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another weird physics question
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Adam Funk
Mar 21, 2012, 5:23:19 PM3/21/12
to
Following the one about the idea that forces are proportional to
1/(r^2) because there are 3 spatial dimensions: is there any similar
explanation for why radiation from one body is proportional to T^4?
--
Anything invented before your 15th birthday is the order of nature.
Anything invented between your 15th and 35th birthday is new and
exciting. Anything invented after that day, however, is against
nature and should be prohibited. [Douglas Adams]
1/(r^2) because there are 3 spatial dimensions: is there any similar
explanation for why radiation from one body is proportional to T^4?
--
Anything invented before your 15th birthday is the order of nature.
Anything invented between your 15th and 35th birthday is new and
exciting. Anything invented after that day, however, is against
nature and should be prohibited. [Douglas Adams]
David DeLaney
Mar 21, 2012, 7:05:37 PM3/21/12
to
On Wed, 21 Mar 2012 21:23:19 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>Following the one about the idea that forces are proportional to
>1/(r^2) because there are 3 spatial dimensions: is there any similar
>explanation for why radiation from one body is proportional to T^4?
THAAAAAT'S thermodynamics, and thus is more complicated to START with.
>Following the one about the idea that forces are proportional to
>1/(r^2) because there are 3 spatial dimensions: is there any similar
>explanation for why radiation from one body is proportional to T^4?
Let's see ... http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
is where there's a derivation of this proportionality, and the simple part
of it is that there's an integral in \nu^3 d\nu, and to do it you do a
variable substitution u = h\nu / kT , so you end up with a T^4 outside the
integral. The \nu^3 comes from Planck's law, intensity of light emitted from
a blackbody surface... see http://en.wikipedia.org/wiki/Planck%27s_law .
But that part's not simple to derive, alas. So no, there's not a -simple-
explanation I can give you. Sorry!
(I _can_ say that since there's a 'per solid angle' in there, if you change
dimensions the exponent of \nu, and therefore of T, will probably change.
But I can't say how or which way.)
Dave
--
\/David DeLaney posting from d...@vic.com "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK>
http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K.
Adam Funk
Mar 27, 2012, 12:09:14 PM3/27/12
to
On 2012-03-21, David DeLaney wrote:
> On Wed, 21 Mar 2012 21:23:19 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>>Following the one about the idea that forces are proportional to
>>1/(r^2) because there are 3 spatial dimensions: is there any similar
>>explanation for why radiation from one body is proportional to T^4?
>
> THAAAAAT'S thermodynamics, and thus is more complicated to START with.
>
> Let's see ... http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
> is where there's a derivation of this proportionality, and the simple part
> of it is that there's an integral in \nu^3 d\nu, and to do it you do a
> variable substitution u = h\nu / kT , so you end up with a T^4 outside the
> integral.
So far, so good.
> On Wed, 21 Mar 2012 21:23:19 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>>Following the one about the idea that forces are proportional to
>>1/(r^2) because there are 3 spatial dimensions: is there any similar
>>explanation for why radiation from one body is proportional to T^4?
>
> THAAAAAT'S thermodynamics, and thus is more complicated to START with.
>
> Let's see ... http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
> is where there's a derivation of this proportionality, and the simple part
> of it is that there's an integral in \nu^3 d\nu, and to do it you do a
> variable substitution u = h\nu / kT , so you end up with a T^4 outside the
> integral.
> The \nu^3 comes from Planck's law, intensity of light emitted from
> a blackbody surface... see http://en.wikipedia.org/wiki/Planck%27s_law .
>
> But that part's not simple to derive, alas. So no, there's not a -simple-
> explanation I can give you. Sorry!
> (I _can_ say that since there's a 'per solid angle' in there, if you change
> dimensions the exponent of \nu, and therefore of T, will probably change.
> But I can't say how or which way.)
of intensity derivation" right, \nu is frequency, so I'm not sure why
its exponent would change if you replace solid angle dΩ (for 3-D
space) with angle (for Flatland) or some kind of hyper-angle (for
more-than-3-D). I'd expect the exponent of something else (rather
than \nu and hence T) to change with the number of spatial
dimensions.
Or do you mean there's a "per solid angle" related to \nu buried in
Planck's law?
--
The generation of random numbers is too important to be left to
chance. [Robert R. Coveyou]
J. Waldby
Mar 31, 2012, 4:53:58 PM3/31/12
to
Adam Funk wrote:
> Following the one about the idea that forces are proportional to
> 1/(r^2) because there are 3 spatial dimensions: is there any similar
> explanation for why radiation from one body is proportional to T^4?
Can you bring me up to speed? What is T here? Also, are we talking
> Following the one about the idea that forces are proportional to
> 1/(r^2) because there are 3 spatial dimensions: is there any similar
> explanation for why radiation from one body is proportional to T^4?
about a cubic body or a spherical body?
J.
J. Waldby
Mar 31, 2012, 4:55:24 PM3/31/12
to
David DeLaney wrote:
> Let's see ... http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
> is where there's a derivation of this proportionality, and the simple part
> of it is that there's an integral in \nu^3 d\nu, and to do it you do a
> variable substitution u = h\nu / kT , so you end up with a T^4 outside the
> integral. The \nu^3 comes from Planck's law, intensity of light emitted from
> a blackbody surface... see http://en.wikipedia.org/wiki/Planck%27s_law .
I get a cold feeling when I think about physics. I believe it is
> Let's see ... http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
> is where there's a derivation of this proportionality, and the simple part
> of it is that there's an integral in \nu^3 d\nu, and to do it you do a
> variable substitution u = h\nu / kT , so you end up with a T^4 outside the
> integral. The \nu^3 comes from Planck's law, intensity of light emitted from
> a blackbody surface... see http://en.wikipedia.org/wiki/Planck%27s_law .
because my first physics teacher in college was a cenobite.
J.
David DeLaney
Mar 31, 2012, 10:38:50 PM3/31/12
to
in temperature between the body doing the radiating and the background it's
radiating into. This is, in part, why it's so much more dangerous to be
out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
and so much more dangerous again to be out in -30 -degree weather; if you
double the temperature difference, heat loss by radiation goes up by a factor
of 16. (Of course for weather, convection & conduction also play large parts.)
J. Waldby
Apr 1, 2012, 1:30:59 AM4/1/12
to
David DeLaney wrote:
> J. Waldby<wichita...@REMOVETHISmsn.com> wrote:
>> Adam Funk wrote:
>>> Following the one about the idea that forces are proportional to
>>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
>>> explanation for why radiation from one body is proportional to T^4?
>>
>> Can you bring me up to speed? What is T here? Also, are we talking
>> about a cubic body or a spherical body?
>
> T is the temperature, though technically you get that it's the difference
> in temperature between the body doing the radiating and the background it's
> radiating into. This is, in part, why it's so much more dangerous to be
> out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
> and so much more dangerous again to be out in -30 -degree weather; if you
> double the temperature difference, heat loss by radiation goes up by a factor
> of 16. (Of course for weather, convection& conduction also play large parts.)
> J. Waldby<wichita...@REMOVETHISmsn.com> wrote:
>> Adam Funk wrote:
>>> Following the one about the idea that forces are proportional to
>>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
>>> explanation for why radiation from one body is proportional to T^4?
>>
>> Can you bring me up to speed? What is T here? Also, are we talking
>> about a cubic body or a spherical body?
>
> T is the temperature, though technically you get that it's the difference
> in temperature between the body doing the radiating and the background it's
> radiating into. This is, in part, why it's so much more dangerous to be
> out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
> and so much more dangerous again to be out in -30 -degree weather; if you
> double the temperature difference, heat loss by radiation goes up by a factor
>
> Dave
Back in MN it got frigid. I had moved there from hot KS and was taken
by surprise. The difference is that Minnesotans expect snow and cold.
Only COans are as prepared due to numerous small cities dotting the
landscape decorated by the Rocky Mountains. Around my block and its
twin sister across the highway to the east, the Zweiln would roll the
giant yellow laser ball. Normally if you cool a small space it is
quickly brought back to the temperature of the rest of this room. Hot
is different from cold. You warm a space up to 30 degrees above, it is
nothing like the residue of heat when you raise it by 430 degrees
fahrenheit. That yellow laser ball only had to be rolled around thrice
each winter season and it kept the temperatures even for all that time.
J.
Adam Funk
Apr 1, 2012, 4:13:37 PM4/1/12
to
On 2012-04-01, David DeLaney wrote:
> J. Waldby <wichita...@REMOVETHISmsn.com> wrote:
>>Adam Funk wrote:
>>> Following the one about the idea that forces are proportional to
>>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
>>> explanation for why radiation from one body is proportional to T^4?
>>
>>Can you bring me up to speed? What is T here? Also, are we talking
>>about a cubic body or a spherical body?
>
> T is the temperature, though technically you get that it's the difference
> in temperature between the body doing the radiating and the background it's
> radiating into.
Isn't gross transfer Q from body 1 to body 2 proportional to (T_1)^4,
> J. Waldby <wichita...@REMOVETHISmsn.com> wrote:
>>Adam Funk wrote:
>>> Following the one about the idea that forces are proportional to
>>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
>>> explanation for why radiation from one body is proportional to T^4?
>>
>>Can you bring me up to speed? What is T here? Also, are we talking
>>about a cubic body or a spherical body?
>
> T is the temperature, though technically you get that it's the difference
> in temperature between the body doing the radiating and the background it's
> radiating into.
so *net* transfer from body 1 to body is proportional to
(T_1)^4 - (T_2)^4
where T is absolute temperature? (Let's be honest: I'm trying to
remember this from about 20 years ago.)
> This is, in part, why it's so much more dangerous to be
> out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
> and so much more dangerous again to be out in -30 -degree weather; if you
> double the temperature difference, heat loss by radiation goes up by a factor
> of 16. (Of course for weather, convection & conduction also play large parts.)
the human body in a cold environment.
--
"Gonzo, is that the contract from the devil?"
"No, Kermit, it's worse than that. This is the bill from special
effects."
Adam Funk
Apr 1, 2012, 4:40:54 PM4/1/12
to
On 2012-03-31, J. Waldby wrote:
> I get a cold feeling when I think about physics. I believe it is
> because my first physics teacher in college was a cenobite.
"Cenobite
> I get a cold feeling when I think about physics. I believe it is
> because my first physics teacher in college was a cenobite.
Nobody worry 'bout me
Why you got to gimme a fight?
Why can't you just let it be?"
--
English has perfect phonetic spelling. It just doesn't have phonetic
pronunciation. [Peter Moylan]
Dr. HotSalt
Apr 1, 2012, 10:36:15 PM4/1/12
to
> > J. Waldby <wichitajayha...@REMOVETHISmsn.com> wrote:
> >>Adam Funk wrote:
> >>> Following the one about the idea that forces are proportional to
> >>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
> >>> explanation for why radiation from one body is proportional to T^4?
Appeal to Wikipedia:
> >>Adam Funk wrote:
> >>> Following the one about the idea that forces are proportional to
> >>> 1/(r^2) because there are 3 spatial dimensions: is there any similar
> >>> explanation for why radiation from one body is proportional to T^4?
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Derivation_of_the_Stefan.E2.80.93Boltzmann_law
(damn wrap anyway)
I never grokked calculus. You're on your own.
> >>Can you bring me up to speed? What is T here?
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html#c1
"A convenient operational definition of temperature is that it is a
measure of the average translational kinetic energy associated with
the disordered microscopic motion of atoms and molecules."
It's the *scalar* average of the velocity values of all the
constituent bits of an object; their vectors average to zero of course
for a stationary object.
> >> Also, are we talking about a cubic body or a spherical body?
is calculated from the surface area of the radiator:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2
> > T is the temperature, though technically you get that it's the difference
> > in temperature between the body doing the radiating and the background it's
> > radiating into.
>
> Isn't gross transfer Q from body 1 to body 2 proportional to (T_1)^4,
> so *net* transfer from body 1 to body is proportional to
>
> (T_1)^4 - (T_2)^4
>
> where T is absolute temperature? (Let's be honest: I'm trying to
> remember this from about 20 years ago.)
>
> > This is, in part, why it's so much more dangerous to be
> > out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
> > and so much more dangerous again to be out in -30 -degree weather; if you
> > double the temperature difference, heat loss by radiation goes up by a factor
> > of 16. (Of course for weather, convection & conduction also play large parts.)
>
> I thought convection was the most important form of heat transfer from
> the human body in a cold environment.
bodies (air molecules) each extracting a bit of heat from your warm
body, then running away with it to be replaced with another cold one.
The faster they're replaced the faster you lose heat.
Absent wind, you get a more-or-less insulating sheath of skin-
temperature air (it can't absorb any more heat by conduction) that
slowly rises all over your body. Your feet get cold of course.
The sheath is still IR-transparent so radiation dominates.
Also, the S-B law can be b0rken:
http://arxiv.org/pdf/1109.5444.pdf
Dr. Hot"kT, bay-bee!"Salt
David DeLaney
Apr 1, 2012, 11:33:45 PM4/1/12
to
(cold clothes) and convection for exposed skin and for breath, and radiation
from all of it except that the clothed parts do a lot less radiating because
of how the heat-transfer works out if you have one or more layers in between
what's radiating and where it's trying to radiate to.
Dave, also dredging this up from years ago
Adam Funk
Apr 2, 2012, 10:13:31 AM4/2/12
to
On 2012-04-02, David DeLaney wrote:
> Adam Funk <a24...@ducksburg.com> wrote:
>>On 2012-04-01, David DeLaney wrote:
>>> This is, in part, why it's so much more dangerous to be
>>> out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
>>> and so much more dangerous again to be out in -30 -degree weather; if you
>>> double the temperature difference, heat loss by radiation goes up by a factor
>>>of 16. (Of course for weather, convection & conduction also play large parts.)
>>
>>I thought convection was the most important form of heat transfer from
>>the human body in a cold environment.
>
> A nekkid one, sure. A clothed one, then you get conduction for most of it
> (cold clothes) and convection for exposed skin and for breath, and radiation
> from all of it except that the clothed parts do a lot less radiating because
> of how the heat-transfer works out if you have one or more layers in between
> what's radiating and where it's trying to radiate to.
>
> Dave, also dredging this up from years ago
From _QI_:
> Adam Funk <a24...@ducksburg.com> wrote:
>>On 2012-04-01, David DeLaney wrote:
>>> This is, in part, why it's so much more dangerous to be
>>> out in zero-degree weather than in 30-degree weather (Fahrenheit, fondly),
>>> and so much more dangerous again to be out in -30 -degree weather; if you
>>> double the temperature difference, heat loss by radiation goes up by a factor
>>>of 16. (Of course for weather, convection & conduction also play large parts.)
>>
>>I thought convection was the most important form of heat transfer from
>>the human body in a cold environment.
>
> A nekkid one, sure. A clothed one, then you get conduction for most of it
> (cold clothes) and convection for exposed skin and for breath, and radiation
> from all of it except that the clothed parts do a lot less radiating because
> of how the heat-transfer works out if you have one or more layers in between
> what's radiating and where it's trying to radiate to.
>
> Dave, also dredging this up from years ago
Stephen
... In cold weather, where does most of your heat escape from?
[Panellists 'oh' and 'er' as they stall, sensing the forfeit.]
Sean
Your head.
Stephen
Oh! Really?
Forfeit: Klaxons sound. Viewscreens flash the words "YOUR HEAD".
Alan
It's supposed to be 75%, that's what I've been told, that comes out
your head.
David
Is it not just the fact that the head is the bit of you that's more,
sort of, naked?
Stephen
Well, that's right, if it is, but only 10% of your heat. You're
actually… if your arm was exposed, more would escape from your arm
than your head.
David
If people went around with bare buttocks a lot, they would say, "In
the cold you should really put on a buttock hat, you lose all your
heat through your buttocks." "Don't be ridiculous, no need these days
to cover your buttocks all the time." In the same way everyone used to
wear hats, now they go around bare-headed a lot.
https://sites.google.com/site/qitranscripts/transcripts/7x10
--
The kid's a hot prospect. He's got a good head for merchandising, an
agent who can take you downtown and one of the best urine samples I've
seen in a long time. [Dead Kennedys t-shirt]
Glenn Knickerbocker
Apr 2, 2012, 2:42:00 PM4/2/12
to
On 4/2/2012 10:13 AM, Adam Funk wrote:
> https://sites.google.com/site/qitranscripts/transcripts/7x10
Later in that same discussion:
> Stephen
> There's nothing special about your head and heat loss,
Except that, well, there is. It's not that you normally lose more heat
there, though. It's that your brain is so selfish. When your wrists
get cold, they shut off blood flow to your hands to protect the rest of
your body. When your ankles get cold, they shut off blood flow to your
feet to protect the rest of your body. So when your temples get cold,
do they shut off blood flow to your head? Duh! They shut off blood
flow to the rest of your body, to protect your brain. So *then* you
lose most of your heat through your head because it's not going to the
rest of your body, and instead of losing a few digits to frostbite
you'll lose internal organs to hypothermia that much faster.
At least, that's what our Boy Scout leaders taught us. Maybe they just
had an earmuff fetish, though.
¬R
> https://sites.google.com/site/qitranscripts/transcripts/7x10
Later in that same discussion:
> Stephen
> There's nothing special about your head and heat loss,
Except that, well, there is. It's not that you normally lose more heat
there, though. It's that your brain is so selfish. When your wrists
get cold, they shut off blood flow to your hands to protect the rest of
your body. When your ankles get cold, they shut off blood flow to your
feet to protect the rest of your body. So when your temples get cold,
do they shut off blood flow to your head? Duh! They shut off blood
flow to the rest of your body, to protect your brain. So *then* you
lose most of your heat through your head because it's not going to the
rest of your body, and instead of losing a few digits to frostbite
you'll lose internal organs to hypothermia that much faster.
At least, that's what our Boy Scout leaders taught us. Maybe they just
had an earmuff fetish, though.
¬R
Adam Funk
Apr 2, 2012, 4:18:49 PM4/2/12
to
On 2012-04-02, Glenn Knickerbocker wrote:
> Except that, well, there is. It's not that you normally lose more heat
> there, though. It's that your brain is so selfish. When your wrists
> get cold, they shut off blood flow to your hands to protect the rest of
> your body. When your ankles get cold, they shut off blood flow to your
> feet to protect the rest of your body. So when your temples get cold,
> do they shut off blood flow to your head? Duh! They shut off blood
> flow to the rest of your body, to protect your brain. So *then* you
> lose most of your heat through your head because it's not going to the
> rest of your body, and instead of losing a few digits to frostbite
> you'll lose internal organs to hypothermia that much faster.
>
> At least, that's what our Boy Scout leaders taught us. Maybe they just
> had an earmuff fetish, though.
I bet you can't say "buttockmuff" with a straight face.
> Except that, well, there is. It's not that you normally lose more heat
> there, though. It's that your brain is so selfish. When your wrists
> get cold, they shut off blood flow to your hands to protect the rest of
> your body. When your ankles get cold, they shut off blood flow to your
> feet to protect the rest of your body. So when your temples get cold,
> do they shut off blood flow to your head? Duh! They shut off blood
> flow to the rest of your body, to protect your brain. So *then* you
> lose most of your heat through your head because it's not going to the
> rest of your body, and instead of losing a few digits to frostbite
> you'll lose internal organs to hypothermia that much faster.
>
> At least, that's what our Boy Scout leaders taught us. Maybe they just
> had an earmuff fetish, though.
--
When a man tells you that he got rich through hard work, ask him
whose? --- Don Marquis
Glenn Knickerbocker
Apr 2, 2012, 5:24:39 PM4/2/12
to
On 4/2/2012 4:18 PM, Adam Funk wrote:
> I bet you can't say "buttockmuff" with a straight face.
With a name like yours, you seriously think you'd have a chance of
> I bet you can't say "buttockmuff" with a straight face.
winning that bet from someone with a name like mine? With a best friend
from the line of the champion of Oyster Bay and rampant beavers?
ŹR
Glenn Knickerbocker
Apr 2, 2012, 5:58:13 PM4/2/12
to
On 4/1/2012 10:36 PM, Dr. HotSalt wrote:
> "A convenient operational definition of temperature is that it is a
> measure of the average translational kinetic energy associated with
> the disordered microscopic motion of atoms and molecules."
>
> It's the *scalar* average of the velocity values of all the
> constituent bits of an object; their vectors average to zero of course
> for a stationary object.
The mean square, rather, since energy is proportional to the square of
> "A convenient operational definition of temperature is that it is a
> measure of the average translational kinetic energy associated with
> the disordered microscopic motion of atoms and molecules."
>
> It's the *scalar* average of the velocity values of all the
> constituent bits of an object; their vectors average to zero of course
> for a stationary object.
velocity--but not in the case of light, whose speed is constant. The
photon's energy is instead proportional to its frequency, so the
temperature is proportional to the mean frequency of the photons.
¬R
David DeLaney
Apr 2, 2012, 7:03:17 PM4/2/12
to
Dave "shall I adjust your buttockmuff, dear Chauncey?" DeLaney
Adam Funk
Apr 3, 2012, 8:18:12 AM4/3/12
to
On 2012-04-02, Glenn Knickerbocker wrote:
Dr. HotSalt
Apr 3, 2012, 9:59:36 AM4/3/12
to
0 new messages