CARNOT'S DIFFICULTY WITH THE SECOND LAW

On Aug 31, 3:59*am, Pentcho Valev wrote:
In 1824 Sadi Carnot deduced the second law of thermodynamics from a
premise that went against the future law of conservation of energy
(the first law of thermodynamics). Here is an oversimplified but
consonant with the quotation below presentation of (part of) Carnot's
1824 argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting part of the heat taken from the warm
body NECESSARILY assist the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after
discovering the first law of thermodynamics (much earlier than the
official discovery), Carnot started to doubt the second:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
p. 225: Sadi Carnot: "Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of
bodies. Wherever there is destruction of motive power there is, at the
same time, production of heat in quantity exactly proportional to the
quantity of motive power destroyed. Reciprocally, wherever there is
destruction of heat, there is production of motive power."
p. 222: Sadi Carnot: "Could a motion (that of radiating heat) produce
matter (caloric)? No, undoubtedly; it can only produce a motion. Heat
is then the result of a motion. Then it is plain that it could be
produced by the consumption of motive power, and that it could produce
this power. All the other phenomena - composition and decomposition of
bodies, passage to the gaseous state, specific heat, equilibrium of
heat, its more or less easy transmission, its constancy in experiments
with the calorimeter - could be explained by this hypothesis. But it
would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER
BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a
warm body, motion cannot be produced."

I think that, almost 200 years later, Carnot's question is both
relevant and unanswered:

WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS
NECESSARY; why, in consuming the heat of a warm body [in the absence
of a cold one], motion cannot be produced [in a cyclical process]?

Pentcho Valev



I am a newbie in Thermodynamics, having only started learning about it
over the summer.

But all the books I read suggest that "laws" of thermodynamics are
really "principles." They are laws that are known to be true by
observation, rather than based upon some hard and fast theory. In
particular, I don't think anyone has proved thermodynamics from
Newton's laws of motion.

Part of the problem is that they apply to systems in equilibrium. And
there is no such thing as a system in equilibrium. So people adopt a
notion called quasi-equilibrium, which in essence seems to mean that
the systems change sufficiently slowly that the laws of thermodynamics
are an excellent approximation.

Which is to say - I think that Carnot's question is still unanswered.
And I don't think anyone is going to find a fully rigorous answer
anytime soon.

My personal guess is that if you wait long enough, that you can
produce motion from heat. Now that time will be very, very long - way
longer than, say, the expected life of the universe. I believe that
this is a consequence of Poincare's recurrence theorem for Hamiltonian
systems: http://en.wikipedia.org/wiki/Poincar...rrence_theorem.
So in my opinion, the second law that says entropy increases is not an
absolute, but only an extremely good approximation. But so good an
approximation that we haven't yet, nor are we likely, to devise an
experiment that violates it.

Stephen