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Old June 21st 13, 12:59 PM posted to sci.astro
Pentcho Valev
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Any heat engine converts heat into work by undergoing the following (very roughly described) four-step cycle:

Step 1: The heat engine is manipulated (usually heated) so that its work-producing force increases from F1 to F2.
Step 2: Work W2=F2*L, where L is the respective displacement, is extracted from the heat engine.
Step 3: The heat engine is manipulated (usually cooled) so that its work-producing force decreases from F2 to F1.
Step 4: Work W1=F1*L is done on the heat engine. Its initial state is restored.

The net work extracted from steps 2 and 4 is positive (Wnet=W2-W1) so if there is something that prevents us from abandoning the second law of thermodynamics, this something should be looked for in steps 1 and 3. Traditional education considers exclusively non-isothermal manipulation of the heat engine in steps 1 and 3 (heating and cooling):

"A necessary component of a heat engine, then, is that two temperatures are involved. At one stage the system is heated, at another it is cooled."

"Figure 2. Thermoelasticity experiments on a stretched elastomer and compressed gas, where W represents a weight. An increase in temperature decreases the length of the elastomer, and increases the volume of the gas."

Yet there are ISOTHERMAL heat engines - the work-producing force is increased or decreased in some chemical way. For instance, there are macroscopic polymers which, when the concentration of hydrogen ions in the solution increases, contract (the work-producing force increases) and lift a weight:

POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. KATCHALSKY, pp. 13-15: "Let the polymolecule be a negatively charged polyacid in a stretched state and have a length L. Now let us add to the molecule a mineral acid to provide hydrogen ions to combine with the ionized carboxylate groups and transform them into undissociated carboxylic groups according to the reaction RCOO- + H+ = RCOOH. By means of this reaction, the electrostatic repulsion which kept the macromolecule in a highly stretched state vanishes and instead the Brownian motion and intramolecular attraction cause a coiling up of the polymeric chains. Upon coiling, the polymolecule contracts and lifts the attached weight through a distance deltaL. On lifting the weight, mechanical work f*deltaL was performed... (...) FIGURE 4: Polyacid gel in sodium hydroxide solution: expanded. Polyacid gel in acid solution: contracted; weight is lifted."

Here is the four-step ISOTHERMAL cycle:

Step 1: The polymer is initially stretched. We add H+ to the system. The work-producing force (of contraction) increases from F1 to F2.
Step 2: The polymers contracts and lifts a weight. Work W2=F2*L is gained by us.
Step 3: We remove the same amount of H+ from the system. The work-producing force decreases from F2 to F1.
Step 4: We stretch the polymer and restore the initial state of the system. Work W1=F1*L is wasted by us.

Now the situation is much clearer: in order for the second law of thermodynamics to remain valid, the net work GAINED from steps 2 and 4, Wnet=W2-W1, should be neutralized by work WASTED in steps 1 and 3.

Yet it is apparent, even from a superficial examination, that the operations in steps 1 and 3 are symmetrical and therefore it is quite reasonable to assume that the net work involved (in steps 1 and 3) would be zero or close to zero. That is, we don't waste work in steps 1 and 3 and Wnet=W2-W1 turns out to be net work extracted from an ISOTHERMAL cycle, in violation of the second law.

A rigorous analysis would show that isothermal heat engines do indeed violate the second law of thermodynamics.

Pentcho Valev

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