🚀 go-pugleaf

> In 1824 Sadi Carnot advanced a false premise and deduced a conclusion
> later called "the second law of thermodynamics":
>
> Kelvin's version: It is impossible to perform a cyclic process with no
> other result than that heat is absorbed from a reservoir, and work is
> performed.
>
> This implies that, when two INTERACTING heat engines absorb heat from
> a reservoir (the surroundings) and perform reversible work, the
> following equality of partial derivatives holds:
>
> dF1 / dX2 = dF2 / dX1
>
> where F1 and F2 are work-producing forces and X1 and X2 are the
> respective displacements.
>
> The above implication is more or less an oxymoron since the equality
> clearly characterizes NON-INTERACTING heat engines. At least in two
> cases (see http://www.wbabin.net/valev/valev2.htm ) the partial
> derivatives are not equal and therefore the second law of
> thermodynamics is false.
>
> Some day physical chemistry professors may realize that "students
> learning by rote" is good (makes professors' life serene) but
> "students thinking critically" is better. They may even discover that
> Katchalsky's and Urry's Polymers (Pk and Pu) as described in
>
> 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"
>
> are the perfect tool for an easy verification of the second law of
> thermodynamics. On acidification ([H+] increases) both Pk and Pu
> contract and can lift a weight. This means that:
>
> dFk / d[H+]  >  0   (Lk constant)
>
> dFu / d[H+]  >  0   (Lu constant)
>
> where F is the work-producing force of contraction and L is the length
> of the polymer.
>
> Pk and Pu differ in that Pk RELEASE protons on stretching whereas Uk
> ABSORB protons on stretching:
>
> d[H+] / dLk  >  0
>
> d[H+] / dLu  <  0
>
> If a Katchalsky's polymer and a Urry's polymer are suspended in the
> same solution, it follows from the above four inequalities that:
>
> dFk / dLu  <  0    (Lk constant)
>
> dFu / dLk  >  0    (Lu constant)
>
> Clearly the second law of thermodynamics is false. If it were true, we
> would have:
>
> dFk / dLu  =  dFu / dLk

Elaboration: The system is closed (exchanges energy but not matter
with the surroundings) and consists of two "chemical springs", a
Katchalsky's polymer (Pk) and a Urry's polymer (Pu), suspended in a
solution (see Urry's paper referred to above for pictures). The
REVERSIBLE work done by the system is:

dW = - Fk*dLk  -  Fu*dLu

where F>0 is the force of contraction and L is the length of the
polymer. Under ISOTHERMAL conditions, the variables Lk and Lu
obviously determine the state of the system - once their values are
fixed, the system remains in a unique equilibrium state. On the other
hand, W obviously depends on Lk and Lu. But this still does not
necessarily imply that W is a function of Lk and Lu. In order for W to
be a function of Lk and Lu, that is, for one to be allowed to write W
(Lk, Lu), the work done must be zero at the end of an isothermal
reversible cycle. Since Lk and Lu determine the state of the system, W
(Lk, Lu) can also be called a state function.

If Kelvin's version of the second law is correct, W is a state
function (reversibility and isothermicity are always required!) and
the (Maxwell's) equation

dFk / dLu (Lk constant)  =  dFu / dLk (Lu constant)

is obeyed by the "chemical springs" system. If the equation is not
obeyed, the second law of thermodynamics is false, that is, the system
is able, cyclically, to absorb heat from the surroundings and convert
it into work.

Pentcho Valev
pvalev@yahoo.com