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? EvgeniiThe 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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