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From: John Jones on 6 May 2010 17:54
Pentcho Valev wrote:
> Kelvin's version of the second law of thermodynamics: It is impossible
> to perform a cyclic process with no other result than that heat is
> absorbed from a reservoir, and work is performed.
>
> THEOREM: Kelvin's version of the second law is true if and only if,
> whenever two INTERACTING heat engines absorb heat from a reservoir
> (the surroundings) and perform reversible work, the following equality
> of partial derivatives holds:
>
> (dF1 / dX2)_X1 = (dF2 / dX1)_X2
>
> where "d" is the sign for partial derivative, F1 and F2 are work-
> producing forces and X1 and X2 are the respective displacements. If
> the two partial derivatives are not equal, the second law is false.
>
> Consider INTERACTING "chemical springs". There are two types of
> macroscopic contractile polymers which on acidification (decreasing
> the pH of the system) contract and can lift a weight:
>
> http://pubs.acs.org/doi/abs/10.1021/jp972167t
> J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
> Dan W. Urry, "Physical Chemistry of Biological Free Energy
> Transduction As Demonstrated by Elastic Protein-Based Polymers"
>
> Polymers designed by Urry (U) absorb protons on stretching (as their
> length, Lu, increases), whereas polymers designed by Katchalsky (K)
> release protons on stretching (as their length, Lk, increases). (See
> discussion on p. 11020 in Urry's paper).
>
> Let us assume that two macroscopic polymers, one of each type (U and
> K) are suspended in the same system. At constant temperature, if the
> second law is true, we must have
>
> (dFu / dLk)_Lu = (dFk / dLu)_Lk
>
> where Fu>0 and Fk>0 are work-producing forces of contraction. The
> values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can
> be assessed from experimental results reported on p. 11020 in Urry's
> paper. As K is being stretched (Lk increases), it releases protons,
> the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
> dLk)_Lu is positive. In contrast, as U is being stretched (Lu
> increases), it absorbs protons, the pH increases and Fk must decrease.
> Therefore, (dFk/dLu)_Lk is negative.
>
> One partial derivative is positive, the other negative: this proves
> that the second law of thermodynamics is false.
>
> Pentcho Valev
> pvalev(a)yahoo.com
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