19th CENTURY THERMODYNAMICS: THE BEGINNING OF THE END OF THEORETICAL SCIENCE
Pentcho Valev
The title promises a lengthy discussion and yet this will be a very short paper. The absurd story of thermodynamics (see parts of it in references [1, 2, 3, 4, 5, 6, 7]) has its marked beginning - only one logical aspect of this initial event will be analysed here.
In the period between 1840 and 1850 Clausius and Kelvin face a serious problem. They have extracted a lot of profit from the conclusion B (all reversible machines working between the same two temperatures have the same efficiency) that Carnot has validly derived from the premise A (heat is an indestructible substance). However it has become clear that A is false (heat is not an indestructible substance and can be converted into work) and Clausius and Kelvin must find some way to save B – otherwise their careers would crumble. But can B be saved? Isn’t it more reasonable to admit that the falsehood of A entails the falsehood of B?
Let us resolve the problem by considering a more abstract but still analogous example. A physical quantity has been found to have the value 5 (under certain conditions) and so we define the premise A: "This physical quantity has the value 5". Then we apply a valid physical argument and come to the conclusion that, since the first quantity has the value 5, another quantity must have the value 14. (Valid physical argument is not yet defined although our intuition tells us what it is). Hence the conclusion B: "That (second) quantity has the value 14". Finally, we form a sentence that logicians call the conditional: If A, then B. Everybody agrees that our conditional (argument) is correct.
Then we realise that we have assessed the first physical quantity in the wrong way. Under the same conditions its value is not 5 but, rather, 37. In other words, A is false. Can we expect B to remain true? In other words, can we expect the value of the second quantity to remain 14? The answer to this question will allow us to both see the irrelevance of mathematical logic with respect to physical reasoning and give a formal definition of valid physical argument.
For purely formal reasons (which will not be discussed here) mathematical logic defines the combination of one or more false premises (here the false premise is A) and a true conclusion (B) as "true". It only defines as "false" the combination of true premises and a false conclusion. We will appreciate those formal reasons by calling the respective argument valid argument. So the former combination (one or more false premises and a true conclusion) will remain "true" in the calculations of mathematical logic but our physical intuition forbids us to call the respective argument valid physical argument. Hence the following definition:
In a valid physical argument true premises entail a true conclusion and false premises entail a false conclusion.
According to this definition, if Carnot’s argument is a valid physical argument, the conclusion B (all reversible machines working between the same two temperatures have the same efficiency) is false since it is produced by the false premise A (heat is an indestructible substance). Therefore, Clausius and Kelvin should have abandoned both B and any theoretical construction based on B. Instead, they have preserved B in a dishonest way (this is another tale) and so opened a Pandora box inside the logical heart of theoretical science.
REFERENCES
1. C. Truesdell, The Tragicomical History of Thermodynamics 1822-1854, New York: Springer-Verlag, 1980
2. J. Uffink, Bluff your way in the second law of thermodynamics, Studies in History and Philosophy of Modern Physics, 32(3), 305-394 (2001)
http://philsci-archive.pitt.edu/archive/00000313/
3. P. Valev, The Law of Self-Acting Machines and Irreversible Processes with reversible Replicas, in D. Sheehan (ed.), Proceedings of the First International conference on Quantum Limits to the Second Law, American Institute of Physics, 430 - 435 (2002):
http://content.aip.org/APCPCS/v643/i1/430_1.html
4. P. Valev, "Science infected with inconsistency", The General Science Journal:
http://www.wbabin.net/physics/valev.htm
5. P. Valev, Biased thermal motion and the second law of thermodynamics, The General Science Journal:
http://www.wbabin.net/valev/valev2.htm
6. P. Valev, "Les sciences de la nature en proie a l'inconsistance", DOGMA:
http://dogma.free.fr/
7. P. Valev, "Introducing logic in chemical thermodynamics courses", Journal of Science Education, No 10, 100-103 (2004)