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  #1  
Old 10-23-2006, 05:11 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
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Wind chill below 0 Kelvin hypothetically possible?

In this post, Asimovian makes reference to a Futurama joke about the temperature, with wind chill, being below absolute zero.

At first, I laughed, because it's silly to consider a temperature below absolute zero, but when I thought about it a little bit, I thought it might be theoretically possible.

As I understand it, wind chill is a (somewhat fuzzy) factor that gets added in to more accurately determine how quickly a warm body will lose heat to the surrounding environment when that surrounding environment is a moving fluid. And the rate at which heat will flow is directly proportional to the temperature differential, modified by the insulation properties of the barrier between, right? So might it make sense for wind chill to actually be below absolute zero?

I don't really know how to do the calculation, but assuming either (a) a rapidly flowing supercooled liquid or (b) an even more rapidly flowing very cold gaseous atmosphere, is it possible, or would the heat energy present in such a quickly moving fluid always keep the "wind chill modified" temperature above 0 K?
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  #2  
Old 10-23-2006, 06:13 PM
Quartz Quartz is offline
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At that sort of temperature, wouldn't the wind actually warm the object through friction?
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  #3  
Old 10-23-2006, 06:18 PM
garygnu garygnu is offline
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Quote:
Originally Posted by Quartz
At that sort of temperature, wouldn't the wind actually warm the object through friction?
Yup. Or, at those low levels of temperature, the percieved lowering of temperature would be a percentage. There are a variety of ways to say no this question, but it makes a good nerd joke.
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  #4  
Old 10-23-2006, 06:22 PM
Taran Taran is offline
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I'm guessing not. By the second law of thermodynamics, you can't move the fluid without heating it, and the heat gain from the fluid movement probably offsets whatever the wind chill would do. That's my intuition, anyway. But how do we prove it?

I found a theoretically-dubious calculation that we can use to calculate wind chill. Converting from Celsius to Kelvins in the equation, we get:

0.045(10.45 + 5.27 square root(V) - 0.28V)(T - 306.15) + 33

...which is as far as I can get. I'm not sure what the theoretical maximum efficiency of a supercooled-fluid-mover is, so I can't calculate the other half. We could solve for it, given reasonable values for fluid volume and density.

On preview: oh, right, friction. That wouldn't help.
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  #5  
Old 10-23-2006, 06:37 PM
David Simmons David Simmons is offline
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Even if the wind were blowing 100 mph and with a temperature of 0 K I don't think you can make the energy of the particles in any object lower than the energy they have at 0 K.
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  #6  
Old 10-23-2006, 07:10 PM
snailboy snailboy is offline
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Quote:
Originally Posted by Quartz
At that sort of temperature, wouldn't the wind actually warm the object through friction?
But the object (usually a person) wouldn't be at that sort of temperature. I mean if we were cold-blooded and our bodies dropped to 40 degrees in 40 degree air, what would it matter if the wind was blowing? On the other hand, I could perceive flowing 5K liquid nitrogen pulling heat from our 98.6 degree bodies faster than a stationary liquid at 0K. (But no liquids exist at 0K, right? We'll ignore that fact though, if possible.)
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  #7  
Old 10-23-2006, 07:35 PM
spingears spingears is offline
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Quote:
Originally Posted by iamthewalrus(:3=
I don't really know
If you are thinking hypotheticaly if at all any thing can be considered possible, impossible or not at all except if you are in a black hole or passed thru a worm hole or one of another kind or two.

Since the whole problem is in a universe of absolute zero K or R there is NO Motion of any kind. Hence No Wind Chill & No Wind Chill
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  #8  
Old 10-23-2006, 07:45 PM
Napier Napier is offline
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I think it certainly could. I think wind chill estimates what temperature would feel as cold with no wind speed, as does whatever weather you're having. This means, causing the same heat flux at the skin's surface.

A heat transfer coefficient of 50 W/(m^2 K) is certainly possible with a brisk breeze, and if you were in the arctic at -70 C, this would be 5000 W/m^2. With a heat transfer coefficient of 5 in still air, you'd have to have a temperature differential of 1000 to get this flux, which suggests a static temperature of -770 C or almost -500 K (that is, 500 Celsius degrees lower than absolute zero).

It's a whole separate debate whether wind chill is a very useful concept. I think it's a bit daffy - it's rare to sense very cold air with no breeze, and you'd then be surprised to hear how cold it really was.
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  #9  
Old 10-23-2006, 07:45 PM
spingears spingears is offline
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Quote:
Originally Posted by iamthewalrus(:3=
Futurama joke about the temperature, with wind chill, being below absolute zero.
It's a joke kid, just a joke.
In a universe or enviornment of absolute zero K or R there is NO WIND and therefore there is NO WIND CHILL. :-)
If anything in that universe is at zero K or R everything is at the same temperature else the temperature is a bit shy of a full deck... er absolute zero but headed in that direction.
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  #10  
Old 10-23-2006, 07:56 PM
t-bonham@scc.net t-bonham@scc.net is offline
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Quote:
Originally Posted by iamthewalrus(:3=As I understand it, [i
wind chill[/i] is a (somewhat fuzzy) factor that gets added in to more accurately determine how quickly a warm body will lose heat to the surrounding environment when that surrounding environment is a moving fluid.
I think your understanding is a little off.

Wind chill is the apparent temperature felt by exposed human skin. It is lower than the actual air temp, because the wind velocity increases the speed with which sweat evaporates from the human skin, thus hastening up the heat transfer, so it is perceived by the human as colder.

Hardly any of this applies near absolute zero.
- There wouldn't be exposed human skin, not living human skin.
- It wouldn't be sweating at that temp.
- There wouldn't be any wind, the gasses in the air would have frozen into solids.
- And since wind chill is 'apparent' and 'perceived', it wouldn't apply; the human who would have perceived it would be dead at those temps.

You're trying to apply rules outside the range they are defined for. Rather like trying to explain atomic level physics with Newtonian laws -- you can't; while Newtonian physics laws work fine in the 'normal' human world, at certain limits you need Einsteinian rules.

Like that, wind chill is an effect that only has meaning in a specific range of temps, roughly from human body temp down to the limit of human habitable temps. (So about 98F/37C down to -80F/-63C.) As it gets very cold, the difference between actual temp and wind chill temp decreases. Basically, once it's extremely cold, the heat is removed from exposed human skin so fast that wind velocity hardly matters. (Growing up in Minnesota winters, wind chill is something we all understand!)
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  #11  
Old 10-23-2006, 09:30 PM
David Simmons David Simmons is offline
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Quote:
Originally Posted by spingears
Since the whole problem is in a universe of absolute zero K or R there is NO Motion of any kind. Hence No Wind Chill & No Wind Chill
Er, ah, if there is not motion then the velocity of the particles is zero and we can determine their position and doesn't this violate the ucertainty principle?

I read somewhere that there is a small residual energy in the particles but the available energy is zero.
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  #12  
Old 10-23-2006, 09:42 PM
scr4 scr4 is offline
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I'd say the answer is yes. "Wind chill" measures how fast an object at 36C (body temperature) loses heat. A flow of 0K air would remove heat more efficiently than a stagnant 0K air (forced convection vs. natural convection).
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  #13  
Old 10-23-2006, 10:01 PM
robby robby is offline
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Quote:
Originally Posted by snailboy
...On the other hand, I could perceive flowing 5K liquid nitrogen pulling heat from our 98.6 degree bodies faster than a stationary liquid at 0K. (But no liquids exist at 0K, right? We'll ignore that fact though, if possible.)
Actually, nitrogen freezes solid at 63 K.

Helium is the only substance still liquid at ~0 K. (It will freeze if you increase the pressure, though.)

Quote:
Originally Posted by scr4
I'd say the answer is yes. "Wind chill" measures how fast an object at 36C (body temperature) loses heat. A flow of 0K air would remove heat more efficiently than a stagnant 0K air (forced convection vs. natural convection).
As has been noted above, any "air" present would not be in gas form, so it wouldn't be flowing at all. It would be solid, unless you are talking about pure helium, which would be liquid.

And "wind chill" would seem to be a poor expression to use in such a circumstance, there not actually being any wind to speak of.
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  #14  
Old 10-23-2006, 10:20 PM
David Simmons David Simmons is offline
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Originally Posted by robby
And "wind chill" would seem to be a poor expression to use in such a circumstance, there not actually being any wind to speak of.
True, but hypothetically even if there were wind you still can't remove energy from particles that are already at their lowest possible energy.
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  #15  
Old 10-23-2006, 10:59 PM
Taran Taran is offline
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But we wouldn't be removing energy from the liquid helium (thank you robby), we'd be removing energy from the exposed body faster. Mind you, I still doubt that it would work...
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  #16  
Old 10-23-2006, 11:27 PM
scr4 scr4 is offline
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Originally Posted by robby
As has been noted above, any "air" present would not be in gas form, so it wouldn't be flowing at all. It would be solid...
Well, it could still move, rubbing against the object in question....
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  #17  
Old 10-24-2006, 09:03 AM
Harmonious Discord Harmonious Discord is offline
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You can't have a wind because as was stated a wind is moving gas. All gases solidify before absolute zero is reached. You can't have a wind chill effect after all gases solidify.
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  #18  
Old 10-24-2006, 09:22 AM
David Simmons David Simmons is offline
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Originally Posted by Taran
But we wouldn't be removing energy from the liquid helium (thank you robby), we'd be removing energy from the exposed body faster. Mind you, I still doubt that it would work...
Suppose the warm body were at 2 K. The wind chill would exist but I don't believe it could be more than 2K. That is, the warm body can't be cooled by more than from 2 K down to 0 K.
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  #19  
Old 10-24-2006, 09:46 AM
robby robby is offline
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Quote:
Originally Posted by Harmonious Discord
You can't have a wind because as was stated a wind is moving gas. All gases solidify before absolute zero is reached...
Helium is a liquid at ~0 K and 1 atm pressure, not a solid.

And it would seem logical that flowing liquid helium at ~0 K would remove heat faster from a warmer object than stationary liquid helium at ~0 K. This effect might be described as being analogous to "wind chill."

David Simmons, when you talk about "wind chill," you are describing a situation where you are at body temperature, and a 30 deg F wind (for instance) is perceived by you as removing heat from you as fast as, for example at 10 deg F stationary air mass. This does not mean that the person's temperature is 30 deg F or 10 deg F. Similarly, our object experiencing "superfluid chill" from flowing liquid helium is not (initially, at least) anywhere near absolute zero. It is much warmer. What we are trying to describe here is how fast the object will cool down.

By the way, some people in this thread seem to think that you can actually achieve at temperature of absolute zero. You can't. The approach to absolute zero is asymptotic. One way to think of this is to realize that it takes as much effort to get from 100 K to 50 K, as it does to get from 10 K to 5 K, as it takes to get from 2 K to 1 K, as it takes to get from 0.0002 K to 0.0001 K, and so on. I think the record low temperature reached is in the nanokelvin range, but absolute zero itself cannot be reached. That's why I've been writing ~0 K (i.e. approximately zero kelvins).
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  #20  
Old 10-24-2006, 09:54 AM
scr4 scr4 is offline
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Actually I'm still not convinced. One could extrapolate and calculate how fast "air" at 0K would remove heat from a 300K object, if air were a gas at that temperature. One could then ask whether 78K air flowing very fast would remove heat faster than that rate. If the answer is yes, you've got a sub-0K wind chill. I haven't done the math but I suspect the answer is yes.
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  #21  
Old 10-24-2006, 09:56 AM
robby robby is offline
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Quote:
Originally Posted by t-bonham@scc.net
I think your understanding is a little off.

Wind chill is the apparent temperature felt by exposed human skin. It is lower than the actual air temp, because the wind velocity increases the speed with which sweat evaporates from the human skin, thus hastening up the heat transfer, so it is perceived by the human as colder...
I think your understanding is a little off.

1. It doesn't matter whether human skin is exposed or not. If I'm wearing a light jacket (covering my skin), I will still suffer hypothermia much faster at 20 deg F with absolutely no breeze, than at 20 deg F with a 50-knot gale blowing.

2. What does sweating have to do with anything? Believe it or not, you will lose heat from cold air whether you are sweating or not.

3. It's not just "perception." A human will really and truly suffer hypothermia and die faster at 20 deg F with absolutely no breeze, than at 20 deg F with a 50-knot gale blowing.

It's true that a normal thermometer does not indicate any difference between the two situations--specifically, in both cases it will read 20 deg F. However, one can easily set up an objective experiment which will demonstrate that even inanimate objects will behave differently in the two situations. For example, one could measure the time it takes for a container of water to cool down from 75 deg F to 40 deg F.
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  #22  
Old 10-24-2006, 10:01 AM
robby robby is offline
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Quote:
Originally Posted by robby
...David Simmons, when you talk about "wind chill," you are describing a situation where you are at body temperature, and a 30 deg F wind (for instance) is perceived by you as removing heat from you as fast as, for example at 10 deg F stationary air mass...
This should read:

"David Simmons, when you talk about "wind chill," you are describing a situation where you are at body temperature, and a 30 deg F wind (for instance) is perceived by you as removing heat from you as fast as (for example) a 10 deg F stationary air mass."
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  #23  
Old 10-24-2006, 10:26 AM
David Simmons David Simmons is offline
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Quote:
Originally Posted by robby
This should read:

"David Simmons, when you talk about "wind chill," you are describing a situation where you are at body temperature, and a 30 deg F wind (for instance) is perceived by you as removing heat from you as fast as (for example) a 10 deg F stationary air mass."
By that description then it would appear that there could be a 30o wind chill factor on a body at 10 K. The heat is being removed at at rate equivalent to a 30o temperature difference under no wind conditions, even though the body itself can't go below o K.
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  #24  
Old 10-24-2006, 11:07 AM
Cheesesteak Cheesesteak is offline
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The wind chill does not make any definitive statement regarding the temperature of the air, therefore it isn't clear that no gasses can exist at negative Kelvin wind chills. If the air is at -50 C and blowing 40mph, it's about a -80 C wind chill. Wind chill depressions get higher when the temperature gets lower, but top out at around 40mph wind speeds.

You can probably get wind chill depressions of 100 degrees when the "air" is super cold and fast moving. If you're in 50K helium gas that's blowing 40mph, you probably have a below 0K wind chill.

Since it's a phoney baloney temperature, only telling you how it "feels" it isn't bound in any way by physical constraints.
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  #25  
Old 10-24-2006, 11:18 AM
Ludovic Ludovic is offline
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Perhaps it isn't as important in wind chill calculations at lesser temperature differentials, but I'm pretty sure that at ambient temps close to 0K the ability of a warm-blooded body to heat the immediate surroundings should be taken into account.

Therefore, a mass of stationary "air" at around 0K would not chill someone as much as a mass of circulating "air" at the same temperature because the body itself would heat the surrounding air enough to create a temperature buffer, which would be reduced when the "air" is circulated. So I'd say a wind chill below 0K is possible.
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  #26  
Old 10-24-2006, 02:41 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
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Sorry to have ignored this thread for so long. To clarify my question and answer a few issues raised.

The general concept of wind chill is applicable in a non-gaseous environment, and even in one where sweat doesn't evaporate. A warm body will lose heat at a faster rate if it is surrounded by a moving fluid at a lower temperature than it will if it is surrounded by a still fluid (at that same lower temperature). If we consider this generalized "fluid flow chill" factor, can it get to negative K?

For those who claim that you can't put anything at a lower energy than 0 K, that's not what I'm asking, and it's not what wind chill claims to measure. It's the rate that's important. It's not even necessary that the real temperature of the environment is anywhere near 0 K, just that the rate of heat loss for the warm body is equivalent to what it would be in a sub-0 K environment. I suppose the real question is whether the heat transfer equation breaks down at temperatures or rates near absolute 0.

For what it's worth, the Futurama quote is likely referring to conditions on another planet, so exotic elements, pressures, and temperatures are valid considerations.
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  #27  
Old 10-24-2006, 03:54 PM
Kevbo Kevbo is offline
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Commonly referenced "wind chill" charts apply only to an object who's surface temperature is maintained at about 95F. (e.g. a human being). That doesn't mean that the effect doesn't occur at other temperatures, but that the strength of the effect depends on the existance of a temperature difference between the air and an object under consideration. Live mammels happen to be an object who's temperature we can reliably assume, so the wind chill charts obscure this crucial fact. A universal wind chill chart would need a third axis for the temperature of the object under consideration.

Objects at the same temperature as the air do not experience any wind chill...heat only flows in response to a temperature gradient.

So to the OP: Wind chill will never lower the temperature of anything to less than the temperature of the air. Since no air will ever be colder than absolute zero, there is no way to exploit wind chill to produce a temperature below absolute zero.
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  #28  
Old 10-24-2006, 04:45 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
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Quote:
Originally Posted by Kevbo
So to the OP: Wind chill will never lower the temperature of anything to less than the temperature of the air. Since no air will ever be colder than absolute zero, there is no way to exploit wind chill to produce a temperature below absolute zero.
As you pointed out, wind chill doesn't measure the actual temperature of the air. It measures the rate at which a warm body will lose heat to the environment.

I'm not asking about using a moving fluid to lower the temperature of an object below zero. I understand that that's impossible by the definition of absolute zero. I'm asking whether a cold moving fluid could cool a warm body at a rate faster than a still fluid at absolute zero would.

Note that neither the fluid nor the body need to reach anything close to absolute zero for this to occur. If a -40 deg F wind can cool a 98 deg F body the same way that -80 still air can, it doesn't matter that the body won't ever reach -80 deg, nor does it matter that the air will never reach -80 deg. Yet we still say that the temperature is "wind chill to -80 deg."

The real question (I think) is whether there's something about Fourier's Law that breaks down at very cold temperatures or very high differences in temperature.
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  #29  
Old 10-24-2006, 06:19 PM
jackdavinci jackdavinci is offline
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Quote:
Originally Posted by robby
It doesn't matter whether human skin is exposed or not. If I'm wearing a light jacket (covering my skin), I will still suffer hypothermia much faster at 20 deg F with absolutely no breeze, than at 20 deg F with a 50-knot gale blowing.
Surely you meant "I will still suffer hypothermia much *SLOWER* at 20 deg F with absolutely no breeze, than at 20 deg F with a 50-knot gale blowing."?

Further, altho sweat will make a difference to perceived temperature, I agree that it isn't factored into the wind chill factor. But while neither sweat nor clothing insulation are factored into the official wind chill, certainly either will make a difference to real life perception of, and actual change in temperature to the affected human life form. With a jacket on, you will still suffer hypothermia more quickly with wind blowing than not, but you will suffer less wtih the jacket at the same wind speed.
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  #30  
Old 10-24-2006, 06:51 PM
Schuyler Schuyler is offline
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Quote:
Originally Posted by iamthewalrus(:3=
As you pointed out, wind chill doesn't measure the actual temperature of the air. It measures the rate at which a warm body will lose heat to the environment.

I'm not asking about using a moving fluid to lower the temperature of an object below zero. I understand that that's impossible by the definition of absolute zero. I'm asking whether a cold moving fluid could cool a warm body at a rate faster than a still fluid at absolute zero would.

Note that neither the fluid nor the body need to reach anything close to absolute zero for this to occur. If a -40 deg F wind can cool a 98 deg F body the same way that -80 still air can, it doesn't matter that the body won't ever reach -80 deg, nor does it matter that the air will never reach -80 deg. Yet we still say that the temperature is "wind chill to -80 deg."

The real question (I think) is whether there's something about Fourier's Law that breaks down at very cold temperatures or very high differences in temperature.
Well if wikipedia is anything to go by, then "wind chill" seems to have a fairly precise definition:

Quote:
Originally Posted by wiki
Wind chill is the apparent temperature felt on exposed skin due to the combination of air temperature and wind speed. ...

The first wind chill formulae and tables were developed by the United States military during World War II, initially by Siple and Passel working in the Antarctic, and were made available by the National Weather Service by the 1970s. In 2001 the formulae were revised to reflect more accurate theories and testing than those done by the military. These formulae are designed specifically for the human body, or even more specifically for the human face. Wind chill also affects animals, and wet, inanimate objects, but different formulae apply to them.
(bolding mine)

So, it would seem that all the talk tangential to the OP of super-cooled fluids and micro-Kelvin does not fall within the scope of the definition of wind chill.

Now, as to the issue of whether a heat transfer coefficient could exceed that between a 98F human and a hypothetical fluid at 0K - this seems like a no-brainer. I could imagine an extremely low-density, still fluid at near-0K, and it would not be able to extract much thermal energy from an exposed patch of skin. However, I could have a jet of liquid Nitrogen that would achieve an instantaneous heat transfer coefficient much greater than that possible from the low-density fluid. In any case, if this is the thrust of the OP, then he/she seems to have addressed it in that latest post.
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  #31  
Old 10-24-2006, 08:46 PM
jackdavinci jackdavinci is offline
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Quote:
Originally Posted by iamthewalrus(:3=
In [url=http://boards.straightdope.com/sdmb/showpost.php?p=7891431&postcount=32]I don't really know how to do the calculation, but assuming either (a) a rapidly flowing supercooled liquid or (b) an even more rapidly flowing very cold gaseous atmosphere, is it possible, or would the heat energy present in such a quickly moving fluid always keep the "wind chill modified" temperature above 0 K?
The answer depends on your calculation. The current wind chill factor formula, which was revised for accuracy in 2001 is listed here. Under that formula, at -100C it would take a wind speed of just over 10,000 km/h to get you to feel like you are at absolute zero. At -150C it would take about 535 km/h to get you there. However, according to web based wind chill calculators, this is only meant to work for temperatures of -50 to 10C and wind speeds of above 4.8 km/hr and below 177 km/hr.

If the wind speed were less than the speed of normal calm air, the perceived temperature would actually be warmer, and in terms of actual heat loss, still air can act as an insulator.

This formula is an improved version of the original formula (derived from the time that water in a plastic cylinder took to freeze under different conditions of wind and temperature) that takes into account the difference between wind speed where it's measures (10m) and where the human face is, the calm wind threshhold (average walking speed), and consistent standard for skin tissue resistance to heat loss. Neither formula currently takes into account solar radiation. There are other formulas that take into account humidity.

So technically, the wind chill as defined by the equation can dip below absolute zero without the variable contraints, but not within them.

If we are talking about actual heat transfer, I'm not sure. It would depend on how conduction and convention. Is there an equation for the temperature change of a solid based on ambient air temperature and pressure?
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  #32  
Old 10-24-2006, 09:43 PM
Northern Piper Northern Piper is offline
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Quote:
Originally Posted by Napier
It's a whole separate debate whether wind chill is a very useful concept. I think it's a bit daffy - it's rare to sense very cold air with no breeze, and you'd then be surprised to hear how cold it really was.
I have to disagree with you. I've often experienced - 20 C with a strong wind, and quite often been in - 35 C with no wind. I much prefer the latter.

Minus 20 C with a strong wind is most unpleasant, and the only urge is to get inside.

Minus 35 C with no wind, on a bright sunny day, makes me feel alive, and it's fun to go for a walk.

Obviously, this is a matter of opinion, so YMMV.
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  #33  
Old 10-24-2006, 10:44 PM
groman groman is offline
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I don't understand all the people who are saying "No" - so what is the lowest possible windchill adjusted temperature then?

Windchill, theoretically, is an adjustment factor that is meant to compensate for the effects of convection. You could have a windchill be positive if the ambient temperature is higher than the temperature of the body in question (usually the human body). It depends on pressure, relative temperatures, absolute temperatures, shapes, wind speed and direction, elasticity and a whole other big sheband of things.

We have a pretty solid grasp of how fast (at least a ballpark) an object made of a given material and of a given surface area would lose heat if surrounded by magically liquid air (pure helium for instance) at ~0K. That speed is not infinity. Now, if the medium suddenly starts moving and the medium temperature is say 50K or 20K or whatever, with convection the same body could possibly lose heat faster than in the 0K case. I fail to see what principle prevents this from happening.

In other words, your medium, even if it's liquid helium at ~0K is not magic. When the object will start losing heat the medium will start gaining heat and the temperature delta will drop resulting in the corresponding decrease in the rate of heat loss. With convection this effect is reduced with the 'ideal' convection behaving exactly like a magic medium that is an infinite heat sink. Liquid helium at ~0K is NOT an ideal heat sink so it can have a windchill factor that makes it approach one. That can be expressed as a temperature below ~0K although that's not useful to any degree.
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  #34  
Old 10-25-2006, 02:27 PM
Napier Napier is offline
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Northern Piper, I think you're agreeing with me. It's rare for people in general to experience very cold conditions, though if you are Northern enough of course it's not rare for you. So, I'm saying that if for example you brought someone into -20 C with a strong wind, they'd think it was terribly cold, and then if you brought them to -35 C with no wind, they would find they much prefer it, and would be surprised that it was 15 C colder than the previous experience. We're agreeing, right?
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  #35  
Old 10-25-2006, 03:19 PM
robby robby is offline
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Quote:
Originally Posted by jackdavinci
Surely you meant "I will still suffer hypothermia much *SLOWER* at 20 deg F with absolutely no breeze, than at 20 deg F with a 50-knot gale blowing."?


Indeed you are correct, sir.
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