Temperature gradient inside a body with gravity
David Jonsson
to be taken into consideration when determining the temperature
gradient inside the body .
This is an easy description of how gravity affects the geothermal heat
gradient.
Consider a small part of the geological body as consisting of even
smaller particles moving around and colliding due to their thermal
energy. When the heated particles moves up in the gravity potential it
looses speed and thus thermal energy. If it moves down it's speed
increases and temperature rises. This is a cause for temperature
gradients in bodies big enough to have noticeable gravitation. This
temperature gradient can not cause heat conduction. When determining
the heat conduction through the earth's crust the effect of the
gravitational heat gradient has to be considered. Let us calculate how
big the non conducting gravitational heat gradient is.
The shift in the thermal energy of the particles moving height Δh in
gravity field will be equal to the shift in thermal energy
ρ g Δh = ρ c ΔT
g Δh = c ΔT
∇T = ΔT / Δh = g / c = 9.81 m/s^2 / ( 800 J/kg/K ) = 0.012 K / m = 12
K / km
This is half of the measured value 25 K / km. Thus the heat transfer
from the interior of the Earth should be taken as only half of the
value incorrectly calculated without the gravitational heat gradient.
This is important in determining global warming.
There is an easy way to experimentally test if the heat gradient in a
volume of the Earth is dominantly gravitational or conductive. If the
heat gradient depends mostly on specific heat capacity then the it is
mostly gravitational. If it depends mostly on thermal conductivity
then the heat gradient is mostly of conducting nature.
Specific heat c in the earth crust = 800 J/kg/K is taken from
http://www.tass-survey.org/richmond/answers/explosion.html
Geothermal gradient measured to be 25 K / km according to
http://gpc.edu/~pgore/Earth&Space/GPS/earthinterior.html
or 20 K / km or more according to
http://en.wikipedia.org/wiki/Geothermal_gradient
David Jonsson
David Jonsson
to be taken into consideration when determining the temperature
gradient inside the body .
This is an easy description of how gravity affects the geothermal heat
gradient.
Consider a small part of the geological body as consisting of even
smaller particles moving around and colliding due to their thermal
energy. When the heated particles moves up in the gravity potential it
looses speed and thus thermal energy. If it moves down it's speed
increases and temperature rises. This is a cause for temperature
gradients in bodies big enough to have noticeable gravitation. This
temperature gradient can not cause heat conduction. When determining
the heat conduction through the earth's crust the effect of the
gravitational heat gradient has to be considered. Let us calculate how
big the non conducting gravitational heat gradient is.
The shift in the potential energy of the particles moving height Δh in
Jo Schaper
You are working on averages, not temperature gradients at specific
locations. Temp gradients under Yellowstone NP, USA, for example,
greatly exceed the 'average' number. The temp gradient beneath other
places doesn't even reach the 20-25 K/km you cite.
If you are trying to draw some data to justify/deny global warming, it
doesn't strike me that earth's gravitational heat gradient (as you call
it) is anything people can influence without reducing the mass of the
planet. Therefore, it should be considered an overall constant, not a
controllable variable for total heat in the system.
David Jonsson
wrote:
> And this is supposed to be significant how?
Sure, since it differs by a factor of two.
> You are working on averages, not temperature gradients at specific
> locations. Temp gradients under Yellowstone NP, USA, for example,
> greatly exceed the 'average' number. The temp gradient beneath other
> places doesn't even reach the 20-25 K/km you cite.
I use the global average in the crust.
Check what the specific heat and the thermal coductivity is of that
rock and we can see how much the gravitational and the heat conducting
thermal gradient is.
> If you are trying to draw some data to justify/deny global warming, it
> doesn't strike me that earth's gravitational heat gradient (as you call
> it) is anything people can influence without reducing the mass of the
> planet. Therefore, it should be considered an overall constant, not a
> controllable variable for total heat in the system.
It can be controlled by adjusting the specific heat of the material it
is is. This is ofcourse also hard.
In fact we have a lot of heat in the earth interior without fusion or
heat left over from ancient times. The same is for the sun and the
planets. The sun and the gas planets would be worth investigating.
They probably are already since an similar theory is applied to
fluids, the lapse rate. It must apply to solids as well.
On the discussion page on Wikipedia's article on athmosperic lapse
rate they have the same equation 3.2 (in the German version)
http://de.wikipedia.org/wiki/Temperaturgradient_%28Meteorologie%29
David
Jo Schaper
with your data. Two factors which your are not taking into consideration
nor the heat of various chemical reactions, nor the heat generated by
natural radioactivity.
David Jonsson
wrote:
I mentioned the missing term. Every other context mentioning the
geothermal gradient mentions heat sources. Heat sources should be
halved and that is very significant.
Geothermal adiabatic lapse rate could be a more suitable term for the
effect since that term is used for the same effect in the atmosphere.
It is not a perfect term since gravity is doing work on the material.
What does this mean for the so often mentioned global heating? If the
heating from the interior of the earth is halved maybe there is no
global heating. I want someone to investigate global heating again
considering this effect. Alternatively, if the global heating is
determined by other means halving the contribution from the interior
of the earth means that the heating is even bigger.
A third option is to investigate if the atmospheric heat gradient is
changed with more carbon dioxide. Global heating doesn't necessarily
have to do with heating. It can be due to an altered non conducting
heat gradient.
As far as I have investigated this it seems that there is no good
understanding of heat sources inside Earth and the same seems to be
the case for the Sun and the big gas planets. Radioactivity is
something people refer to to make it all look as if it is in balance.
Lapse rate in the Sun has been mentioned but I don't know to which
degree. Maybe the missing neutrino flux from the Sun can be explained
by the fact that the heat gradient in the Sun isn't all conducting
heat which would require less heat sources and less nuclear reactions
in the sun.
Why lapse rate isn't considered in solid matter compared to gases and
fluids is that heat is distributed and altered in different ways.
There is a lot to investigate and I don't seem to have the time now.
David
Stuart
wrote:
> On Nov 28, 3:43 pm, Jo Schaper <jonot34schape...@56socketdot.net>
> wrote:
>
> > And this is supposed to be significant how?
>
> Sure, since it differs by a factor of two.
First of all, what you describe or tried to describe was the
"adiabatic gradient" which results from the Earth's self compression
as a result of its gravitational field.
That measured gradients differs from your expected adiabat has nothing
to do with global warming. The crust contains radiogenic heat sources
and the earth's interior is convecting are just two things that render
your conclusions baseless.
Stuart
don findlay
Stuart wrote:
> That measured gradients differs from your expected adiabat has nothing
> to do with global warming. The crust contains radiogenic heat sources
> and the earth's interior is convecting are just two things that render
> your conclusions baseless.
>
> Stuart
("...and the Earth's interior is convecting..." ) That's the
convection driven by subduction due to the sinking oceanic slab
(sinking because the continental lithosphere is forcing it down), ...
- that right, Stuart, eh? ... convection is driven by the sinking
slab being forced down by the continental lithosphere? You might as
well say that the continental lithosphere, just by being there, is
driving convection.
(Up against the ropes and yelling "Hit me, ..Hit me, ...Hit me with
your rythm stick!") ( You really are a mug for punishment, you know.)
David Jonsson
> On Nov 29, 2:10 pm, David Jonsson <davidjonssonswe...@gmail.com>
> wrote:
>
> > On Nov 28, 3:43 pm, Jo Schaper <jonot34schape...@56socketdot.net>
> > wrote:
>
> > > And this is supposed to be significant how?
>
> > Sure, since it differs by a factor of two.
>
> First of all, what you describe or tried to describe was the
> "adiabatic gradient" which results from the Earth's self compression
> as a result of its gravitational field.
Please show.
> That measured gradients differs from your expected adiabat has nothing
> to do with global warming. The crust contains radiogenic heat sources
> and the earth's interior is convecting are just two things that render
> your conclusions baseless.
Show this. What is the equation for heat conduction through the Earth
crust? It is not simply the measured heat gradient multiplied with the
measured heat conduction coefficient. That false equation is used to
determine the heat sources in the globe. Still half the effect is
there so there could still be heat sources and convecting interior.
David
Stuart
wrote:
> On Dec 7, 3:10 am, Stuart <bigdak...@aol.com> wrote:
>
> > On Nov 29, 2:10 pm, David Jonsson <davidjonssonswe...@gmail.com>
> > wrote:
>
> > > On Nov 28, 3:43 pm, Jo Schaper <jonot34schape...@56socketdot.net>
> > > wrote:
>
> > > > And this is supposed to be significant how?
>
> > > Sure, since it differs by a factor of two.
>
> > First of all, what you describe or tried to describe was the
> > "adiabatic gradient" which results from the Earth's self compression
> > as a result of its gravitational field.
>
> Please show.
Show what? Truth be told, I only assumed you were trying in some
odd way to compute the adiabatic gradient.
You're equating the work done on moving a block of matter
in a gravitational field with an equivalent change of heat in the
block.
I don't see why the heat content of the block should change at all.
The work
done on the block in rasing or lowering it, changes its gravipotential
energy, not its heat content or temperature.
Now if that block is under pressure due to the overburden of other
matter in
a gravitational field... different story. Essentially if you have an
adiabatic gradient,
displacing matter up and down, it will still have the same temperature
as its surroundings.
Its not the simply moving up or down, but the change in pressure that
causes matter
in this scenario to change temperature.
You should Google Adams-Williamson equation and adiabatic temperature
gradient.
>
> > That measured gradients differs from your expected adiabat has nothing
> > to do with global warming. The crust contains radiogenic heat sources
> > and the earth's interior is convecting are just two things that render
> > your conclusions baseless.
>
> Show this. What is the equation for heat conduction through the Earth
> crust? It is not simply the measured heat gradient multiplied with the
> measured heat conduction coefficient.
Yeah, but the measured heat gradient will be influenced by the
presence of heat sources,
that are not taken into account in your simple expression.
Your expression is simply not useful for this purpose.
Stuart
David Jonsson
> On Dec 11, 3:58 pm, David Jonsson <davidjonssonswe...@gmail.com>
> wrote:
>
> > On Dec 7, 3:10 am, Stuart <bigdak...@aol.com> wrote:
>
> > > On Nov 29, 2:10 pm, David Jonsson <davidjonssonswe...@gmail.com>
> > > wrote:
>
> > > > On Nov 28, 3:43 pm, Jo Schaper <jonot34schape...@56socketdot.net>
> > > > wrote:
>
> > > > > And this is supposed to be significant how?
>
> > > > Sure, since it differs by a factor of two.
>
> > > First of all, what you describe or tried to describe was the
> > > "adiabatic gradient" which results from the Earth's self compression
> > > as a result of its gravitational field.
>
> > Please show.
>
> Show what? Truth be told, I only assumed you were trying in some
> odd way to compute the adiabatic gradient.
My way is very intuitive. Heat is motion. If moving upwards the motion
decelerate due to gravity. If moving downwards it accelerates. This
means there is a heat gradient.
As you see above in the references to Wikipedia there are different
ways to acheive the "adiabatic" gradient so I was asking you to show
and refer to the one you use.
> You're equating the work done on moving a block of matter
> in a gravitational field with an equivalent change of heat in the
> block.
If there is heat in the block then the parts of the block are moving.
When they move upwards they loose speed and thus temperature and when
they move downwards they gain speed and thus temperature.
> I don't see why the heat content of the block should change at all.
> The work
> done on the block in rasing or lowering it, changes its gravipotential
> energy, not its heat content or temperature.
It does not change spatially as seen from itself as a reference frame.
> Now if that block is under pressure due to the overburden of other
> matter in
> a gravitational field... different story. Essentially if you have an
> adiabatic gradient,
> displacing matter up and down, it will still have the same temperature
> as its surroundings.
No, then you are not using kinetic theory of heat. Any kinetic theory
of heat will have a gradient in an accelerating field like gravity.
> Its not the simply moving up or down, but the change in pressure that
> causes matter in this scenario to change temperature.
That could also have an effect. I have calculated that for air (arXiv)
and water (IWONE 2007) but never for a solid. The only difference for
a solid compared to a fluid would be to use the Young modulus instead
of the bulk modulus but that doesn't seem to be used in geology which
leads to the same expression as for a fluid
thermal volume expansion = 1/V ∂V/∂T
bulk modulus K = −V ∂p/∂V
leads to
∂p/∂T = K (1)
or
∂p = K ∂T (2)
The volumetric force f = - ∇ p in combination with (2) leads to
f = - ∇ p = - ∂p/∂r = - K ∂T/∂r (3)
In acceleration fields with Newton's law F=ma per volume and with
acceleration g
f = g (4)
We now have sufficient data to determine the thermal gradient ∂T/∂r by
combining (3) and (4)
∇T = ∂T/∂r = - g/K
For the crust, granite, it becomes
= 2700 kg/m^3
g = 9.81 m/s^2
K = 44 GPa
= 0.0000085 /K
∇T = ∂T/∂r = - g/K = - 2700 * 9.81/44000000000/0.0000085 = - 0.070 K/
m = - 70 K/km
This figure is 2-3 times more than observed. This calculation actually
shows the required heat gradient to maintain constant density and
volume regardless of depth. Since the volume is decreasing with
increased depth (?) the heat gradient will be smaller.
> You should Google Adams-Williamson equation and adiabatic temperature
> gradient.
I have looked a lot for the adiabatic temperature gradient before.
Adams-Williamson (AW) equation I checked first time today and found
http://rses.anu.edu.au/~hrvoje/PHYS3070/Lecture9.ppt
d/dr = -^2Gm/r^2/K
I can't see how they can use that equation since the value would
depend on the temperature and thus the heat gradient.
What is the accepted value of AW for the crust? I would say there are
additional terms for d/dr which depend on temperature. Alternatively
the AW value fore volume density change could be used in aboves method
to determine the crust heat gradient.
I have found these documents which seems to cover the subject
http://www.geo.cornell.edu/geology/classes/geol388/pdf_files/density.pdf
http://bowfell.geol.ucl.ac.uk/~lidunka/C365/cd/C365/docs/lecture1.htm
> > > That measured gradients differs from your expected adiabat has nothing
> > > to do with global warming. The crust contains radiogenic heat sources
> > > and the earth's interior is convecting are just two things that render
> > > your conclusions baseless.
>
> > Show this. What is the equation for heat conduction through the Earth
> > crust? It is not simply the measured heat gradient multiplied with the
> > measured heat conduction coefficient.
>
> Yeah, but the measured heat gradient will be influenced by the
> presence of heat sources,
> that are not taken into account in your simple expression.
I describe one effect. Sources, if any, would appear as additional
terms.
total gradient = gravitational/adiabatic + source dependent terms +
eventual something more.
Why is the gravitational/adiabatic heat gradient never used for the
solid crust?
David
(I hope Usenet didn't break the formatting and character sets. Check
the original on Google Groups in that case.)
Stuart
wrote:
> On Dec 13, 4:34 am, Stuart <bigdak...@aol.com> wrote:
>
>
>
> > On Dec 11, 3:58 pm, David Jonsson <davidjonssonswe...@gmail.com>
> > wrote:
>
> > > On Dec 7, 3:10 am, Stuart <bigdak...@aol.com> wrote:
>
> > > > On Nov 29, 2:10 pm, David Jonsson <davidjonssonswe...@gmail.com>
> > > > wrote:
>
> > > > > On Nov 28, 3:43 pm, Jo Schaper <jonot34schape...@56socketdot.net>
> > > > > wrote:
>
> > > > > > And this is supposed to be significant how?
>
> > > > > Sure, since it differs by a factor of two.
>
> > > > First of all, what you describe or tried to describe was the
> > > > "adiabatic gradient" which results from the Earth's self compression
> > > > as a result of its gravitational field.
>
> > > Please show.
>
> > Show what? Truth be told, I only assumed you were trying in some
> > odd way to compute the adiabatic gradient.
>
> My way is very intuitive. Heat is motion. If moving upwards the motion
> decelerate due to gravity. If moving downwards it accelerates. This
> means there is a heat gradient.
Your way isn't physcics sorry.
Simply moving an object doesn't cause it to heat up, whether or not
it is in the presence of a gravitational field.
Just because you have derived an equation that is dimensionally
correct, does not make it physcis.
>
> As you see above in the references to Wikipedia there are different
> ways to acheive the "adiabatic" gradient so I was asking you to show
> and refer to the one you use.
It doesn't matter, since what you're doing has nothing to with
the adiabatic gradient.
>
> > You're equating the work done on moving a block of matter
> > in a gravitational field with an equivalent change of heat in the
> > block.
>
> If there is heat in the block then the parts of the block are moving.
> When they move upwards they loose speed and thus temperature and when
> they move downwards they gain speed and thus temperature.
I'm sorry, but you simply do not understand the physics of heat.
Please Google "lattice vibrations phonons" etc. The random vibrations
or motions of the atomic
constituents of an object are not altered by a mere translational
velocity of the object.
If what you said were true, then special relativity what have terms in
relating to the heating
up an object as accelerated close to the speed of light. It doesn't;
as objects move faster and faster
they become more massive, not hotter.
<snip>
I'm sorry but your basic physcis is wrong.
Stuart
David Jonsson
How come this is the case for gases and fluids then?
> > As you see above in the references to Wikipedia there are different
> > ways to acheive the "adiabatic" gradient so I was asking you to show
> > and refer to the one you use.
>
> It doesn't matter, since what you're doing has nothing to with
> the adiabatic gradient.
It is the contemporary for solids.
> > > You're equating the work done on moving a block of matter
> > > in a gravitational field with an equivalent change of heat in the
> > > block.
>
> > If there is heat in the block then the parts of the block are moving.
> > When they move upwards they loose speed and thus temperature and when
> > they move downwards they gain speed and thus temperature.
>
> I'm sorry, but you simply do not understand the physics of heat.
>
> Please Google "lattice vibrations phonons" etc. The random vibrations
> or motions of the atomic
> constituents of an object are not altered by a mere translational
> velocity of the object.
The crust is not in translational motion and I haven't said so either.
The lattice vibrations will increase on the down stroke and slow down
going upwards just like a bouncing ball.
The picture on the top right of this page shows it well.
http://en.wikipedia.org/wiki/Phonon
Imagine gravity to cat sideways in that picture. Vibration would be
affected.
Why would the lattice vibrations be unaffected by gravitation? One
could eventually argue that the atoms in the lattice moves so short
distances that potential energy shift isn't big enough to shift
vibration one or more steps up in it's discreet set of quantum values.
David
brad
> Imagine gravity to cat sideways in that picture. Vibration would be
> affected.
>
> Why would the lattice vibrations be unaffected by gravitation? One
> could eventually argue that the atoms in the lattice moves so short
> distances that potential energy shift isn't big enough to shift
> vibration one or more steps up in it's discreet set of quantum values.
>
>
> - Show quoted text -
another source to look at- THE ORIGIN of the SOLAR SYSTEM, edited by
S.F.Dermott . Terrestrial Planet Evolution and the Observational
Consequences of their Formation. by D. C. Tozer. this book is a
compendium of papers presented at the School of Physics at the
University of Newcastle upon Tyne - 29 March - 9 April 1976.
don findlay
David Jonsson wrote:
>
> > Please Google "lattice vibrations phonons" etc. The random vibrations
> > or motions of the atomic
> > constituents of an object are not altered by a mere translational
> > velocity of the object.
>
> The crust is not in translational motion and I haven't said so either.
> The lattice vibrations will increase on the down stroke and slow down
> going upwards just like a bouncing ball.
>
> The picture on the top right of this page shows it well.
> http://en.wikipedia.org/wiki/Phonon
> Imagine gravity to cat sideways in that picture. Vibration would be
> affected.
Do you see that interesting behaviour as in any way having anything to
do with crystal *growth*?
David Jonsson
> David Jonsson wrote:
>
> > > Please Google "lattice vibrations phonons" etc. The random vibrations
> > > or motions of the atomic
> > > constituents of an object are not altered by a mere translational
> > > velocity of the object.
>
> > The crust is not in translational motion and I haven't said so either.
> > The lattice vibrations will increase on the down stroke and slow down
> > going upwards just like a bouncing ball.
>
> > The picture on the top right of this page shows it well.
> >http://en.wikipedia.org/wiki/Phonon
> > affected.
>
> Do you see that interesting behaviour as in any way having anything to
> do with crystal *growth*?
Since that is another topic I suggest you raise the issue in another
group. I have ideas regarding this as well. If you want the
traditional answer I think you should turn elsewhere. I for example
don't know why they want to study crystal growth in free fall on space
stations. What limit crystal growth is the curvature of space time in
the crystal. I think this idea was first raised by some Russian. You
cannot simply pack atoms in a regular manner if spacetime is curved.
The two dimensional example is like putting squares together in a
slightly curved plane like a parabolic dish. It can be done in a large
dish with small squares but after a while a square cannot simply be
fit and the regular structure is broken. So instead of trying to grow
crystals on space stations orbiting Earth, where the curvature of
space is approximately as high as here., crystals should be grown very
far from matter or between large bodies of matter where curvature is
almost flat. Or it should be done near black holes where curvature is
very high. The curvature is not totally dominant in a crystal lattice
for how atoms or molecules align. Specifically heat gradients change
the curvature in a lattice. Metal hardening and metal fatigue are two
processes where the crystal lattice arrangement is affected. The
hardening process is where there is less tension in a crystal and/or
between crystals. It simply has a size small enough where its space is
sufficiently flat. In metal fatigue the crystals are so big that the
atoms or molecuels don't fit with each other and thus strength of the
material is affected. I investigated some time ago and found that
there are not theories for metal hardening or metal fatigue. It is an
empirical subject only. Curvature in a crystal can be different from
that of empty space. Curvature in a material is affected by heat
gradients and if the gradient is only in one dimension, like it
commonly is since crystal size is so small compared to the
gravitational body, crystal growth shouldn't be affected and curvature
is basically flat.
Now I have just answered your question. The subject should be studied
further especially since it can offer theory to exclusively empirical
sciences of big importance in society. A suitable first start is to
see if crystal size created under small heat gradients can be
explained by the curvature here on Earth. I haven't studied general
relativity so I don't know how big it is. I think a good first start
is to assume that crystals can't be bigger than the distance where the
lattice constant, the distance between atoms, is curved away. If we
assume that the inter atomic distance of say aluminium is according to
http://elements.etacude.com/Si.php
284 pm and the crystals grow to 0.1 mm, based on my experience. Then
we can deduce the curvature of space to be 284 pm / 0.1 mm ~= 3*10^-6
or a curvature radius of (0.1 mm)^2 / 300 pm = 33 m. Is this
reasonable? It seems like curvature in the metal is very much higher
than in air.
More easy is to understand the situation in negative curvature. How
big can the crystal be before the spacing between the lattices become
so big that another lattice fits between? I assume that is the crystal
size.
The more elastic the crystal is the easier it will be coerced to fit
in a crystal even if curvature acts against it.
David
David Jonsson
http://superstruny.aspweb.cz/images/fyzika/astronomy/gravity3d.gif
It is not perfect but the best I could find with Google images. The
atoms are illustrated with the crossings in the black grid. The violet
ball just marks the center.
There is tension and eventual shear in a deformed simple cubic crystal
like this. To deform it to this shape requires energy and weakens it's
strength. On the other hand smaller crystal size would make the
crystal less deformed and thus stronger but on the other hand more
crystals would form and increase the area of weaker binding between
crystals. There should thus be an optimal crystal size for the
strength of the entire material. Metal fatigue is a condition when the
relation is far from optimal. Hardened metals are materials where the
crystal size has become optimal. Metal fatigue contains more internal
energy than hardened materials. The process of hardening is applying
compressing force in a material undergoing thermal expansion. Negative
work is being done on the material. Metal fatigue would then be the
opposite. Either thermal expansion combined with positive pressure or
thermal retraction together with negative pressure would then cause
metal fatigue. In lack of better theories this is how I understand
those phenomena of material strength alterations and gravity or
gravity like effects on crystal formation. This could also apply to
non isotropic pressure volume work and eventually with shear forces
since they also involve volume changes.
Anyone interested in verifying this experimentally is advised to do
the following.
Take a set of wires. Heat them and cool them repeatedly. Let some of
the wires be exposed to forces maximal in the elastic domain of the
wires during cooling and other during heating. On the cooling wires
with maximum force you see that work is being done by the wires. This
energy is being taken from the binding forces between the crystals and
between the atoms.
On the heated wires with maximum force you see that work is being done
on the wires. This work or energy is being added to the binding
energies of the material.
If the heated while loaded wires become weaker after this process then
this theory is supported. These wires would then have metal fatigue.
If the cooled wile loaded wires become stronger after this process
then this theory is supported. These wired would then have been
hardened.
David
don findlay
Well, ..in view of the implications of an expanding/ growing/ getting
bigger Earth it certainly does seem a relevant line of thought .
Thanks for your reply. The questions of crystal nucleation, growth,
and paragenesis are paramount.
josephus
that is faint praise if ever I have heard it. Don is so lame that he
just makes up stuff.
josephus
--
I go sailing in the Summer and
look at STARS in the Winter.
"Everybody is igernant, only on differt subjects"
Will Rogers
"it aint what you know that gets you in trouble
it is what you know that aint so"
Josh Billings.
David Jonsson
atoms in the lattice can only vibrate at certain frequencies due to
quantum mechanical constraints. This would mean that the heat gradient
must be high enough to make a shift for one atom so that it will have
a different temperature at one end of its vibrating motion compared
with the other end. How could temperature otherwise be increased and
heat be made to flow?
Can someone calculate the highest possible non conducting heat
gradient in silicon dioxide, which is the most common component in the
Earth crust, based on the reasoning above?
That heat gradients need a certain size to be conducting is well known
for super fluid helium. In low motion the heat or speed difference
between different fluid particles is not high enough to be
transferred. Thus no transfer of energy nor any viscous effect takes
place.
David
brad
wrote:
> Here is a picture how a crystal would look with curvature.http://superstruny.aspweb.cz/images/fyzika/astronomy/gravity3d.gif
you are mixing concepts. " a crystal is a solid body bounded by PLANE
natural s urfaces, which are the external expression of a regular
internal arrangement of constituent atoms or ions ." ( Elements of
Mineralogy by Mason & Berry ) this regular arrangement is a result
of ionic or covalent bonding . when you speak of crystals deforming
you are displacing the crystal lattice along a cleavage plane . that
is, along a plane where the regular crystalline structure is bonded
generally more weakly to another layer of that same regular
structure . to change the crystal structure ( the regular alignment of
the chemical identity of that crystal ) you must add energy that may
or may not place that chemical identity into a new crystal class. when
you speak of metals you can no longer think of a crystal lattice at
all because metals share all their electrons ( metallic bond ) the
melting point of SiO2 is between 1600 and 1700 C depending on the
crystalline form ( remember SiO2 comes in several varieties) the
boiling point is 2200 to 2600 C . to add more energy breaks the bonds
and releases the constituents altogether .
Aidan Karley
76ad4b...@c33g2000hsd.googlegroups.com>, David Jonsson wrote:
> That heat gradients need a certain size to be conducting is well known
> for super fluid helium.
>
My (admittedly uncertain) knowledge of the properties of HeII is
telling me that, because all the atoms are in the same energy state,
macroscopically they can't be differentiated, and in consequence any
particular body of HeII will have precisely the same temperature. i.e.,
temperature gradient of zero.
A parallel argument can be made for the position of any two atoms
in the body of HeII, leading to the more confidently known property of
superfluidity (bulk flow with zero viscosity).
--
Aidan Karley, FGS,
Aberdeen, Scotland
A light wave is more like a crime wave than a water wave.
David Jonsson
I didn't specifically mean that the curvature would be visible
geometrically.
When I surfed on the subject I saw an article mentioneing measurement
and lattice spacing variation.
The Change in Lattice Spacing at a Crystal Boundary
J. E. Lennard-Jones, Beryl M. Dent
http://links.jstor.org/sici?sici=0950-1207(19281101)121%3A787%3C247%3ATCILSA%3E2.0.CO%3B2-A
Here are similar articles
http://www.iop.org/EJ/article/0370-1298/64/5/305/prav64i5p465.pdf
http://links.jstor.org/sici?sici=0950-1207(19331001)142%3A846%3C237%3ATTEOQB%3E2.0.CO%3B2-1
http://link.aps.org/doi/10.1103/PhysRev.52.613
http://dspace.rri.res.in:8080/dspace/handle/2289/1736
http://www.iop.org/EJ/article/0959-5309/51/3/307/prv51i3p432.pdf
Another thing to investigate in this context is the Casimir force. The
phonons in the crystal can each consist over overtones as shown here
http://en.wikipedia.org/wiki/Image:Phonon_k_3k.gif
A lot of high frequency radiation from the zero point energy can thus
fit for a certain phonon. Maybe they differ just a little as to make
them fitting only for a specific phonon only as big as the crystal. If
the crystal is to big the different wavelenghts don't fit in the same
phonon any more.
David
David Jonsson
gravity on the heat gradient in the earth crust. My latest conclusions
is that the effect is marginal. A brief explanation follows.
If the atoms are connected with spring like structure then there will
be no adiabatic heat gradient. The atom below and above an atom in a
crystal lattice will experience the same impulse from an atom in
between. To imagine crystal structures as atoms connected with springs
between themselves seems common. I can not say if this model is
applicable. If there is some nonlinearity in the spring function F =
f(Δh) (where F is the force on the atom and Δh is the displacement of
the atom) then there will be an adiabatic heat gradient. Δh/a seems to
be maximum 10% in solids where a is the spacing between atoms in a
crystal. If nonlinearity is assumed to maximal there would only be
force interaction between atoms at the points of maximum of one atoms
displacement. That would imply a maximal adiabatic non conducting heat
gradient of only one tenth of the one i initially suggested. It seems
like this effect is marginal after all but i still think solid stats
physicists should calculate it.
Due to the similarity between solids and fluids I would even question
if there is any noticeable adiabatic heat gradient in fluids.
David
Crown-Horned Snorkack
> I have done some progress on the initial issue on the effect from
> gravity on the heat gradient in the earth crust. My latest conclusions
> is that the effect is marginal. A brief explanation follows.
>
> If the atoms are connected with spring like structure then there will
> be no adiabatic heat gradient. The atom below and above an atom in a
> crystal lattice will experience the same impulse from an atom in
> between. To imagine crystal structures as atoms connected with springs
> between themselves seems common. I can not say if this model is
> applicable. If there is some nonlinearity in the spring function F =
> the atom) then there will be an adiabatic heat gradient. Äh/a seems to
> be maximum 10% in solids where a is the spacing between atoms in a
> crystal. If nonlinearity is assumed to maximal there would only be
> force interaction between atoms at the points of maximum of one atoms
> displacement. That would imply a maximal adiabatic non conducting heat
> gradient of only one tenth of the one i initially suggested. It seems
> like this effect is marginal after all but i still think solid stats
> physicists should calculate it.
>
> Due to the similarity between solids and fluids I would even question
> if there is any noticeable adiabatic heat gradient in fluids.
>
or solid.
Consider a gas where Maxwell distribution holds. And place it in a
gravity field.
The gas at the bottom has high pressure and density, and some average
temperature and energy per molecule. Some molecules have a low energy,
some higher.
As the molecules rise up against the field of gravity, they all lose
energy. But the molecules which had the least energy lose their energy
altogether - and fall back down.
So, the higher you go, the lower the density and pressure of the gas
will be. But while the molecules with least energy fell down, those
with higher energy lose some of their energy. The result is that in a
Maxwell distribution where all molecules are free to rise and fall,
the average energy of molecules, their distribution and their density
is independent of height. The total density of molecules decreases but
temperature stays unchanged.
Now, if you try to lift a parcel of gas collectively, so that the less
energetic molecules cannot fall back down past the more energetic
molecules then yes, the temperature will fall as the parcel rises.
Instead of falling back down, the less energetic molecules collide
with the more energetic ones and take their energy away.
If you heat the floor of a room, hot air rises up and heats the whole
room by convection - but the ceiling will be slightly colder than
floor because of adiabatic cooling. But if you heat the ceiling, hot
air stays at the ceiling. It will not sink to the floor and heat the
floor.
Now, in addition to convection, there is conduction. Much slower
process. But if you put something hot on top of something cold, heat
eventually conducts downwards as well. The process only ends when the
temperature is equalized. Likewise, then something warm is below and
slightly cooler is above, and the temperature gradient is equal or
smaller than adiabatic gradient, slow conduction of heat will continue
instead of the fast conduction, but eventually the temperature
differences become zero. This applies to gases, liquids and solids
all.
David Jonsson
wrote:
>
> Actually, gravity does not cause a temperature gradient in gas, liquid
> or solid.
I can not accept what you say. The adiabatic heat gradient is too
established and reasonable in gaseous media.
I still have some thoughts about it. What happens if we have a solid
like a kilometre long silver pillar up in the air. It would not have
the gradient and when it experience the adiabatic heat gradient from
the surrounding air it should start to conduct heat. Simultaneously
the air temperature would be cooled down by the pillar in the bottom
and heated up at the top. What would the stationary condition be?
Equivalently the air in a bore hole in the Earth crust would
experience the gradient. I wonder if all those measurements of the
heat gradient in bore holes have taken this effect into consideration.
The adiabatic heat gradient of air in a bore hole would be (see above
for derivation) ∇T = gravitational acceleration / specific heat
capacity = g / c = 9.81/1000 = 0.01 K/m = 10 K/km which is very close
to the measured value of 25 K/km. Could this mean that the real heat
gradient in the crust is only 15 K/km? This would also lower the heat
conduction through the crust and the total heat generated in the Earth
interior to about 60% of the currently assumed value. At 25 K/km the
Earth is said to conduct 75 mW/m². At 15 K/km it would conduct 45 mW/
m². This value is important in determining global heating.
David
David Jonsson
> or solid.
I can not accept what you say. The adiabatic heat gradient is too
established and reasonable in gaseous media.
I still have some thoughts about it. What happens if we have a solid
like a kilometre long silver pillar up in the air. It would not have
the gradient and when it experience the adiabatic heat gradient from
the surrounding air it should start to conduct heat. Simultaneously
the air temperature would be cooled down by the pillar in the bottom
and heated up at the top. What would the stationary condition be?
Equivalently the air in a bore hole in the Earth crust would
experience the gradient. I wonder if all those measurements of the
heat gradient in bore holes have taken this effect into consideration.
The adiabatic heat gradient of air in a bore hole would be (see above
for derivation) ∇T = gravitational acceleration / specific heat
capacity = g / c = 9.81/1000 = 0.01 K/m = 10 K/km which is very close
to the measured value of 25 K/km. Could this mean that the real heat
gradient in the crust is only 15 K/km? This would also lower the heat
conduction through the crust and the total heat generated in the Earth
interior to about 60% of the currently assumed value. At 25 K/km the
Earth is said to conduct 75 mW/m². At 15 K/km it would conduct 45 mW/
m². This value is important in determining global heating.
David
--
David Jonsson
Sweden
phone callto:+46703000370