A Space & astronomy forum. SpaceBanter.com

Go Back   Home » SpaceBanter.com forum » Astronomy and Astrophysics » Astronomy Misc
Site Map Home Authors List Search Today's Posts Mark Forums Read Web Partners

AMBIGUITY IN THE SECOND LAW OF THERMODYNAMICS



 
 
Thread Tools Display Modes
  #1  
Old April 6th 13, 07:27 PM posted to sci.astro
Pentcho Valev
external usenet poster
 
Posts: 8,078
Default AMBIGUITY IN THE SECOND LAW OF THERMODYNAMICS

Here is the Kelvin-Planck statement of the second law of thermodynamics:

It is impossible to construct an engine that, operating in a cycle, will produce no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work.

"No effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work" could mean:

(A) At the end of the cycle, both the engine and the surroundings return to the initial state except for the heat disappearance and the result of the work production (e.g. some weight somewhere in the surroundings was initially on the ground but remains lifted after the cycle is over).

(B) At the end of the cycle, both the engine and the surroundings return to the initial state except for the heat disappearance, the result of the work production, AND the unavoidable changes that occur in the body of the OPERATOR - someone or something that assists the process.

It can be shown that, with the interpretation (A), the Kelvin-Planck statement of the second law is true. With the interpretation (B), however, the Kelvin-Planck statement of the second law is false. That is, perpetuum mobile of the second kind IN THE PRESENCE OF AN OPERATOR is possible in principle..

Pentcho Valev
  #2  
Old April 7th 13, 11:43 AM posted to sci.astro
Pentcho Valev
external usenet poster
 
Posts: 8,078
Default AMBIGUITY IN THE SECOND LAW OF THERMODYNAMICS

Heat engines convert, cyclically, thermal energy (heat) into mechanical energy (work). Here is an illustration:

http://www.chemistry.wustl.edu/~edud...es/HeatEng.jpg

For a closed system (exchanges energy but not matter with the surroundings) the first law of thermodynamics defines the internal energy change, dU, to be:

dU = dQ - dW = dQ - FdX /1/

where dQ is the heat absorbed, dW is the work done by the system on the surroundings, F is the work-producing force and dX0 is the respective displacement.

Let us consider a system of two heat engines doing work UNDER ISOTHERMAL CONDITIONS (that is, the system converts heat absorbed from the surroundings into work but operates so slowly, virtually reversibly, that the temperature of both the system and the surroundings remains unchanged). The work done by this system on the surroundings is:

dW = dW1 + dW2 = F1dX1 + F2dX2 /2/

Is W a function of X1 and X2? If yes, the second law of thermodynamics is obeyed - at the end of the (isothermal) cycle W returns to its initial value and no net work is done on the surroundings. The following theorem is relevant:

Theorem: W is a function of X1 and X2 if and only if the mixed partial derivatives are equal:

http://www.youtube.com/watch?v=Y-lEuHpTS9k
"Mixed Partial Derivatives"

Since F1 and F2 are in fact the first partial derivatives, the theorem can be expressed in the following way:

Theorem: W is a function of X1 and X2, that is, the second law is obeyed, if and only if:

dF1/dX2 = dF2/dX1 /3/

where "d" is the partial derivative symbol.

The two sides of /3/ have physical meanings and, even more importantly, are easily MEASURABLE. This leads to the following conclusion:

If experiments show that the two sides of /3/ are equal, the second law is confirmed. If, however, experiments unambiguously show that the two sides of /3/ are not equal - e.g. dF1/dX2 is positive and dF2/dX1 is negative - the second law of thermodynamics is false and will have to be abandoned.

It is easy to see that:

dF1/dX2 = dF2/dX1 = 0

when the two heat engines do not interact, and that:

dF1/dX2 is not equal to dF2/dX1

when the two heat engines interact in some asymmetric way.

Pentcho Valev
  #3  
Old April 7th 13, 10:18 PM posted to sci.astro
Pentcho Valev
external usenet poster
 
Posts: 8,078
Default AMBIGUITY IN THE SECOND LAW OF THERMODYNAMICS

ftp://ftp.esat.kuleuven.ac.be/pub/SI...orts/06-46.pdf
"From the pedagogical point of view, thermodynamics is a disaster. As the authors rightly state in the introduction, many aspects are "riddled with inconsistencies". They quote V.I. Arnold, who concedes that "every mathematician knows it is impossible to understand an elementary course in thermodynamics". Nobody has eulogized this confusion more colorfully than the late Clifford Truesdell. On page 6 of his book "The Tragicomical History of Thermodynamics" 1822-1854 (Springer Verlag, 1980), he calls thermodynamics "a dismal swamp of obscurity". Elsewhere, in despair of trying to make sense of the writings of some local heros as De Groot, Mazur, Casimir, and Prigogine, Truesdell suspects that there is "something rotten in the (thermodynamic) state of the Low Countries" (see page 134 of Rational Thermodynamics, McGraw-Hill, 1969)."

http://arxiv.org/ftp/arxiv/papers/1201/1201.4133.pdf
"The concept of entropy introduced by R. Clausius, which is intimately associated with the second law, resembles the entropy featuring in the theory of probability only by perception. It does not have the extent of generality in description of natural phenomena the thermodynamics claims. C. Truesdell wrote in this connection: "Seven times in the past thirty years have a tried to follow the argument Clausius offers to conclude that the integrating factor T exists in general, is a function of temperature alone, and is the same for all bodies, and seven times has it blanked and graveled me... I cannot even explain what I cannot understand." The character itself of formulating the theory of thermal processes, which originates in the works of the founders of thermodynamics and is still persisting up to the present days, gave grounds to C. Truesdell to call thermodynamics "the dismal swamp of obscurity"."

http://philsci-archive.pitt.edu/archive/00000313/
"From this anthology it emerges that although many prominent physicists are firmly convinced of, and express admiration for the Second Law, there are also serious complaints, especially from mathematicians, about a lack of clarity and rigour in its formulation. At the very least one can say that the Second Law suffers from an image problem: its alleged eminence and venerability is not perceived by everyone who has been exposed to it. What is it that makes this physical law so obstreperous that every attempt at a clear formulation seems to have failed? Is it just the usual sloppiness of physicists? Or is there a deeper problem? And what exactly is the connection with the arrow of time and irreversibility? Could it be that this is also just based on bluff? Perhaps readers will shrug their shoulders over these questions. Thermodynamics is obsolete; for a better understanding of the problem we should turn to more recent, statistical theories. But even then the questions we are about to study have more than a purely historical importance. The problem of reproducing the Second Law, perhaps in an adapted version, remains one of the toughest, and controversial problems in statistical physics. (...) This summary leads to the question whether it is fruitful to see irreversibility or time-asymmetry as the essence of the second law. Is it not more straightforward, in view of the unargued statements of Kelvin, the bold claims of Clausius and the strained attempts of Planck, to give up this idea? I believe that Ehrenfest-Afanassjewa was right in her verdict that the discussion about the arrow of time as expressed in the second law of the thermodynamics is actually a RED HERRING."

http://www.youtube.com/watch?v=4vuW6tQ0218
"Look, matey, I know a dead parrot when I see one, and I'm looking at one right now."

Pentcho Valev
 




Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
EINSTEIN RELATIVITY: THE UNAMBIGUOUS AMBIGUITY Pentcho Valev Astronomy Misc 3 May 22nd 07 08:11 AM
ambiguity-free planetary classification Blurrt Policy 6 August 28th 06 06:27 PM
Is temporal sign ambiguity inherent in Einstein's general relativistic field equation? John Bell Astronomy Misc 10 February 2nd 06 09:26 PM
gravitational-wave sources (was: Is temporal sign ambiguity inherent in Einstein's general relativistic field equation?) brian a m stuckless Policy 0 February 2nd 06 08:12 PM
Is temporal sign ambiguity inherent in the application of Einstein's general relativistic field equation? John Bell Research 0 January 9th 06 11:59 AM


All times are GMT +1. The time now is 12:29 PM.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Copyright ©2004-2024 SpaceBanter.com.
The comments are property of their posters.