On 05.02.2012 23:05 Russell Standish said the following:
On Fri, Feb 03, 2012 at 08:50:40PM +0100, Evgenii Rudnyi wrote:
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
The context is there - you will just have to look for it. I rather
suspect that use of these tables refers to homogenous bulk samples
of the material, in thermal equilibrium with a heat bath at some
given temperature.
I do not get your point. Do you mean that sometimes the surface effects
could be important? Every thermodynamicist know this. However I do not
understand your problem. The thermodynamics of surface phenomena is well
established and to work with it you need to extend the JANAF Tables with
other tables. What is the problem?
It would be good if you define better what do you mean by context
dependent. As far as I remember, you have used this term in respect to
informational capacity of some modern information carrier and its number
of physical states. I would suggest to stay with this example as the
definition of context dependent. Otherwise, it does not make much sense.
If we were to take you at face value, we would have to conclude that
entropy is ill-defined in nonequlibrium systems.
The entropy is well-defined for a nonequilibrium system as soon as one
can use local temperature. There are some rare occasions where local
temperature is ambiguous, for example in plasma where one defines
different temperatures for electrons and molecules. Yet, the two
temperatures being defined, the entropy becomes again well-defined.
More to the point - consider milling whatever material you have
chosen into small particles. Then consider what happens to a
container of the stuff in the Earth's gravity well, compared with the
microgravity situation on the ISS. In the former, the stuff forms a
pile on the bottom of the container - in the latter, the stuff will
be more or less uniformly distributed throughout the containers
volume. In the former case, shaking the container will flatten the
pile - but at all stages the material is in thermal equilibrium.
In your "thermodynamic context", the entropy is the same throughout.
No it is not. As I have mentioned in this case one just must consider
surface effects.
It only depends on bulk material properties, and temperature. But
most physicists would say that the milled material is in a higher
entropy state in microgravity, and that shaking the pile in Earth's
gravity raises the entropy.
Furthermore, lets assume that the particles are milled in the form
of tiny "Penrose replicators" (named after Lionel Penrose, Roger's
dad). When shaken, these particles stick together, forming quite
specific structures that replicate, entraining all the replicators
in the material. (http://docs.huihoo.com/reprap/Revolutionary.pdf).
Most physicists would say that shaking a container of Penrose
replicators actually reduces the system's entropy. Yet, the
thermodynamic entropy of the JNAF context does not change, as that
only depends on bulk material properties.
We are again at the definition of context dependent. What are saying now
is that when you have new physical effects, it is necessary to take them
into account. What it has to do with your example when information on an
information carrier was context dependent?
Evgenii
We can follow your line of thinking, and have a word entropy that is
only useful in certain contexts, then we'll need to make up a
different word for other contexts. Alternatively, we can have a
word that applies over all macroscopic contexts, and explicitly
qualify what that context is. The underlying concept is the same in
all cases though. It appears to me, that standard scientific usage
has become to use the same word for that concept, rather than coin
different words to describe the same concept in all the possible
different contexts that there are.
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