Rubber Band Heat Engines Do Violate the Second Law of Thermodynamics

"Stretchy Science: A Rubber Band Heat Engine. Learn how a rubber band can turn heat into mechanical work with this simple activity. [...] Your blow dryer essentially turned your rubber band into a heat engine - a machine that turns thermal energy into mechanical work." https://www.scientificamerican.com/a...ber-band-heat/

http://readingpenrose.files.wordpres...and-engine.gif

These are non-isothermal heat engines - they do not violate the second law of thermodynamics. (At least it would be difficult, if not impossible, to calculate their maximal efficiency and compare it with the efficiency of the Carnot engine.)

However there are ISOTHERMAL analogs which almost obviously violate the second law of thermodynamics (one should only evaluate the work involved in a quasi-static cycle):

http://www.gsjournal.net/old/valev/val3.gif

A. KATCHALSKY, POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, p. 15, Figure 4: "Polyacid gel in sodium hydroxide solution: expanded. Polyacid gel in acid solution: contracted; weight is lifted."
https://www.ncbi.nlm.nih.gov/pmc/art...00645-0017.pdf

"When the pH is lowered (that is, on raising the chemical potential, μ, of the protons present) at the isothermal condition of 37°C, these matrices can exert forces, f, sufficient to lift weights that are a thousand times their dry weight." http://www.google.com/patents/US5520672

Pentcho Valev

Textbook analysis of a non-isothermal cycle involving a heat engine that uses an idealized rubber band:

http://electron6.phys.utk.edu/Physic...cs/2ndlaw.html
"Consider a heat engine that uses a rubber band in the three-step cycle shown.
Start with a stretched rubber band of length L0 , tension J0, and temperature TA.
Take the band through a sequence of reversible processes.
A -- B:
The rubber band is stretched under constant tension J0 to a length 2L0 while in contact with a heat reservoir of temperature TB.
B -- C:
While in contact with a heat reservoir of temperature TC the tension of the rubber band is increased from J0 to 2J0 at constant length 2L0 .
C -- A:
While in contact with a heat reservoir of temperature TA, tension and length decrease linearly from (2J0, 2L0) to (J0, L0).
(a) Find the ratios TB/TA and TC/TA. What is the ratio Thot/Tcold?
(b) Find the work done by the heat engine as it moves through one cycle A -- B -- C -- A.
(c) During one cycle A -- B -- C -- A, how much heat is extracted from the hot reservoir and how much heat is dumped into the cold reservoir?
(d) Find the efficiency of this rubber-band heat engine and compare it to the efficiency of a Carnot engine operating between the same temperatures." [END OF QUOTATION]

Analogous but much simpler analysis can be applied to an ISOTHERMAL cycle involving a heat engine that uses a pH-sensitive polymer, e.g. the one shown in fig. 4 in Katchalsky's article:

POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. Katchalsky, p. 15, Figure 4: "Polyacid gel in sodium hydroxide solution: expanded. Polyacid gel in acid solution: contracted; weight is lifted."
http://www.ncbi.nlm.nih.gov/pmc/arti...0645-0017..pdf

The following four-step isothermal cycle, if carried out quasi-statically (reversibly), clearly violates the second law of thermodynamics:

1. The polymer is initially stretched. The operator adds hydrogen ions (H+) to the system. The force of contraction increases.
2. The polymers contracts and lifts a weight.
3. The operator removes the same amount of H+ from the system. The force of contraction decreases.
4. The operator stretches the polymer and restores the initial state of the system.

The net work extracted from the cycle is positive unless the following is the case:

The operator, as he decreases and then increases the pH of the system (steps 1 and 3), does (loses; wastes) more work than the work he gains from weight-lifting.

However electrochemists know that, if both adding hydrogen ions to the system and then removing them are performed quasi-statically, the net work involved is virtually zero (the operator gains work if the hydrogen ions are transported from a high to a low concentration and then loses the same amount of work in the backward transport).

Pentcho Valev

Non-isothermal heat engines - do not violate the second law of thermodynamics:

http://readingpenrose.files.wordpres...and-engine.gif

Isothermal analogs - do violate the second law of thermodynamics:

http://www.gsjournal.net/old/valev/val3.gif

The former are popular and universally taught, the latter are totally unknown. Thermodynamicists suggest that isothermal heat engines don't even exist:

"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."
http://physics.bu.edu/~duffy/py105/Heatengines.html

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Isothermal heat engines violating the second law of thermodynamics and representing, perhaps, the most primitive biological motors (their role in living systems may have been masked by the appearance, in the course of evolution, of more powerful and fast-working motors using energy other than heat):

http://image.slidesharecdn.com/1-sma...als-28-638.jpg

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