Re: The 2nd Law of Thermodynamics - Irrelevant to Origins

Paul J Gans wrote:
gesres@xxxxxxxxxxxxxxx wrote:
<<Show me where Mark Perakh (and others) say that a restriction of the
second law, in its general form, to closed systems is required, or
exists.>>

The most general form of the second law is dS >= 0 (according to H.C.
Van Ness, "Understanding Thermodynamics". Since open systems can
have dS can be less than zero, it's clear that dS >= 0 applies to
closed systems only.

I suspect that there are a few minor caveats left out.

dS >= 0 applies ONLY to closed systems.

But that's NOT the Second Law. dS >= 0 is true in closed
systems, but so what? Heat capacity at constant pressure is
always positive, but that has nothing to do with the second
law.



If dS>0 is the most general, other statements are just more specific
and cannot contradict the more general form.

It is NOT the most general.

However, if you combine it with the inequalities of Clausius, you
CAN derive the directionality criteria for many other systems.


By taking into account inflows and outflows of energy, you're simply
defining a new closed system to encompass those flows. For instance,
the sun and earth comprise an essentially closed system.

No they don't. Please do not start obfuscating something that
you don't really understand.


Thermodynamics has to be just about the most subtle subject
in all of physics. There really ought to be a law against even
trying to discuss it without understanding that from the outset.

It seems to have taken such a long time for the essential
content to become even reasonably clear to people that we are
left with an enormous historical residue of understandings and
half-understandings to deal with. Even lots of physicists remain
deeply confused about the subject and it's all too easy to make
serious errors.

It isn't that the initial pioneers were so wrong-headed or anything
of that sort. It's that the roots of the subject were in describing
the behaviour of heat engines, and were so intuitive and practical,
while the applications turned out to be so enormously general.

Even Caratheodory went only so far in reducing the subject to
its essentials, and he introduced all sorts of structures and
requirements that aren't really central. How the subject generalizes
to chemical systems was the input of Gibbs, and his roots were
really on the side of statistical mechanics. And thermodynamics
is just not complete without discussing its applicability to chemical
transformations. It is very general, perhaps THE most generallly
applicable branch of the physical sciences, and therein lies the
problem.

It seems that everybody and his mother is willing to
opine on the subject, even when they are no doubt well
aware that they have no idea even what the word
entropy is really supposed to mean. And the fact that
creationists have taken hold of it and draw all sorts of insane
conclusions from it just makes things worse.

One of the very best short treatments of the subject that
I have seen was in an article that I think was called
`A Guide to Entropy and the Second Law,' by Elliot Lieb
and a co-author, whose name I don't remember. It's a
very mathematical approach, probably not much
use for a beginner, but it really reduces the subject to
its essentials.

If I had my way, we would do as they do, and replace
the second law and most of the other laws by an entropy
principle, and the axioms of thermodynamics by certain
statements about the relationships between macroscopic
thermodynamic states of systems and the scaling
properties thereof. If the subject is stated in this fashion the
need to talk about vague, though intuitively clear
notions like `heat,' `hot,' and `cold' is eliminated.

Their statement of the entropy principle involved
the notion of one state being adiabatically accessible
from another, which is defined as a special kind of
ordering relation on the states of systems.

Their entropy principle went something like this, and
please pardon any inaccuracies that I may introduce:

`There exists a real valued function on all states of
all systems, including simple and compound systems,
called entropy (S), such that:

(A) S is monotonic. For states X and Y of a system
which are comparable, we have:

S(X) <= S(Y) if and only if X < Y

(B) S is additive and extensive. If X and Y are states
of two systems, and if the pair (X,Y) denotes a
state of the compound system, then:

S(X,Y) = S(X) + S(Y)

and

For each real r > 0 and state X and its scaled
copy rX contained in G(r), where G is the state
space of the system and G(r) the scaled state
space:

S(rX) = r S(x)

The relation `<' between states, means that one
state is adiabatically accessible from another, and
one has to give that a physical interpretation.

The meanings and physical interpretations of all of
the words used, such as comparable, have also to
be given and specific explanatory examples have
to be provided.

But in a sense, the really crucial point is just the
existence of an entropy function universally across
all systems, and which has the necessary properties.

The first statement about adiabatic accesibillty can
easily be replaced by one about irreversible and
reversible adiabatic processes.

The very non-trivial physical content is all in the
scaling, extensivity and additivity properties of the
entropy, and there is clearly no need this way for a
restriction to closed systems to aid in the formal
construction of the subject, because the statements
apply just as well to compound systems.

The entropy principle as given can be shown
to imply the existence of adiabats, along which
entropy is constant, and after this the temperature
can be proven to be a consequence of and directly
related to the existence of the entropy.

The whole question then becomes what requirements
on the ordering of adiabatic accessibility, on the state
space, are sufficient to guarantee the existence of the
entropy function. Simple and reasonable axioms can
be given which are sufficient to guarantee it.

In this kind of an approach, it's very clear that the
notion of entropy is what is central, while idealized
notions like closed systems are practically entirely
bypassed, and it's clear the subject lends itself to
a local treatment.

The Clausius inequality and all the other statements
of the law all will of course follow. All of the other
thermodynamic potentials arise from the notions
of energy, entropy, temperature, pressure, volume,
and any other pairs of intensive and extensive state
variables.

I don't really expect that the way in which the subject
is taught should or can change much, though.

But, in any case, people who have never even
heard of the Clausius inequality shouldn't even
begin to quibble about what is the most general
form of the second law.

David

.

Relevant Pages

  • Re: The 2nd Law of Thermodynamics - Irrelevant to Origins
    ... Thermodynamics has any bearing on the subject of origins. ... Isn't any increase in entropy on the ... The second law always holds, ... information theory is not thermodynamics. ...
    (talk.origins)
  • Re: The 2nd Law of Thermodynamics - Irrelevant to Origins
    ... Thermodynamics has any bearing on the subject of origins. ... Isn't any increase in entropy on the ... The second law always holds, ... information theory is not thermodynamics. ...
    (talk.origins)
  • Re: Time: Relativity and Entropy?
    ... Has the Second Law Been Falsified? ... disorder, or entropy, always increases, has been shown to be untrue." ... the bedrocks on which modern theoretical physics is based. ... of thermodynamics, if it happened in a larger system. ...
    (sci.physics)
  • Re: The 2nd Law of Thermodynamics - Irrelevant to Origins
    ... Van Ness, "Understanding Thermodynamics". ... of the second law at all. ... closed systems only. ... general form to an open system once we know ...
    (talk.origins)
  • Re: Lizard engines and rat engines
    ... >>> Rather than having a second law that merely limits the scope of potential ... >>> systems that increase the RATE of entropy gain in closed systems through ... >> water in a bottle, stopper the bottle, and put the bottle in your freezer. ... > what the web has to say about "closed systems" and the 2nd law. ...
    (sci.bio.evolution)