Open, closed, and isolated systems

[Iggy]

Yes, Juanrga, I understand your argument.

 

Your point is that d_iE is conserved in a closed system and Greiner's point is that U is not conserved in a closed system. Since your point doesn't contradict his point you're left objecting to his use of the word conserve -- it simply has to be used in relation to your quantity. Greiner is "confused" and "confounded" for describing a different quantity with that word. It isn't worth arguing.

 

 

The particle count being conserved... it is a useful idealization when defining isolated, closed, and open systems. Most sources will explain the nature of the idealization explicitly. It will be quicker for me to find one than explain...

 

1.1 Thermodynamic systems

 

In this first section, we will put aside the notion that matter is composed of atoms (or more exotic particles) and consider a macroscopic description of thermodynamics, the study of transformations of energy and other conserved quantities. For many situations, at a sufficiently large length scale we can forget about microscopic interactions and fluctuations; the microscopic world shows up only as relations between temperature, density, pressure, viscosity, thermal conductivity, chemical reaction rates etc. One very important aspect of statistical mechanics is predicting these properties from microscopic laws. Also at small scales (nanotechnology) and for special systems such as Bose-Einstein condensates, the macroscopic description can break down. First, however, we turn to the description of this macroscopic world. We know from mechanics that there are fundamental conservation laws applying to isolated systems. These include energy, momentum and the total number of any type of particle that cannot be created or destroyed (for example the number of hydrogen atoms in a chemical reaction). Most systems we consider will be (macroscopically) at rest or mechanically connected to the Earth, so let's ignore momentum for now. This suggests the following classification of thermodynamic systems:

 

Isolated

Cannot exchange energy, or particles with the environment. Both of these remain conserved quantities.

 

Closed

Can exchange energy with the environment, for example by heat conduction, or by doing work as in a piston. Particles still conserved, but energy on average determined by the temperature (defined below) of the environment if at equilibrium (defined below).

 

Open

Can exchange both energy and particles with the environment, as in a container without a lid. No conserved quantities, energy determined on average by the temperature and particles determined on average by the chemical potential(s) (defined below) at equilibrium.

 

http://www.maths.bris.ac.uk/~macpd/statmech/snotes.pdf

Everyone knows that idealizations and useful approximations aren't pedantically true. Arguing that the people who author them are confused, rolling your eyes at them, and making little passive aggressive insults at them on that basis is bad form.

 

I'm sure it's unfair for me to continue commenting on your argument style without an interest in debating the points you've raised so I really will step out now.

[juanrga]

Yes, Juanrga, I understand your argument.

 

Your point is that d_iE is conserved in a closed system and Greiner's point is that U is not conserved in a closed system. Since your point doesn't contradict his point you're left objecting to his use of the word conserve -- it simply has to be used in relation to your quantity. Greiner is "confused" and "confounded" for describing a different quantity with that word. It isn't worth arguing.

 

You claim that you understand my argument, but then you completely ignore what I have said. For instance, I say that E is conserved in closed, isolated, and open systems and you read this as "Your point is that d_iE is conserved in a closed system", something that I have not said. It cannot be a problem of English language not being my native tongue, because E and d_iE are mathematical expressions...

 

You repeat Greiner's point of that U is not conserved in a closed system, but he is wrong because there exist closed systems that conserve U. All those systems for which the production of internal energy is zero are systems that conserve internal energy. Greiner confounds d_iU=0 with dU=0 and the same are doing you.

 

I will give another try, in a last hope that this discussion can be used to improve the article draft.

 

As is well-known a quantity is conserved when its production is zero (otherwise the quantity is not conserved). Consider systems that conserve internal energy

 

d_iU = 0 (1)

 

This law can be written in the equivalent form

 

dU - d_eU = 0 (2)

 

Both (1) and (2) provide the general expression of the law of conservation of internal energy for closed, open, and isolated systems, because both (1) and (2) holds with independence of the value of d_eU.

 

For a closed system the flow term is

 

d_eU = dQ + dW (3)

 

Substituting (3) in (2), we obtain the more popular form

 

dU = dQ + dW (4)

 

The same pdf that you have just linked states about (4): the "first law of thermodynamics is a statement of conservation of energy".

 

I am pretty sure that you will not find a reference saying that the first law of thermodynamics is a statement of conservation of energy only when dU=0. Expression (4) is a statement of conservation of energy also for nonzero values of dU.

 

In the same pdf that you link the author says about (4) "The physical content of the first law as a restriction on physical processes is clear. It is impossible to create a machine which creates energy out of nowhere".

 

Effectively, for closed systems (4) is equivalent to (1), and (1) in words says that energy cannot be created out of nothing.

 

No only energy is conserved in closed systems, but it is also conserved in open systems. I cited the section "15.4 Energy conservation in open system" of a celebrated modern textbook, but it seems that some people insists on ignoring that as well...

 

The pdf that you link makes the same misguided statement about particles being conserved in closed systems. But at least it adds in the introduction that by particle he means a "particle that cannot be created or destroyed". By particle I mean... particle

 

The particle count being conserved... it is a useful idealization when defining isolated, closed, and open systems. Most sources will explain the nature of the idealization explicitly. It will be quicker for me to find one than explain...

 

Any basic textbook in thermodynamics contains a chapter devoted to systems for which particles are not conserved but are created or produced by means of different kind of reactions.

Edited May 1, 2012 by juanrga

[juanrga]

A new version of the draft is available.

 

After discussion and comments in this thread, I have given more complete quotations of Greiner, Neise, & Stöcker and next a general background about what is the law of conservation of energy and what is not. I have added a citation to the textbook cited in this thread and corrected another mistake by Greiner, Neise, & Stöcker regarding the first law of thermodynamics for open systems.

 

Walter Greiner, Ludwig Neise, & Horst Stöcker write that "the total energy [math] E [/math] (mechanics, electric, etc.) is a conserved quantity for" isolated systems, but add that for both closed and open systems "the energy is not longer a conserved quantity" [5]. This is a misconception. The law of conservation of energy is an universal law that states that the total energy [math] E [/math] cannot be created or destroyed; that is, [math] d_i E = 0 [/math]. This law applies to isolated, closed, and open systems, because does not depend on the value of the flow term [math] d_e E [/math].

 

The law of conservation of energy can be written in the equivalent form [math] d E - d_e E = 0 [/math]. For a closed system, the flow term contains only heat and work [math] d_e E \equiv d Q + d W [/math], and the law of conservation reduces to [math] d E = d Q + d W [/math] --also known as the first law of thermodynamics--. The law of conservation of energy does not say that [math] d E [/math] has to be zero. It is evident that Greiner, Neise, & Stöcker confound the law of conservation of energy [math] d_i E = 0 [/math] with the condition that energy is a constant [math] d E = 0 [/math].

 

Moreover, they affirm that [math] d E = d Q + d W [/math] "is always true" [5]; however, this expression does not apply to open systems, because there is an extra component in [math] d_e E [/math] due to the flow of mass --it is worth to remark that the general conservation law [math] d_i E = 0 [/math] applies to any open system--. Details about this additional mass-flow term can be found in the section "15.4 Energy conservation in open system" of a modern textbook [6].

 

Greiner, Neise, & Stöcker also affirm that the particle number is conserved in closed and isolated systems, but this is another misconception. In presence of chemical reactions, disintegration of radioactive nuclei, and similar processes, the particle numbers are not conserved because [math] d_i N_k \neq 0 [/math]. Now the trio of authors are confounding the law of conservation of particles [math] d_i N = 0 [/math] with the flow of particle being zero [math] d_e N = 0 [/math] due to impermeable walls.

 

They also write: "It is obvious that at least the isolated system is an idealization, since in reality an exchange of energy with surrounds cannot be prevented in the strict sense". The universe, as a whole, is an isolated system by definition. No idealization is involved here.

 

The draft includes corrections, provided by Dr. Matta, to the part about proper open quantum systems.

 

Comments, suggestions, and corrections are welcomed.

[studiot]

Walter Greiner, Ludwig Neise, & Horst Stöcker

 

Man hat im 1987 diese buch verlangt.

 

Is this modern?

[juanrga]

Greiner, Neise, & Stöcker

 

Man hat im 1987 diese buch verlangt.

 

Is this modern?

 

If you read the OP, the textbook by Greiner et al. was already cited [5] in the first version of the draft. The modern textbook which I have added to the new draft is the reference [6]:

Details about this additional mass-flow term can be found in the section "15.4 Energy conservation in open system" of a modern textbook [6].

Edited May 4, 2012 by juanrga