On 02.02.2012 22:18 Russell Standish said the following:
On Thu, Feb 02, 2012 at 07:45:53PM +0100, Evgenii Rudnyi wrote:
On 01.02.2012 21:51 Stephen P. King said the following:
On 2/1/2012 3:10 PM, Evgenii Rudnyi wrote:
First the thermodynamic entropy is not context depended. This
must mean that if it is the same as information, then the
latter must not be context dependent as well. Could you please
give me an example of a physical property that is context
dependent?
Temperature is context dependent. If we consider physics at the
level of atoms there is no such a quantity as temperature.
Additionally, thermodynamic entropy does require Boltzmann's
constant to be defined with is a form of context dependency as it
specifies the level at which we are to take micro-states as
macroscopically indistinguishable.
The Boltzmann's constant, as far as I understand, is defined
uniquely. If you talk about some other universe (or Platonia)
where one could imagine something else, then it could be. Yet, in
the world that we know according to empirical scientific studies,
the Boltmann's constant is a fundamental constant. Hence I do not
understand you in this respect.
Boltzmann's constant is a unit conversion constant like c an Plank's
constant, nothing more. It has no fundamental significance.
Indeed, temperature is not available directly at the level of
particles obeying classical or quantum laws. However for example
it could be not a problem with the temperature but rather with the
description at the particle level.
Anyway, I would suggest to stick to empirical scientific knowledge
that we have. Then I do not understand what do you mean that
temperature is context dependent either.
Temperature is an averaged quantity, so whilst technically an
example of emergence, it is the weakest form of emergence.
Evgenii is stating an oft-repeated meme that entropy is not
context-dependent.
It is context dependent because it (possibly implicitly) depends on
what we mean by a thermodynamic state. In thermodynamics, we usually
mean a state defined by temperature, pressure, volume, number of
particles, and so on. The "and so on" is the context dependent part.
There are actually an enormous number of possible independent
thermodyamic variables that may be relevant in different situations.
In an electrical device, the arrangement of charges might be another
such thermodynamic variable.
Also, even in classic "schoolbook" thermodynamics, not all of
temperature, pressue, volume and particle number are relevant.
Dropping various of these terms leads to different ensembles
(microcanonical, canonical and grand canonical).
Of course, context dependence does not mean subjective. If two
observers agree on the context, the entropy is quite objective. But
it is a little more complex than something like mass or length.
This is explained very well in Denbigh& Denbigh.
I guess that you have never done a lab in experimental thermodynamics.
There are classical experiment where people measure heat of combustion,
heat capacity, equilibrium pressure, equilibrium constants and then
determine the entropy. If you do it, you see that you can measure the
entropy the same way as other properties, there is no difference. A good
example to this end is JANAF Thermochemical Tables (Joint Army-Naval-Air
Force Thermochemical Tables). You will find a pdf here
http://www.nist.gov/data/PDFfiles/jpcrdM9.pdf
It is about 230 Mb but I guess it is doable to download it. Please open
it and explain what is the difference between the tabulated entropy and
other properties there. How your personal viewpoint on a thermodynamic
system will influence numerical values of the entropy tabulated in
JANAF? What is the difference with the mass or length? I do not see it.
You see, the JANAF Tables has started by military. They needed it to
compute for example the combustion process in rockets and they have been
successful. What part then in a rocket is context dependent?
This is the main problem with the books on entropy and information. They
do not consider thermodynamic tables, they do not work out simple
thermodynamic examples. For example let us consider the next problem:
-----------------------------------------------
Problem. Given temperature, pressure, and initial number of moles of
NH3, N2 and H2, compute the equilibrium composition.
To solve the problem one should find thermodynamic properties of NH3, N2
and H2 for example in the JANAF Tables and then compute the equilibrium
constant.
From thermodynamics tables (all values are molar values for the
standard pressure 1 bar, I have omitted the symbol o for simplicity but
it is very important not to forget it):
Del_f_H_298(NH3), S_298(NH3), Cp(NH3), Del_f_H_298(N2), S_298(N2),
Cp(N2), Del_f_H_298(H2), S_298(H2), Cp(H2)
2NH3 = N2 + 3H2
Del_H_r_298 = Del_f_H_298(N2) + 3 Del_f_H_298(H2) - 2 Del_f_H_298(NH3)
Del_S_r_298 = S_298(N2) + 3 S_298(H2) - 2 S_298(NH3)
Del_Cp_r = Cp(N2) + 3 Cp(H2) - 2 Cp(NH3)
To make life simple, I will assume below that Del_Cp_r = 0, but it is
not a big deal to extend the equations to include heat capacities as well.
Del_G_r_T = Del_H_r_298 - T Del_S_r_298
Del_G_r_T = - R T ln Kp
When Kp, total pressure and the initial number of moles are given, it is
rather straightforward to compute equilibrium composition. If you need
help, please just let me know.
-----------------------------------------------
So, the entropy is there. What is context dependent here? Where is the
difference with mass and length?
Evgenii
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