flux between two bodies in a vacuum is determined by the temperature differential according to wikipedia.

https://en.wikipedia.org/wiki/Heat_transfer#Radiation

I would imagine radiative heat transfer being a minor contributor compared to conductive losses via the stopper however.

(edit beaten by the other two!)
Post edited at 10:52
Nick Harvey - on 25 Nov 2016
In reply to TobyA:
Would the colder outside wall of the flask mean that more of the heat radiation is absorbed by it and thus less is reflected back to the inside wall? Otherwise, I guess you are right, though it feels wrong.

Also, I wonder what percentage of the heat loss is actually from radiation as opposed to conduction through the neck/lid?
galpinos on 25 Nov 2016
In reply to TobyA:

It's not a true vacuum, it's only a "partially excavated vacuum" so there is loss via conduction and convection, not just through the stopper and opening. The radiation is minimised by an internal reflective coating. It is affected by external temperature but not massively.

The maths is in the Thermodynamics section on the wiki:

https://en.wikipedia.org/wiki/Vacuum_flask

planetmarshall on 25 Nov 2016
In reply to galpinos:


Invented by a Scot too, like all the best things.

nniff - on 25 Nov 2016
In reply to TobyA:

I rather thought that the whole point of vacuum flasks was to interupt the primary means by which heat was lost by sticking a vacuum in the way. the priomary means by which heat is lost is via the top and the elements of the flask's inside and outside that are connected. Proportionally, that's a far greater area for a samll flask than it is for a small one. I think......

I have a stainless steel vacuum mug - it's a curious thing becuase you can pour boiling water into it and hold it by the base and sides, which are cold, unlike a normal mug. But the lip heats up (not a lot) and is warmer than the rest of it - the complete opposite of a standard mug.
ultrabumbly on 25 Nov 2016
In reply to TobyA:

As others have mentioned, just as it is emitting thermal radiation outwards it is subject to incidental thermal radiation from its surroundings. However being reflective on both the outer and inner surface the transmission/reflection in both directions will be low. In short there is an effect but not much compared to the stopper and other mechanisms when it is both closed and open.

Some sums here: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html (concise presentation allowing for temp differences).

TobyA on 25 Nov 2016
In reply to ultrabumbly:

Right, thanks everyone. So being colder outside DOES make a difference to radiated heat loss, but it should be a very small loss?

And in reality, flasks lose most of their heat via the cap and where the walls meat at the neck.

Does that sound about right?

Many thanks!
Hardonicus - on 25 Nov 2016
In reply to TobyA:
And of course being colder outside also substantially increases the heat loss by conduction through the cap!
Post edited at 11:34
Luke90 on 25 Nov 2016
In reply to TobyA:

Seems like a fair summary.
ultrabumbly on 25 Nov 2016
In reply to TobyA:
yup. Instead of thinking of it as the flask and "outside" if you instead think of it as two kids spinning round, firing nerf guns indiscriminately with their rate of fire proportional to their absolute temperature. Though the higher temp kid has a greater rate of fire and or bigger bullets the cooler one will still hit him with the odd round. It isn't a case of the warmer kid deciding to fire at the colder kid for shitsngiggles or vice versa they are going to keep firing at everything above absolute zero.
Post edited at 11:40
Nick Harvey - on 25 Nov 2016
In reply to TobyA: And in a massive hijack - guess where James and I are going this winter?! I'm coming out of a fatherhood-induced-retirement!

Andy2 - on 25 Nov 2016
In reply to TobyA:

When you pour out some liquid, it is replaced by air from outside. The remaining liquid and the replacement air then come into thermal equilibrium. If it's cold outside, the remaining liquid in the flask will lose more heat to the replacement air, and so will be colder next time you open the flask.

Probably.
WaterMonkey - on 25 Nov 2016
In reply to TobyA:

Why not do some experiments. Make a flask of coffee, leave on the side in the kitchen for 4 hours and then pour some out and measure the temperature.
Do the same again but leave in a fridge or freezer for 4 hours.

I'd be genuinely interested to see the results.

(Make sure the inside of the flask is the same temperature when you make the coffee though by rinsing with boiling water first each time)
GrahamD - on 25 Nov 2016
In reply to TobyA:

Although heat transfer from one surface to another is a function of absolute temperature difference, it is also a function of emmisivity. Basically shiny surfaces do not emit or absorb very much so there isn't much heat transfer.
Marek - on 25 Nov 2016
In reply to GrahamD:

Indeed. So sadly I got out my trusty fag packet, turned it over and figured out that a pint flask (internal reflective surface of course) of boiling water in freezing temperatures will take about 2 hours to lose 1 degree C just through radiation. So yes, radiation doesn't contribute much to heat loss. OK, it's the end of the week, I was bored (of work) ...
Robert Durran - on 25 Nov 2016
In reply to TobyA:
I think you can make it obvious by considering the situation where the outside temperature is the same as the temperature of your coffee (unrealistic, but no matter). The whole system will be in thermal equilibrium so your coffee will not cool down at all, whereas it will if (realistically) the outside is cooler. In the first situation the coffee gains as much radiated heat from outside as it loses, whereas in the second, it loses more than it gains.
Post edited at 18:04
Jimbo C - on 25 Nov 2016
In reply to TobyA:

As a side query, would the contents of a vacuum flask cool down more slowly if it was kept up-side down?

Assuming the stopper doesn't leak of course.
ultrabumbly on 25 Nov 2016
In reply to Jimbo C:

probably not. There is some element that, for simplicity, you can think of as partial reflection when going from one medium to another. In effect by removing the contents, air, cap interfaces and having only contents to cap transition,you would most probably see greater heat transmission. As the stopper is "more in contact" with the outside world this is where the greatest temperature gradient will be in effect.
MG - on 25 Nov 2016
In reply to TobyA:

As others have said, outside temperature changes will have an effect. Radiation is proportional to absolute temperature to the fourth power, however. So convert you temperatures to kelvin and raise to the four to judge the effect. Conduction and convection are linearly related to temperature difference, so use that for the stopper effect!
TobyA on 25 Nov 2016
In reply to Jimbo C:

I would think no because air at the top would limit conducted heat loss through the non vacuum cap?
AlanLittle - on 25 Nov 2016
In reply to planetmarshall:

> Invented by a Scot too, like all the best things.

Thermodynamics too iirc
captain paranoia - on 25 Nov 2016
In reply to TobyA:

> And in reality, flasks lose most of their heat via the cap and where the walls meat at the neck.

Yes. Especially so for stainless steel flask, since metal is a good thermal conductor (better than glass), so heat travels up the inner wall to the neck, and then down to the outer wall, where it escapes by all three heat transfer mechanisms; conduction, convection and radiation.
davidbeynon on 25 Nov 2016
In reply to AlanLittle:

>Thermodynamics too iirc

Thermodynamics is not one of the "best things". It is the bullet with everythings name on it!

Typical scottish invention!
ultrabumbly on 26 Nov 2016
In reply to davidbeynon:

Lord Kelvin was actually born in Belfast iirc.
springfall2008 - on 26 Nov 2016
In reply to TobyA:

Why don't you test it and see, get two identical flasks and leave one in the freezer all day - test the liquid after 12 hours using a thermometer?

Bottom line, if you could put one flask in a tub of boiling water the contents will never go cold so point proven??

ads.ukclimbing.com
Jim C - on 26 Nov 2016
In reply to WaterMonkey:
If you put it in a freezer the 'hot' ( liquid with more energy) will freeze quicker than. 'Cold' liquid.
( but not sure if that liquid will freeze in a sealed flask)
Post edited at 19:58
TobyA on 26 Nov 2016
In reply to Jim C:

> If you put it in a freezer the 'hot' ( liquid with more energy) will freeze quicker than. 'Cold' liquid.

I've heard this in the past, can you explain why it is meant to be true? I once tried it with two buckets of water, one full of cold water from the tap and one full of steaming hot water from the hot tap. I put them on the back porch on a -20 night and the cold one froze over on the top first so from that it didn't seem true.

We also tried to see if a frying pan in direct sun on 41 degree day in Australia would get hot enough to cook an egg. It didn't which made for a very disappointing youtube video.

Jack B on 26 Nov 2016
In reply to TobyA:

As already been mentioned, there is radiation going both ways across the vacuum gap. The things which change the power transfer are area, temperature and emissivity (aka shinyness). Area and emissivity are the same for both directions, so it all boils down to the temperature difference, and power scales as T^4, so it can make a big difference. So we can wirite:

P=kT^4

where P is power radiated from on side, k is some constant, always the same for that flask, and T is absolute temperature. For convenience, lets define j=k*1 billion. For boiling water at 373K, P=19.36j. For the outside of the flask in a warm room at 300K, P=8.10j. For a freezer at 273K, its 5.55j. So the nett heat flow to a warm room is 11.26j, and to a cold room 13.81j. Finally that means that heat is lost 23% faster to the freezer than the warm room.

Of course, in reality, loss through radiation in the vacuum is probably a lot smaller than conduction through the rim and stopper, and convection through residual gas. So the way they scale will be much more important.
Ron Rees Davies - on 27 Nov 2016
In reply to TobyA:
> If you put it in a freezer the 'hot' ( liquid with more energy) will freeze quicker than. 'Cold' liquid.

> I've heard this in the past, can you explain why it is meant to be true?

It's called the Mpemba effect, and nobody has ever really explained it properly. Combinations of supercooling in really cold water and thermal currents in hot water are postulated.

However according to a report on the BBC this week it has now effectively been discredited by a paper detailing experiments using a wide range of starting parameters (including a replication of Mpemba's original experiment) all failing to show evidence of the effect.
Post edited at 00:30
mbh - on 27 Nov 2016
In reply to TobyA:

Vacuum flasks will lose heat to the outside by three means, conduction, convection and radiation. Let us ignore convection since the gap width between the walls is small, and induction through the plastic cap. That leaves conduction through the walls at the neck, conduction through the residual air in the 'vacuum' space and radiation across that space. If there were no vacuum, but just air at atmospheric pressure, then I find that all three heat loss mechanisms are around 1 W, giving a temperature drop rate of about 2.5 degrees per hour. Does that sound about right? If there were a perfect vacuum then that you would still have a temperature loss rate of 1.5 ish degrees per hour since the radiation loss and conduction loss through the neck will not change. So a real flask would sit somewhere between in this range, and if the vacuum is broken that should result in at worst a doubling of the temperature drop rate.

For the vacuum to make any difference, you need to get the mean free path of the air molecules to be longer than the gap width. Any less than that and the molecules get in each other's way and it doesn't matter how many of them you have. That means that the pressure has to be less than a few hundredths of a millibar, or about 1 Pa, which is one hundred thousand times lower than atmospheric pressure. I don't know if that is achievable in real flasks on the hill.

In working all this out, I used: gap width 5mm, stainless wall thickness 0.5 mm, flask diameter/height 5 cm/20cm, coffee at 80 degrees, outside air at 0 degrees, emissivity of shiny stainless 0.1, 10cm travel length for heat transfer from hot coffee to outside, via the neck, 1 litre coffee, thermal conductivities: air at 1 atmosphere 0.024 W/K m, stainless steel 16 W/K m.
john arran - on 27 Nov 2016
In reply to mbh:

> In working all this out, I used: gap width 5mm, stainless wall thickness 0.5 mm, flask diameter/height 5 cm/20cm, coffee at 80 degrees, outside air at 0 degrees, emissivity of shiny stainless 0.1, 10cm travel length for heat transfer from hot coffee to outside, via the neck, 1 litre coffee, thermal conductivities: air at 1 atmosphere 0.024 W/K m, stainless steel 16 W/K m.

Brazilian or Colombian blend?
mbh - on 27 Nov 2016
In reply to john arran:

Don't mind, but no milk please, or soup.
springfall2008 - on 27 Nov 2016
In reply to mbh:

Surely the rate of heat loss depends on the outside temperate, as the liquid inside will never get colder than the outside?
mbh - on 27 Nov 2016
In reply to springfall2008:

Yes, you are right. The rate of temperature decrease will drop as the coffee cools, and it won't ever get colder than outside. But, long before that, it will cool to the point where you wouldn't want to drink it. I am just exploring the drinkable zone on a cold hill, where the temperature difference might be as much as 80 degrees or so.
Alasdair Fulton - on 27 Nov 2016
In reply to TobyA:

All this chat of freezing water reminded me of a silly video I recorded last week:

http://www.youtube.com/watch?v=57X5LGmU5Xo
Jim C - on 27 Nov 2016
In reply to Ron Rees Davies:
Interesting that this has has come out this week considering it was first proposed in 1963 , Do you have a link handy ?
( if not I will have a search)

There are some interesting videos of very hot water being thrown into freezing air and apparently vaporising , but I don't know if that is related?

I had read the Mpemba effect explanations, and they did sound reasonably convincing, but not having done the experiments myself, we rely on others to refute it by controlled experimentation. 50 decades does seem a long time to refute it !
Post edited at 19:38
Ron Rees Davies - on 27 Nov 2016
In reply to Jim C:

> Interesting that this has has come out this week considering it was first proposed in 1963 , Do you have a link handy ?

No - I did look for it online and couldn't find any reference. I think it was on the PM program on ?Tuesday or Thursday that BBC Radio4 had the guy on discussing it, not an actual news item. Maybe it's not actually published yet but he definitely discussed a pretty conclusive peer reviewed scientific publication not just anecdotal tests.
Hyphin - on 27 Nov 2016
In reply to TobyA:

Surely the biggest problem with vacuum flasks is after the first cup, the vacuum becomes a bit irrelevant. The liquid removed is replaced by freezing cold air, the remaining liquid then uses up all its energy to heat up that air. Solution, don't open it till you're in a warm environment.
Jim C - on 27 Nov 2016
In reply to Ron Rees Davies:
> No - I did look for it online and couldn't find any reference. I think it was on the PM program on ?Tuesday or Thursday that BBC Radio4 had the guy on discussing it, not an actual news item. Maybe it's not actually published yet but he definitely discussed a pretty conclusive peer reviewed scientific publication not just anecdotal tests.

If you can narrow down the day you might be able to scratch that itch, I know that these things drive me mad.
http://www.bbc.co.uk/programmes/b006qskw/episodes/guide

PM Tues 24th Nov at 53:30 in
Thanks Ron

(Currently watching the series Chemistry a volatile history, but alas as yet no explanation of Mpemba effect, but lots of good stuff in it. )


Post edited at 20:42
Luke90 on 27 Nov 2016
In reply to Hyphin:

Certainly true but air's specific heat capacity is several times lower than water's so, assuming a 50/50 air/water split, the air heats up more than the water cools down.
Jim C - on 27 Nov 2016
In reply to Ron Rees Davies:

> No - I did look for it online and couldn't find any reference. I think it was on the PM program on ?Tuesday or Thursday that BBC Radio4 had the guy on discussing it, not an actual news item. Maybe it's not actually published yet but he definitely discussed a pretty conclusive peer reviewed scientific publication not just anecdotal tests.

http://www.nature.com/articles/srep37665
andrew ogilvie - on 27 Nov 2016
In reply to Jim C:

This is the famous mpemba effect which was discussed by a research physicist on radio 4 this week , he could find no evidence for it whatsoever. Published in peer reviewed journal last week
Marek - on 27 Nov 2016
In reply to andrew ogilvie:

> This is the famous mpemba effect which was discussed by a research physicist on radio 4 this week , he could find no evidence for it whatsoever. Published in peer reviewed journal last week

I have no idea about this particular case, but bear in mind that 'peer reviewed' means absolutely nothing if you don't state which journal. There's a rich history of dubious research published in obscure journals with inappropriate 'peers'.
wintertree - on 27 Nov 2016
In reply to Luke90:

> Certainly true but air's specific heat capacity is several times lower than water's so, assuming a 50/50 air/water split, the air heats up more than the water cools down.

The mass specific heat capacity of air is ~ 0.25 that of water.

However the density of air is ~0.001 that of water, so the volume specific heat capacity of air is ~ 0.00025 that of water. The air trapped in the flask would make naff all difference even it it was as cold as physically possible.

On the other hand, open the lid and allow the air to convect and it's another story.
Robert Durran - on 27 Nov 2016
In reply to Luke90:
> Certainly true but air's specific heat capacity is several times lower than water's so, assuming a 50/50 air/water split, the air heats up more than the water cools down.

A 50/50 split by mass would mean the flask is all but empty. For a 50/50 split by volume (more relevant), the water would hardly, presumably, cool down at all.

Edit: See Wintertree beat me to it!
Post edited at 23:17
Ron Rees Davies - on 27 Nov 2016
In reply to Marek:

> I have no idea about this particular case, but bear in mind that 'peer reviewed' means absolutely nothing if you don't state which journal. There's a rich history of dubious research published in obscure journals with inappropriate 'peers'.

See the post above the one you replied to. The paper is published in 'Nature'.

Marek - on 28 Nov 2016
In reply to Ron Rees Davies:

> See the post above the one you replied to. The paper is published in 'Nature'.

Indeed. Note to self: read more the thread before posting.
Luke90 on 28 Nov 2016
In reply to wintertree:

Thanks for the correction/addition. I could try to argue that, technically, nothing I said was outright incorrect but I had in all honesty completely forgotten to take into account the disparity in mass. Idiotic of me.
captain paranoia - on 28 Nov 2016
In reply to Jim C:

> 50 decades does seem a long time to refute it !

I think Mpemba would have been burnt as a witch for suggesting it 500 years ago...

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