| Topic: |
Science > Physics |
| User: |
"Uno Lapideus" |
| Date: |
29 Aug 2006 07:07:49 AM |
| Object: |
Entropy confusion, please help! |
Trying to explain entropy to kids, I find that I need some help with
understanding the concept... The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
Intuitively, I think of the atoms in a white-hot piece of iron as
"moving more randomly" than does the atoms in a piece of iron that
has been in a freezer for a few days. Likewise, I think of the state of
affairs immediately following the "big bang" as a whole lot more
chaotic than the absolute thermal uniformity of a Universe that, some
time far in the distant future, has reached "absolute equilibrium"
Obviously, my thinking is flawed. Can someone please help me get this
entropy stuff straight?
Many thanks in advance,
Uno
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| User: "Sorcerer" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 08:31:31 AM |
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"Uno Lapideus" <henry@microtechnonstop.com> wrote in message
news:1156853269.106702.219230@h48g2000cwc.googlegroups.com...
| Trying to explain entropy to kids, I find that I need some help with
| understanding the concept... The second law of thermodynamics is
| usually stated as "Heat (energy) flows from higher temperature
| objects to lower temperature objects, until thermal equilibrium is
| reached" (please correct me if I'm wrong here...), sometimes as
| "in a closed system, entropy (a measure of disorder) will always
| increase" and sometimes as "natural processes cause things to move
| from improbable and unstable orderly states (less entropy) to probable
| and stable disorderly states (more entropy)."
| Now, for example, is not ice (water crystals) a "stable and
| ordered" form, liquid water a a more random form, and steam the most
| chaotic form, of H2O molecule "order"? I also remember reading
| somewhere that "entropy is zero in an object that has no thermal
| motion, such as a fictitious crystal at 0 K"...
| This is where I find confusion: Since heat indeed flows from hotter to
| colder objects , it seems to me that, at least in the water example,
| entropy goes from higher to lower... And if "absolute zero" is
| where we find the highest form of order (zero entropy), isn't
| universal entropy running from maximum disorder (big bang, with its
| very high temperature) towards minimum disorder (the absolute zero
| "heat death" of a completely "run dowm" Universe)?
| Intuitively, I think of the atoms in a white-hot piece of iron as
| "moving more randomly" than does the atoms in a piece of iron that
| has been in a freezer for a few days. Likewise, I think of the state of
| affairs immediately following the "big bang" as a whole lot more
| chaotic than the absolute thermal uniformity of a Universe that, some
| time far in the distant future, has reached "absolute equilibrium"
| Obviously, my thinking is flawed. Can someone please help me get this
| entropy stuff straight?
| Many thanks in advance,
| Uno
Obviously crystalline ice is a more "ordered" system than water,
water is a more "ordered" system than steam (water has a surface,
a globule of water in a weightless environment is spherical), clouds
(water vapour, or low temperature steam) are shapeless.
Heat is really the motion of the molecules and will spread randomly,
so that fast molecules (hot) will transfer that energy to slow molecules
(cold) until equilibrium is reached and all the molecules have
approximately the same speed. However, with a phase change
such as water becoming ice the molecules have so little energy
that they can clump together, and once clumped they stay clumped,
hence snowflakes. However, the formation of snowflakes is not
a closed system, heat is lost (kinetic energy is transferred) to
the surrounding nitrogen and oxygen (air). The formation of the
snowflake (ice crystal) is really a result of vibration when there
was still sufficient energy for the vibration to occur, built upon
a dust mote, and it is that energy that gave the flake the order.
If you take a clean bucketful of virgin snow and melt it, you'll
see that it is "dirty", i.e. contains the dust particles around which
the snow formed.
The globular form of ice is called hail and lacks the crystalline
structure of the snowflake.
As to the big bang, there is no evidence to support such a crackpot
theory. The red shift of distant galaxies is a function of distance and
that is ALL the empirical data tells us. Assuming it is the result of
velocity is conjecture only, there are other explanations.
Androcles' Paradox:
If the galaxy is further away then it has greater red shift, and if
we attribute that to velocity then we are compelled to conclude
that galaxies are not merely moving away from us (expansion)
but they are *accelerating* as well, and that makes us unique,
being at the centre.
Androcles.
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| User: "kunzmilan" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 09:31:29 AM |
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Another argument. What was disordered before big bang?
We have elementary particles, atoms, molecules. Atoms arise from
elementary particles,
molecules from atoms. Spontaneously. Elementary particles are less
complicated than atoms, atoms are less complicated than molecules. We
can continue, molecules are less complicated than cells, cells are
less complicated than whole organisms.
This "complication" can be measured by symmetry elements, their number
and order.
Entropy is just the logarithmic measure of symmetry. This is the
original Boltzmann's idea, he only used instead of the term "symmetry"
the term "probability". Since probability is determined by symmetry,
his slip was not great, but it had great consequencies. At 0^0 K (no
thermal motion and no quantas of thermal energy), we have only one
element of symmetry, the identity, and the entropy is zero. If energy
of thermal motion grows, there are more possible states, how the
energy is distributed between molecules, and the entropy grows.
kunzmilan
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| User: "Uno Lapideus" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 09:00:56 AM |
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Thanks, Androcles (Sorcerer?)!
What you wrote makes sense.
Do you have any comments on the "zero entropy at 0K" statement? I
"know" that absolute zero is not possible to reach, but if we assume
some ideal crystal actually being completely without thermal activity
(0K), what can be said about the entropy of the crystal structure
(system)?
Cheers,
Uno
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| User: "Sorcerer" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 11:02:29 AM |
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|
"Uno Lapideus" <henry@microtechnonstop.com> wrote in message
news:1156860056.421242.298900@74g2000cwt.googlegroups.com...
| Thanks, Androcles (Sorcerer?)!
| What you wrote makes sense.
| Do you have any comments on the "zero entropy at 0K" statement? I
| "know" that absolute zero is not possible to reach, but if we assume
| some ideal crystal actually being completely without thermal activity
| (0K), what can be said about the entropy of the crystal structure
| (system)?
| Cheers,
| Uno
Physical laws are mathematical generalizations and do not
apply to special cases.
Entropy is a general observation about how the system will change,
in other words hot spreads out to cold and reaches equilibrium
throughout the closed system, but in its frozen state equilibrium
has been reached. There can be no change without an energy input,
and if there is an energy input then the system is not closed and is no
longer at 0K.
From Boyle's law, PV= constant and from Charles's law, V/T = constant,
hence mathematically the volume of a gas at constant pressure at 0K
is zero. But... since there are no gases at 0K, so it makes no sense to
say the volume of the gas is zero, physically. The gas will change
state to liquid before it reaches 0K, and the gas laws no longer apply
and never did to liquids or solids anyway.
Similarly, the permittivity and permittivity of a material has a value,
but the permeability and permittivity of vacuum is meaningless.
Thus if the speed of light in glass is controlled by the properties
of the glass, that does NOT imply that vacuum can control the speed
of light. Hence Maxwell's laws are mathematical generalizations
which do not apply when a parameter such as permeability is removed.
Some people think that 1/0 = infinity, but that is false. Division
by zero is undefined.
Examples are V/T = k, a constant can never be infinity,
and Doppler's equation for a sonic boom,
f' = f. c/(c-v), where v = c.
The new frequency is not infinite, it is undefined. Meaningless,
in fact. A sonic boom is all the sound energy emitted from the plane
arriving at an instant along with the plane, but it cannot be MORE
energy than was emitted.
In other words the equation is fine for all values except zero.
Androcles
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| User: "Mpilot" |
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| Title: Re: Entropy confusion, please help! |
02 Sep 2006 02:30:44 AM |
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An alternative way to explain entropy in a simple way is with
Information Theory.
There is a strong conncection between the number and probability of
states in an Information System and a Physical System. The founder of
the Physical Entropy Concept (Boltzmann) and the founder of Information
Theory (Shannon) both define the complexity / entropy of a system as a
quantitative measure of the number and probability of different states
a Physical / Information, where the Entropy in Bits = k.ln(2) Joule /
Kelvin Physical Entropy. On the URL www.mdpi.org/entropy a lot of
examples of this concept can be found. On the URL
http://www.ma.utexas.edu/mp_arc/c/06/06-237.pdf you can find a recent
short paper in which these principles are applied to theoretically
derive Boltzmann's Entropy Law, based on Quantum Theory only.
Uno Lapideus wrote:
Trying to explain entropy to kids, I find that I need some help with
understanding the concept... The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
Intuitively, I think of the atoms in a white-hot piece of iron as
"moving more randomly" than does the atoms in a piece of iron that
has been in a freezer for a few days. Likewise, I think of the state of
affairs immediately following the "big bang" as a whole lot more
chaotic than the absolute thermal uniformity of a Universe that, some
time far in the distant future, has reached "absolute equilibrium"
Obviously, my thinking is flawed. Can someone please help me get this
entropy stuff straight?
Many thanks in advance,
Uno
.
|
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| User: "kunzmilan" |
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| Title: Re: Entropy confusion, please help! |
03 Sep 2006 03:31:13 AM |
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If we try to explain entropy, we should made it, as Boltzmann did. He
used a very simple example, which should be solved by all students of
thermodynamics.
Let's have 7 molecules which distribute between them 7 quantas of
velocities by collisions. We can suppose that at first, only one
molecule a(7) is moving. When it collide with another immobile molecule
b(0), the results can be
a(7) + b(0) = a(6) + b(1) till
a(7) + b(0) = a(0) + b(7)..
These states are described and counted by partitions:
(7,0,0,0,0,0,0) till
(1,1,1,1,1,1,1), at all 15 possible partition orbits.
The first partition has 7 equivalent states, (7,0,0,0,0,0,0) till
(0,0,0,0,0,0,7). The last partition only one state. The largest orbit
corresponds to the partition (3,2,1,1,0,0,0). Its volume is calculated
by its symmetry, measured by the polynomial coefficient 7!/3!2!1!1!,
where the term 3! corresponds to 3 molecules with zero motion.
The system will fall spontaneously from the original state orbit onto
the largest orbit, where it has the most degrees of freedom.
If we add new quantas of motion, there will appear new larger orbits,
since partitions of larger numbers n grows faster than n itself. The
phase space will be simply truncated.
The entropy measure H is the logarithmic measure of symmetry. Since
both Boltzmann constant and Avogadro number are rather large numbers,
the rough Stirling approximation of n! is convenient.
The attempt to replace Boltzmann by Shannon with his axiomatic approach
is void.
(7,0,0,0,0,0,0) till
(1,1,1,1,1,1,1),
is simply
(a,a,a,a,a,a,a) till
(a,b,c,d,e,f,g).
The first partition has only one equivalent state 7!/7!, the last one
7!/(1!)^7 states, since it has the least redundancy. The symmetry of
messages is measured by another polynomial coefficient.
Both coefficients are multiplicative. Simply multiply (a+b+c+d+e+f+g)^7
and find the products of both polynomial coefficients for all orbits
(7,0,0,0,0,0,0) = 7*1 ...
(3,2,1,1,0,0,0) = 420*420
till
(1,1,1,1,1,1,1) = 1*7!
The sum is 7^7.
Orbits can be seen simply in the products (a+b+c)^m.
Information entropy is maximal, if each symbol is used only once, or
all twice, etc..
The observed distribution of velocities of molecules has another shape.
kunzmilan
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| User: "=?UTF-8?Q?Jeff=E2=80=A6Relf?=" |
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| Title: A more compressed File/Star has denser Information/_Neg_Entropy. |
03 Sep 2006 03:37:29 PM |
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Hi Uno_Lapideus, You wondered how to explain entropy to kids;
and, indirectly, about information theory.
Tell your kids: " Everything eventually dissipates. "
Or, if they gamble, say: " The house always wins in the end. "
If the sun were fully dissipated, becoming a perfect vacuum,
all information ( i.e. all contrast with space ) would be lost, not gained.
Likewise, our universe is getting cooler and thinner, increasing entropy.
The use of the word entropy in information theory is Ass_Backwards !
Entropy is contrast, _Not_ gaussianity ( not pseudorandomness ).
At absolute zero, an ideal vacuum contains no information ( i.e. no contrast ).
Negentropy is how much Gibbs_Free_Energy can be lowered by ignition.
A more compressed File/Star has denser Information/_Neg_Entropy.
Yet, having less redundancies ( or more contrast with a vacuum ),
it's more gaussian ( i.e. more pseudorandom ).
Ignoring the liquid water definition of life, this is how I model life:
Vices are just different ways to burn out ( and all things burn out ).
They're ok ( to a point ), because they're a celebration of life;
but which ones get condoned ( e.g. sex, gasoline and reproduction ) and
which ones don't ( e.g. smoking ) is a _Soft_ ( pseudorandom ) science.
Each is imprisoned in a virtual casino... the house always wins in the end.
Like you're both God _And_ Devil ( i.e. " God/Devil " )
to the animals and plants you raise to feed yourself
( i.e. like you punish and reward them, to control them ),
you're a God/Devil's tenant and a God/Devil to your tenants.
Negentropy ( consumable Gibbs_Free_Energy ) is the top God/Devil
because, like a lit match, consumption
both creates and destroys all that ever was.
Although control is the goal, it's a mirage.
Time is pseudo-directional ( i.e. spatial )
because, like a dice toss is known to be pseudorandom ( i.e. causal ),
all randomness is pseudorandom.
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| User: "Henning Makholm" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 08:48:04 AM |
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Scripsit "Uno Lapideus" <henry@microtechnonstop.com>
The second law of thermodynamics is usually stated as "Heat (energy)
flows from higher temperature objects to lower temperature objects,
until thermal equilibrium is reached" (please correct me if I'm
wrong here...),
It is so oversimplified that it is almost false, and certainly not
useful as a definitive statement of the second law.
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"?
Yes.
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower...
No. The cold object that heat flows to gains entropy, but the hot
object that heat flows _from_ loses entropy. The second law says that
the the cold object will gain more entropy that the hot one loses.
A system where temperatures differ from place to place has less
_total_ entropy than one in which everything is at equilibrium
(assuming that everything else is equal, i.e. same total energy
content and so forth).
And if "absolute zero" is where we find the highest form of order
(zero entropy), isn't universal entropy running from maximum
disorder (big bang, with its very high temperature) towards minimum
disorder (the absolute zero "heat death" of a completely "run dowm"
Universe)?
No, that is a misunderstanding of the heat death. The heat-dead
universe does not end up with zero temperature everywhere, just with
the _same_ temperature everywhere. That temperature will be rather
cold, but still warmer than the coldest regions of the present
universe.
Likewise, I think of the state of affairs immediately following the
"big bang" as a whole lot more chaotic than the absolute thermal
uniformity of a Universe that, some time far in the distant future,
has reached "absolute equilibrium"
Here it gets hard. As far as I have understood, the answer is that the
universe right after the big bang did have a fair amount of disorder
regarding the _movement_, but back then there wasn't much space to be
disorderly _in_, so the _position_ of things was fairly constrained,
leading to a very low entropy all in all.
--
Henning Makholm "What the hedgehog sang is not evidence."
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| User: "kunzmilan" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 11:36:51 AM |
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Entropy measures symmetry on the molecular level. It can be supposed
that there are similar laws for higher levels of organization. Kinetic
energy of molecules in equilibrium state (highest entropy) is described
by the normal distribution. This distribution is observed not only at
molecules. Solar system is an example of a system in practical
equilibrium. Temperature is not its integrating factor. Molecules in
equilibrium do not have all one velocity. Why should have all
macroscopic objects some same temperature?
kunzmilan
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| User: "noshellswill" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 01:28:00 PM |
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On Tue, 29 Aug 2006 15:48:04 +0200, Henning Makholm wrote:
<clip>
Likewise, I think of the state of affairs immediately following the
"big bang" as a whole lot more chaotic than the absolute thermal
uniformity of a Universe that, some time far in the distant future,
has reached "absolute equilibrium"
Here it gets hard. As far as I have understood, the answer is that the
universe right after the big bang did have a fair amount of disorder
regarding the _movement_, but back then there wasn't much space to be
disorderly _in_, so the _position_ of things was fairly constrained,
leading to a very low entropy all in all.
HM:
Penrose ( R2R ) does NOT this size/entropy_increase explanation at all.
Surely, I'll be ---NOT EVEN WRONG--- in presenting his view, but ... he
appears to divide entropy contributions into those of Weyl_geometry [ a
huge spacial curvature contributor , and zero at t==0 ) ] and a tiny
entropy contributed by photons/particles.
The enlarging phase_space available to photons ( as the universe expands
) remains insignificant compared to Weyl entropy.
**REM** Somebody kindly -- who knows what they are talking about -- set
out this issue conflict clearly.
nss
**********
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| User: "Mpilot" |
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| Title: Re: Entropy confusion, please help! |
04 Sep 2006 05:01:19 AM |
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To explain Entropy to kids, Information Diagrams are a good means.
There is a 1-1 correspondence between Entropy Measures an Set Theory.
Therfore, it is valid to use an Information Diagram, which is a
variation of a Venn Diagram, to represent the Entropy of an Object an
the relationship between the Entropy of more Objects. In any good
Introduction to Information Theory, Information Diagrams are explained.
Uno Lapideus wrote:
Trying to explain entropy to kids, I find that I need some help with
understanding the concept... The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
Intuitively, I think of the atoms in a white-hot piece of iron as
"moving more randomly" than does the atoms in a piece of iron that
has been in a freezer for a few days. Likewise, I think of the state of
affairs immediately following the "big bang" as a whole lot more
chaotic than the absolute thermal uniformity of a Universe that, some
time far in the distant future, has reached "absolute equilibrium"
Obviously, my thinking is flawed. Can someone please help me get this
entropy stuff straight?
Many thanks in advance,
Uno
.
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| User: "Andy Resnick" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 02:04:13 PM |
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|
Uno Lapideus wrote:
Trying to explain entropy to kids, I find that I need some help with
understanding the concept...
You and me, both. Entropy can be thought of as either "energy not
available for useful work", or "a measure of information/randomness",
and probably a few other things.
The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
So far, so good. Entropy is related to the flow of heat via the second
law of thermodynamics. When you speak of "probable" and "disorderly"
states, you are no longer talking about thermodynamics, but statistical
mechanics, the foundation of thermodynamics. And statistical things
(like the state of a system) are subject to fluctuations, and so it is
possible that some fluctuations will decrease the entropy. The two
pictures are not contradictory- in terms of statistical mechanics, there
may be short times when heat flows from the cold object to the hot
object. With a probability similar to that of a broken egg
spontaneously re-assembling.
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
I see the source of your confusion- the entropy of a system depends on a
lot more than just the temperature. The entropy of a crystal is indeed
lower than that of a fluid, but that's partially due to the difference
in temperature, and partially due to the volume available to each
particle, and partially due to the freedom each particle has to move- I
can exchange two particles in a fluid and you would never know, but if I
change particles around in a crystal (like a binary alloy, or a spin
lattice), I need to be more careful. In terms of statistical mechanics,
the entropy is related to the number of (un-measurable) 'microstates'
which all give the same (measureable) 'macrostate'.
A uniform vapor has a high entropy because the macrostate (a volume of
vapor) corresponds to an untold number of microstates (specifying the
position and velocity of each particle in the vapor), not because it is
'hot'.
Does that help?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "Uno Lapideus" |
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| Title: Re: Entropy confusion, please help! |
30 Aug 2006 12:33:13 AM |
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Andy Resnick wrote:
A uniform vapor has a high entropy because the macrostate (a volume of
vapor) corresponds to an untold number of microstates (specifying the
position and velocity of each particle in the vapor), not because it is
'hot'.
Andrew,
Thanks for your informative response!
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Still confused...
Uno
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| User: "Mpilot" |
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| Title: Re: Entropy confusion, please help! |
30 Aug 2006 03:55:17 AM |
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|
Entropy is simple an extensive measure of the level number of the
energy state of a system.
Quantum mechanics predicts that a system can be in either one of states
where n=1,2...n numerates the energy level.
Now suppose we do the following experiment. We take two identical
systems (the same number of molecules, temperatures, presuures, volumes
etc) and combine them into one system. The question now is: What
happens to the energy level n. Any monotonous function of n can be used
to distingish netween the energy levels n. The question now is: Does an
extensive function S(n) exist ? In other words: Does a function S of n
exist such that in the above experiment we have S -> 2S ? If such a
function exists is it unique ? The answer to both questions is YES and
this is the Entropy function S(n).
This Entropy function S(n) can be theoretically be derived from quantum
theory to have the form S = c + k.ln(n), where c and k are constants.
So the entropy is nothing more than a quantum theoretically derived
extensive measure of the energy level n of a system.
Uno Lapideus wrote:
Andy Resnick wrote:
A uniform vapor has a high entropy because the macrostate (a volume of
vapor) corresponds to an untold number of microstates (specifying the
position and velocity of each particle in the vapor), not because it is
'hot'.
Andrew,
Thanks for your informative response!
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Still confused...
Uno
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| User: "" |
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| Title: Re: Entropy confusion, please help! |
30 Aug 2006 12:42:55 PM |
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Uno Lapideus <henry@microtechnonstop.com> wrote:
[...]
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Part of the problem is that the picture of entropy as "disorder,"
while sometimes useful, can also be misleading. "Order" here has
a technical meaning -- it is, roughly, a count of the number of
microscopic physical states that can give the same macroscopic state
-- and it may not have much connection to our intuitive picture of
what looks "orderly."
In this particular case, a galaxy certainly seems more ``ordered''
than a cloud of gas. But if you sit down and do the calculation
you'll find that the actual entropy of a group of stars (plus the
radiation emitted during the gravitational collapse of the cloud
of gas) is *greater* than the entropy of the cloud before collapse.
This is a consequence of some very counterintuitive features of
self-gravitating systems: for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness''). If you insist on
thinking of entropy as ``disorder,'' you're stuck with a picture
in which a star or a galaxy is less orderly than a diffuse cloud of
gas.
For the spherically symmetric case (a star rather than a whole
galaxy), the calculation was first done by Antonov, published in
Vest. Leningrad Univ. 7 (1962) 135; there's a translation in IAU
Symposium 113 (1995) 525. The computation was repeated and
elaborated by Lynden-Bell and Wood, Mon. Not. R. Astr. Soc.
138 (1968) 495. There's a nice summary in a talk by Lynden-Bell,
which you can obtain at http://arXiv.org/abs/cond-mat/9812172 .
For a quick reference, see the beginning of chapter 5 of Zeh's
book _The Physical Basis of the Direction of Time_.
Steve Carlip
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| User: "Edward Green" |
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| Title: Re: Entropy confusion, please help! |
30 Aug 2006 08:08:13 PM |
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wrote:
Uno Lapideus <henry@microtechnonstop.com> wrote:
[...]
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Part of the problem is that the picture of entropy as "disorder,"
while sometimes useful, can also be misleading. "Order" here has
a technical meaning -- it is, roughly, a count of the number of
microscopic physical states that can give the same macroscopic state
-- and it may not have much connection to our intuitive picture of
what looks "orderly."
In this particular case, a galaxy certainly seems more ``ordered''
than a cloud of gas.
It is, even thermodynamically. It is the the _net_ effect including
the role of the radiation bath which is "less ordered", as you say.
But if you sit down and do the calculation
you'll find that the actual entropy of a group of stars (plus the
radiation emitted during the gravitational collapse of the cloud
of gas) is *greater* than the entropy of the cloud before collapse.
This is a consequence of some very counterintuitive features of
self-gravitating systems <...>
Or not. Systems contrive to increase their overall entropy by partial
condensation all the time. Should we be more bemused by the galaxy
than we are by the condensation of steam into water droplets? Doesn't
that reduce configurational entropy?
<crank mode on>
I'll have to ghost of Feynman come back and enunciate this. _Then_
you'll stroke your chin and go "hmm...", sir!
<crank mode off>
<...> for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness'').
The flow of heat from hot areas to cold areas increases the entropy of
the cold area and decreases the entropy of the hot area, but always
increases the entropy of the cold area more. That's why the heat flows
in the first place. Spontaneous condensation follows a similar
calculus, with decrease in configuration entropy taking the place of
decrease in entropy of the hot side.
I'm not sure what this has to do with "negative heat capacity".
If you insist on
thinking of entropy as ``disorder,'' you're stuck with a picture
in which a star or a galaxy is less orderly than a diffuse cloud of
gas.
Possibly true, but a different semantic problem than the one just
addressed.
For the spherically symmetric case (a star rather than a whole
galaxy), the calculation was first done by Antonov, published in
Vest. Leningrad Univ. 7 (1962) 135; there's a translation in IAU
Symposium 113 (1995) 525. The computation was repeated and
elaborated by Lynden-Bell and Wood, Mon. Not. R. Astr. Soc.
138 (1968) 495. There's a nice summary in a talk by Lynden-Bell,
which you can obtain at http://arXiv.org/abs/cond-mat/9812172 .
For a quick reference, see the beginning of chapter 5 of Zeh's
book _The Physical Basis of the Direction of Time_.
One might draw the impression from your citations that this is some
effect peculiar to the condensation of stars and galaxies, whereas the
overall accounting is analogous to the condensation of water on your
windowpane. Chiefly there is a difference of scale, with gravity
taking the role of the attractive portion of the intermolecular
potentials. Not as impressive, and so mundane.
I'm not sure any of this directly addresses the OP's question, though.
.
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| User: "" |
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| Title: Re: Entropy confusion, please help! |
31 Aug 2006 04:18:21 PM |
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Edward Green <spamspamspam3@netzero.com> wrote:
carlip-nospam@physics.ucdavis.edu wrote:
Uno Lapideus <henry@microtechnonstop.com> wrote:
[...]
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Part of the problem is that the picture of entropy as "disorder,"
while sometimes useful, can also be misleading. "Order" here has
a technical meaning -- it is, roughly, a count of the number of
microscopic physical states that can give the same macroscopic state
-- and it may not have much connection to our intuitive picture of
what looks "orderly."
In this particular case, a galaxy certainly seems more ``ordered''
than a cloud of gas.
It is, even thermodynamically. It is the the _net_ effect including
the role of the radiation bath which is "less ordered", as you say.
It depends on what you mean by "radiation bath." Start, for example,
with a collection of gravitating particles with no other interactions
and with nothing else present (in particular, no electromagnetism).
If the initial configuration is dense enough, the collection will
evolve into a tight spherical cluster plus a few particles ejected
off into space at high speeds. If you count these ejected particles
as "radiation," you're right.
But if you sit down and do the calculation
you'll find that the actual entropy of a group of stars (plus the
radiation emitted during the gravitational collapse of the cloud
of gas) is *greater* than the entropy of the cloud before collapse.
This is a consequence of some very counterintuitive features of
self-gravitating systems <...>
Or not. Systems contrive to increase their overall entropy by partial
condensation all the time. Should we be more bemused by the galaxy
than we are by the condensation of steam into water droplets? Doesn't
that reduce configurational entropy?
There are certainly similarities, but also big diffeernces. In
particular...
<...> for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness'').
The flow of heat from hot areas to cold areas increases the entropy of
the cold area and decreases the entropy of the hot area, but always
increases the entropy of the cold area more. That's why the heat flows
in the first place. Spontaneous condensation follows a similar
calculus, with decrease in configuration entropy taking the place of
decrease in entropy of the hot side.
In normal situations, heat flows from a hot area to a cold area,
cooling the hot area and warming the cold area until equilibrium
is reached. In a system with negative heat capacity, heat flowing
out of the hot area makes the hot area *hotter*, so there's no
equilibrium. This leads to a runaway situation ("gravothermal
catastrophe"), with highly inhomogeneous outcome that doesn't
look "ordered" at all. Note also that this implies that any
homogeneous state, even in contact with a large heat bath, is
unstable.
[...]
One might draw the impression from your citations that this is some
effect peculiar to the condensation of stars and galaxies, whereas the
overall accounting is analogous to the condensation of water on your
windowpane. Chiefly there is a difference of scale, with gravity
taking the role of the attractive portion of the intermolecular
potentials. Not as impressive, and so mundane.
Lynden-Bell has proposed that all first order phase transitions
involve negative specific heats at the molecular level. See
rxiv.org/abs/cond-mat/9812172.
Steve Carlip
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| User: "Edward Green" |
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| Title: Re: Entropy confusion, please help! |
31 Aug 2006 06:10:16 PM |
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wrote:
Edward Green <spamspamspam3@netzero.com> wrote:
wrote:
In this particular case, a galaxy certainly seems more ``ordered''
than a cloud of gas.
It is, even thermodynamically. It is the the _net_ effect including
the role of the radiation bath which is "less ordered", as you say.
It depends on what you mean by "radiation bath." Start, for example,
with a collection of gravitating particles with no other interactions
and with nothing else present (in particular, no electromagnetism).
If the initial configuration is dense enough, the collection will
evolve into a tight spherical cluster plus a few particles ejected
off into space at high speeds. If you count these ejected particles
as "radiation," you're right.
If there is nothing else around, that will have to do. ;-)
I'll claim that I didn't mean to require the necessity of radiation:
anyway, this gravitational behavior is nicely modeled by an isolated
constant volume system containing a quantity of water molecules, of an
internal energy such that its equilibrium state is a two phase (liquid
and gas) system. Supposing the system is for some reason initially in a
single non-equilbrium fluid phase, it can spontaneously evolve into a
"tight cluster" of molecules (the liquid phase) plus "a few particle
ejected off into space at high speeds" (the vapor phase).
Don't get me wrong -- I think this is probably a very elegant
demonstration of condensation in a many particle system whose
attractive force is gravity rather than intermolecular potentials,
complete with a "vapor phase" in equilibrium with the "condensed
phase"! But on the flip, reductionist, side, I'd still argue that we
have shown the essential simularity to the condensation we know at
home, rather than some unprecdented feature of large gravitational
systems.
But if you sit down and do the calculation
you'll find that the actual entropy of a group of stars (plus the
radiation emitted during the gravitational collapse of the cloud
of gas) is *greater* than the entropy of the cloud before collapse.
This is a consequence of some very counterintuitive features of
self-gravitating systems <...>
Or not. Systems contrive to increase their overall entropy by partial
condensation all the time. Should we be more bemused by the galaxy
than we are by the condensation of steam into water droplets? Doesn't
that reduce configurational entropy?
There are certainly similarities, but also big diffeernces. In
particular...
<...> for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness'').
The flow of heat from hot areas to cold areas increases the entropy of
the cold area and decreases the entropy of the hot area, but always
increases the entropy of the cold area more. That's why the heat flows
in the first place. Spontaneous condensation follows a similar
calculus, with decrease in configuration entropy taking the place of
decrease in entropy of the hot side.
In normal situations, heat flows from a hot area to a cold area,
cooling the hot area and warming the cold area until equilibrium
is reached. In a system with negative heat capacity, heat flowing
out of the hot area makes the hot area *hotter*, so there's no
equilibrium. This leads to a runaway situation ("gravothermal
catastrophe"), with highly inhomogeneous outcome that doesn't
look "ordered" at all. Note also that this implies that any
homogeneous state, even in contact with a large heat bath, is
unstable.
Well, it is certainly possible to demonstrate condensation in a closed
vessel in contact with a heat bath, as well as in an insulated vessel
-- indeed, the more usual situation. A cloud of intially homogeneous
steam, under appropriate conditions and in contact with a heat bath at
suitable temperature, will spontaneously condense, ejecting heat into
the surrounding bath and leaving a condensed phase in equilibrium with
a rarified phase.
The one possibly unique feature of the astronomical phase transition
that you mention (painting in broad strokes), seems to be the role of
"negative heat capacity". But you go on to mention...
Lynden-Bell has proposed that all first order phase transitions
involve negative specific heats at the molecular level. See
rxiv.org/abs/cond-mat/9812172.
.... tending to negate that uniqueness.
Lynden-Bell's proposal immediately makes a kind of hand-waving sense:
suppose an intially homogeneous but thermodyanamically unstable
distribution of particles at a uniform temperature. Now suppose some
random fluctuation tends to cluster some of the particles and eject
heat into the surrounding sea. If the clustered particles exhibited a
normal positive heat capacity they would become colder than the
surroundings and the heat would soon flow back, tending to cancel the
fluctuation. If, on the other hand, the cluster had a negative heat
capacity, it would become hotter, tending to eject more heat into the
surroundings, and continue the phase transition.
Alright, I tend to agree with Lynden-Bell. (He will be so gratified).
All spontaneous condensations, from a droplet on the windowpane to a
galaxy, probably involve something understandable as a negative heat
capacity, part of a self-sustaining nucleation of the phase transition
(nucleation: another word of power). However, this is mechanistic
icing on the broad thermodynamic cake, in which the apparent decrease
in entropy in the segregation of a one phase system into two phases,
particularly a rarified and a condensed phase, is offset by an increase
in entropy associated with a redistribution of the energy -- and that's
what allows the change to go forward.
Do me a favor, Dr. Carlip: at least include me as a co-author on the
paper you ought to be writing illuminating how gravitational
condensation is a well behaved member of the family of all
condensations ("Scientists now view condensation of galaxies as
essentially similar to condensation of vapor on the window"). It will
soon be a delightful standard oolie, if it is not already -- and your
knowledge of the literature, coupled to initial resistance to my
proposal, makes me think it is not.
Ed Green
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| User: "Ben Newsam" |
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| Title: Re: Entropy confusion, please help! |
01 Sep 2006 04:18:33 AM |
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On 31 Aug 2006 16:10:16 -0700, "Edward Green"
<spamspamspam3@netzero.com> wrote:
Do me a favor, Dr. Carlip: at least include me as a co-author on the
paper you ought to be writing
LOL!
--
Posted via a free Usenet account from http://www.teranews.com
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| User: "Edward Green" |
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| Title: Re: Entropy confusion, please help! |
02 Sep 2006 09:09:22 AM |
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Ben Newsam wrote:
On 31 Aug 2006 16:10:16 -0700, "Edward Green"
<spamspamspam3@netzero.com> wrote:
Do me a favor, Dr. Carlip: at least include me as a co-author on the
paper you ought to be writing
LOL!
Oh well... perhaps my offer of co-authorship was a _tad_ premature.
But mark my words -- this will somebody be a standard oolie. There is
nothing essentially different from a thermodynamic point of view about
a condensation resulting in a star and a condensation resulting in a
water droplet. Different scales, different forces, equivalent
bookkeeping.
.
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| User: "Timo A. Nieminen" |
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| Title: Re: Entropy confusion, please help! |
02 Sep 2006 03:05:45 PM |
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On Sun, 2 Sep 2006, Edward Green wrote:
But mark my words -- this will somebody be a standard oolie. There is
nothing essentially different from a thermodynamic point of view about
a condensation resulting in a star and a condensation resulting in a
water droplet. Different scales, different forces, equivalent
bookkeeping.
Hmm. Chandrasekhar has some nice stuff about the probability distribution
of gravitational fields in a "gas" of indentical randomly-distributed
stars -- an ideal gas of stars -- that seems to me to be mostly used in
plasma physics (with an assumption that (a+b)^2 = a^2 + b^2 thrown in for
good measure) [1,2].
We recently did some stuff treating polymer molecules in suspension as an
ideal gas. They're not actually an ideal gas, because we optically trap
enough of them so that the concentration becomes higher than the ideal gas
regime, but ideal gas 1st principles simulations work very well
qualitatively. Nothing new about treating small particles in suspension
this way; this is the stuff that Einstein is really famous for, at least
citation-wise [3].
I haven't been following the thread, but it looks to me from your last
pronouncement that you've re-discovered something that's known but not
usually taught.
[1] The paper is in Reviews of Modern Physics, about 1942 or 1943, called
something like "Stochastic processes in astronomy and astrophysics".
[2] This "added assumption" offended me, so I thought I'd do it right. A
month later, with the aid of a most skilled integration lackey, I managed
to show that the effect was negligible for my practical purposes. Details
recorded in chapter 4 of my thesis.
[3] The relevant papers are collected in English translation in a cheap
little Dover book, "Investigations on the Brownian movement" or similar.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "Edward Green" |
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| Title: Re: Entropy confusion, please help! |
03 Sep 2006 03:02:26 PM |
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Timo A. Nieminen wrote:
I haven't been following the thread, but it looks to me from your last
pronouncement that you've re-discovered something that's known but not
usually taught.
No doubt it would be miraculous to make some observation that only
required squinting in the right way that wasn't known before.
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| User: "Andy Resnick" |
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| Title: Re: Entropy confusion, please help! |
30 Aug 2006 07:51:56 AM |
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Uno Lapideus wrote:
Andy Resnick wrote:
A uniform vapor has a high entropy because the macrostate (a volume of
vapor) corresponds to an untold number of microstates (specifying the
position and velocity of each particle in the vapor), not because it is
'hot'.
Andrew,
Thanks for your informative response!
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...
Richard Tolman has a book out discussing the thermodynamics of general
relativity:
http://www.amazon.com/Relativity-Thermodynamics/dp/0486653838/sr=1-2/qid=1156941585/ref=pd_bbs_2/002-8037146-6223252?ie=UTF8&s=books
It's a Dover book and cheap. I have not read it, but his book on
statistical mechanics is excellent.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "Ken Shackleton" |
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| Title: Re: Entropy confusion, please help! |
29 Aug 2006 01:33:06 PM |
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Uno Lapideus wrote:
Trying to explain entropy to kids, I find that I need some help with
understanding the concept... The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
I have found that equating entropy with disorder can be very
confusing....so don't do it. Every process will be less than 100%
efficient, this is because some of the energy [or heat] that goes into
driving the process will be lost and is no longer available to do work.
A prime example is a car engine....burning gasoline creates a great
deal of energy, of which only about 25% is actually put into moving
that car forward. The rest is lost as wasted heat that goes out the
tailpipe, and is dissipated through the radiator and heats the air.
Other loses are due to friction causing waste heat in brakes and other
mechanical parts. All this wasted heat warms up the atmosphere,
increasing its entropy.
This rule is true for every process....nothing is free from the second
rule, it applies everywhere, all the time.
Ken
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
Intuitively, I think of the atoms in a white-hot piece of iron as
"moving more randomly" than does the atoms in a piece of iron that
has been in a freezer for a few days. Likewise, I think of the state of
affairs immediately following the "big bang" as a whole lot more
chaotic than the absolute thermal uniformity of a Universe that, some
time far in the distant future, has reached "absolute equilibrium"
Obviously, my thinking is flawed. Can someone please help me get this
entropy stuff straight?
Many thanks in advance,
Uno
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| User: "G=EMC^2 Glazier" |
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| Title: Re: Entropy confusion, please help! |
04 Sep 2006 07:22:09 AM |
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Uno Tell your kids when their rooms are very messy.its a form of entropy
Reason is "Entropy can be described as the degree of disorder in a
system" Have them look at an ice cube in water they are seeing entropy
in action as the ice disappears.(melts) Bert
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| User: "=?UTF-8?Q?Jeff=E2=80=A6Relf?=" |
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| Title: Entropy goes up when daddy's M-80 firecracker liquifies his mellon. |
04 Sep 2006 03:03:10 PM |
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Hi Bert, Entropy is uniformity, gaussianity, a lack of discrete structure.
( See: WikiPedia.org/wiki/Non-gaussianity )
Tell the kids:
Entropy goes up when daddy's M-80 firecracker liquifies his mellon.
Randomness ( i.e. what is or isn't known ), has nothing to do with entropy.
Contrary to what information theory says,
a compressed file has _Less_ entropy ( compared to the uncompressed version ),
because it's more compact ( i.e. less uniform ).
.
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| User: "kunzmilan" |
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| Title: Re: Entropy goes up when daddy's M-80 firecracker liquifies his mellon. |
06 Sep 2006 10:22:08 AM |
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Randomness ( i.e. what is or isn't known ), has nothing to do with entropy.
Only frequencies of symbols are evaluated by information entropy. The
string aaaabbbbcccc has the same entropy as any other from 34650 such
strings, e.g. abcabcccbbaa. Information entropy measures only
possibilities. Thermodynamical entropy depends on mixing, e.g.
different kinds of molecules, molecules with different temperatures.
kunzmilan
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