Trying to Understand Temperatures

[EndoftheTrail]

In Fahrenheit — does a 10-degree difference always equate to the same "difference in warmth" up and down the scale? Say for example that I have a vest that will boost my bag warmth from 40F to 30F. Assuming everything else stays the same, will the same vest boost warmth from 30F to 20F or -30F to -40F?

[Mike Barney]

You have a couple of questions there.
First F to C Temperature conversion is linear, commonly 9/5 x C + 32 converts C to F (and vice versa).

The "10 F" difference you're asking about provides the same amount of resistance to the cold across a temperature range. One difference is that when vendors make gear for much greater extremes do more than just add thickness. For example, on bags for much colder temps, you often get more baffels, draft tubes and neck collars.

Does that help any?

[Michael Martin]

Short Answer: Yes

An additional 10 degrees of warmth is independent of the ambient temp…If you are a large, flat surface with a low air exchange rate — like the walls in your house.

Long Answer: No

As you add insulation for colder temperatures, two phenomena conspire to rob you of warmth. The first is "chimney effect" convective heat transfer, commonly known as a draft. As you increase the temperature difference between the warm side and cold side of your insulation, the rate of air exchange through your shell fabric and envelope protrusions (like zippers, waist, neck, and hem on your vest example) increases. The second applies to smaller, non-flat surfaces like your torso, arms, and fingers in order of increasing "smallness". Adding insulation to these surfaces increases the surface area on the outside of the insulation, and therefore increases the heat transfer rate, making the insulation less warm. The net result of these two effects is that your vest that adds 10 degrees at 40F will add somewhat less at -30F.

Cheers,

-Mike

[Brett .]

Michael, right. And there is another effect, thermal conduction is proportional to the temperature difference between your body and ambient air temp. So you loose more heat going from 0C to -10C than you do from 10C to 0C.
Calculate it here
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
but dont use "0", theres a bug in the formula, maybe use 15, 5, and -5. the differences in Q/t will not be the same, ie nonlinear.
This nonlinearity can be seen in a graph of sleeping bag down density vs. temperature rating. Colder bags add more down the lower the rating goes.

note, made an error in the text; should have been g/m^3

[Brett Peugh]

So then the colder a bag gets below 10, the more exponential the amount of down that gets added becomes to create a lower degree bag?

[Michael Martin]

Hi Brett-

Yah! Isn't Hyperphysics great?

I'm not sure what non-linear conduction effect you're referring to, or even exactly which page on hyperphysics you mean as their URL is the same for all pages.

Do you mean the Q/t = (kA*deltaT)/d formula on the "Conduction Cooling of Body" page?

If so, I did not see any non-linearity in that equation. As you said, heat transfer from thermal conduction to the air is proportional to deltaT. What non-linearity do you mean?

FWIW, radiation effects are non-linear WRT temperature, and I did neglect to mention that in my original post to keep it simple.

Cheers,

-Mike

[Brett Peugh]

I wonder what the right side of that curve looks like? So there probably is a point where it would just be more beneficial to wear your high loft insulating layer inside of a bag versus getting a heavier bag?

[Logan Wealing]

I will weigh in my opinion on this topic as an engineer.

It is my opinion that Mike is actually correct. The equations outlined below refer to conduction only which is indeed a linear relationship as Mike pointed out. Maybe the physics website is adding in the radiation effects as well?

If we look at Fourier's Law as Mike suggested:

deltaQ/delta(t)=(-)k*A*deltaT/delta(x)

Where:

Q = amount of heat transferred
t = time
k = materials thermal conductivity
A = surface area of heat transfer
T = temperature difference
x = distance between surfaces

If we treat all the variables as constants EXCEPT the thermal conductivity, we must the inspect the formula for k:

k = [deltaQ/delta(t)]*[L/(A*deltaT)]

Where:

k = materials thermal conductivity
Q = amount of heat transferred
t = time
L = thickness of heat conduction path
A = surface area of heat transfer
T = temperature difference

As you can see from the equation for thermal conductivity, it DOES vary based on T, the temperature difference between the two surfaces. This is the only variable in the entire equation that we are changing for this inspection.

So – in short – as the temperature difference increases so does the amount of heat transferred.

Note: this only applies to conduction. This does not include calculations for other modes of heat transfer such as radiation or convection etc.

[George Matthews]

In addition to the physics, I believe it is important to relate the ten degree change increments to biological units. For example, most humans are comfortable within a relevant range of say 55 to 85 degrees F with minor adjustments by adding or subtracting clothing or coverings. After about 95 deg. F., 105 then 115, most humans are very hot. We've moved to the high end of the relevant range. The range extends to the point of heat induced death.

Now on the other end of the biological unit's range, in this case a human, about 45 deg. F. is the beginning of cold. We add clothing or covering. However, after maybe 15 deg. F., the ten degree F. drops become incrementally less significant. Of course, this low end extends to the point of a frozen death.

Out walking I've been in 8 deg. F. on the low end and 106 deg F. on high end. There was little difference to me between 8 vs 18, but a noticeable one at 28, and big difference going to 38. On the high end, 106 to 96 – little . 96 to 86 more. 86 to 76 big.

[EndoftheTrail]

Sorry, non-scientist here, so please excuse my crude way of understanding.

Let's say that I have 3 bags: 10C, 0C, and -10C that are all spot on for me.

Let's further say that I have a vest that gives my 10C bag a true five degree boost, enabling me to sleep just as comfy down to 5C.

OK, reading all the above, and assuming that all conditions are the same except for temp change — am I correct in saying that:

1. Going from 10C to 5C — requires wearing the vest (as defined).

2. Going from 0C to -5C will likely require a vest plus something else.

3. Going from -10CF to -15C will likely require (2) above plus something more.

In other words, the same numerical five-degree difference in the three scenarios above are actually all different — meaning changes in CELCIUS IS NOT PROPORTIONAL???

Brett's graph above uses Celsius — which is why I changed my scenarios to Celsius. But what about Fahrenheit? Are temp changes in Fahrenheit proportional or also non-proportional?

[Logan Wealing]

Benjamin,

I think that you have the right idea. It does come down to fuzzy science at a certain point and the best suggestion I would make would be to take what we have outlined and use that information to test it out in practice. The tried and true methodology of try & fail is a good place to start. All this being in your back yard before a trip of course for safety concerns.

George,

I do agree with you about the relative "perceived" temperatures our body equates to. However one explanation would be that our sense of temperature is better suited to a smaller range of temperatures. These would be in the middle range that you suggested. The hard science does prove however that you will loose heat energy more as it gets colder. You may not be able to feel this as well at first, but as time continues you will loose that heat energy faster and thus become "cold" in a shorter length of time due to colder temperatures outside.

[Michael Martin]

Hi Benjamin-

Fahrenheit or Celsius makes no difference, other than the fact that a 1 degree F change is equal to 5/9 of a degree C as Mike B. mentioned.

For the specific example of a vest on your torso, the "increased surface area" effect I mentioned above is pretty small. (However, it is crucial for things like gloves where a thin glove liner might even be colder than bare skin in some conditions — but that is another discussion.) ;-)

The "draft effect" depends on the design features of both your sleeping bag and vest. If you can seal out drafts effectively, then your "5 degree" vest will add *approximately* 5 degrees to all three of your bags. But, if your bag is "leaky" or if wearing the vest increases air exchange from inside to outside your bag, say by causing gaps around your neck or waist, then you'll need to add more to go from 0C to -5C and even more to go from -10C to -15C like your example.

Cheers,

-Mike

[EndoftheTrail]

Hmmm… am I getting contradictory feedback?

Michael — as described above, please assume completely the same scenarios except for temp change — and no bag leakage. Are you in effect saying that regardless of the particular temperature at the moment (be it 10C or 0C or -10C) — if all I need is a 5 degree boost, then my vest (as described) will work?

[Michael Martin]

>> Are you in effect saying that regardless of the particular temperature at the moment (be it 10C or 0C or -10C) — if all I need is a 5 degree boost, then my vest (as described) will work?

Short Answer: Yes. ;-)

But like Logan Mentioned, it's kind of fuzzy science depending on what assumptions you make. For example, does adding a vest compress any insulation in the system? Does it affect the vapor permeability? Also, remember that at colder temperatures, a higher percentage of your body heat will be lost through respiration (assuming a thicker bag is used and your skin temperature is the same), so you may need to raise your skin temperature (with a thicker bag, vest, etc) to compensate.

So Long Answer: Still No. :-(

Cheers,

-MIke

[George Matthews]

HELL EXPLAINED BY A CHEMISTRY STUDENT

The following is an actual question given on a University of Washington chemistry mid term.

The answer by one student was so "profound" that the professor shared it with colleagues, via the Internet, which is, of course, why we now have the pleasure of enjoying it as well :

Bonus Question: Is Hell exothermic (gives off heat) or endothermic (absorbs heat)?

Most of the students wrote proofs of their beliefs using Boyle's Law (gas cools when it expands and heats when it is compressed) or some variant.

One student, however, wrote the following:

First, we need to know how the mass of Hell is changing in time. So we need to know the rate at which souls are moving in to Hell and the rate at which they are leaving. I think that we can safely assume that once a soul gets to Hell, it will not leave. Therefore, no souls are leaving. As for how many souls are entering Hell, let's look at the different religions that exist in the world today.

Most of these religions state that if you are not a member of their religion, you will go to Hell. Since there is more than one of these religions and since people do not belong to more than one religion, we can project that all souls go to Hell. With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially. Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand proportionately as souls are added.

This gives two possibilities:

1. If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose.

2. If Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over.

So which is it?

If we accept the postulate given to me by Teresa during my Freshman year that, "It will be a cold day in Hell before I sleep with you," and take into account the fact that I slept with her last night, then number two must be true, and thus I am sure that Hell is exothermic and has already frozen
over. The corollary of this theory is that since Hell has frozen over, it follows that it is not accepting any more souls and is therefore, extinct……leaving only Heaven, thereby proving the existence of a divine being which explains why, last night, Teresa kept shouting "Oh my God."

[Brett .]

Ben, your original question to me was if conductive heat loss was linear w.r.t. temperature difference. I said it was not, but maybe I was wrong. Certainly heat loss is proportional to delta t, but the graph is a straight line, so still meets the definition of 'linear'. Fact remains though that you will loose more heat going from x to x-10 than from x+10 to x.
Sorry to add confusion to the debate!

[Philip Mitchell]

Nice one, George :)

[EndoftheTrail]

Thank you all — I think I got it. :)

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