From: John Jones on 6 May 2010 17:58 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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