"Entropy always increases": Is this the second law of thermodynamics?

"The second law of thermodynamics states that the entropy, or disorder, of a closed system is always increasing." https://www.youtube.com/watch?v=mGDJO2M7RBg

My comment on YouTube:

"Entropy always increases" is in fact a theorem deduced by Clausius in 1865:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "Hence we obtain: THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state."

Clausius' deduction was based on three postulates:

Postulate 1 (implicit): The entropy is a state function.

Postulate 2: Clausius' inequality (formula 10 on p. 33 in Uffink's paper) is correct.

Postulate 3: Any irreversible process can be closed by a reversible process to become a cycle.

All the three postulates are totally unjustified - clever scientists are well aware of that:

Uffink, p.39: "A more important objection, it seems to me, is that Clausius bases his conclusion that the entropy increases in a nicht umkehrbar [irreversible] process on the assumption that such a process can be closed by an umkehrbar [reversible] process to become a cycle. This is essential for the definition of the entropy difference between the initial and final states.. But the assumption is far from obvious for a system more complex than an ideal gas, or for states far from equilibrium, or for processes other than the simple exchange of heat and work. Thus, the generalisation to all transformations occurring in Nature is somewhat rash."

Pentcho Valev

A version of the second law of thermodynamics which is obviously false - "BY THE SAME AMOUNT" ("EQUALLY") is an unrealistic requirement:

"A catalyst reduces the time taken to reach equilibrium, but does not change the position of the equilibrium. This is because the catalyst increases the rates of the forward and reverse reactions BY THE SAME AMOUNT." http://www.bbc.co.uk/bitesize/higher...um/revision/2/

"In the presence of a catalyst, both the forward and reverse reaction rates will speed up EQUALLY... [...] If the addition of catalysts could possibly alter the equilibrium state of the reaction, this would violate the second rule of thermodynamics..." https://www.boundless.com/chemistry/...lyst-447-3459/

Consider the dissociation-association reaction

A - B + C

which is in equilibrium. We add a catalyst, and it starts splitting A so efficiently that the rate of the forward (dissociation) reaction increases by a factor of, say, 745492. If the second law of thermodynamics is obeyed, the catalyst must increase the rate of the reverse (association) reaction by exactly the same factor, 745492. But this is obviously unrealistic, even idiotic! In the reverse reaction the catalyst's function is entirely different - now it must get together B and C and then join them to form A. This may increase the reaction rate, but it would be nonsense to expect exactly the same factor, 745492.

There is no reason why the catalyst should increase the rates of the forward and reverse reactions "by the same amount" - some catalysts accelerate the forward reaction to a greater extent, others may favor the reverse reaction:

"Rhenium dissociates hydrogen molecules into atoms better than tungsten does; conversely, tungsten recombines hydrogen atoms back into hydrogen molecules better than rhenium."

Here is more explanation:

http://microver.se/sse-pdf/edgescience_24.pdf
"A small, closed, high temperature cavity contained two metal catalysts (rhenium and tungsten), which were known to dissociate molecular hydrogen (H2) to different degrees (Figure 1). (Rhenium dissociates hydrogen molecules into atoms better than tungsten does; conversely, tungsten recombines hydrogen atoms back into hydrogen molecules better than rhenium.) Because the dissociation reaction (H2 - 2H) is endothermic (absorbs heat), and the recombination reaction (2H - H2) is exothermic (liberates heat), when hydrogen was introduced into the cavity, the rhenium surfaces cooled (up to more than 125 K) relative to the tungsten (Figure 2). Because the hydrogen-metal reactions were ongoing in the sealed cavity, the rhenium stayed cooler than the tungsten indefinitely. This permanent temperature difference - this steady-state nonequilibrium - is expressly forbidden by the second law, not just because the system won’t settle down to a single-temperature equilibrium, but because this steady-state temperature difference can, in principle, be used to drive a heat engine (or produce electricity) solely by converting heat back into work, which is a violation of one of the most fundamental statements of the second law (Kelvin-Planck formulation)."

http://link.springer.com/article/10....701-014-9781-5
"In 2000, a simple, foundational thermodynamic paradox was proposed: a sealed blackbody cavity contains a diatomic gas and a radiometer whose apposing vane surfaces dissociate and recombine the gas to different degrees (A_2 - 2A). As a result of differing desorption rates for A and A_2 , there arise between the vane faces permanent pressure and temperature differences, either of which can be harnessed to perform work, in apparent conflict with the second law of thermodynamics."

https://en.wikipedia.org/wiki/Duncan%27s_Paradox
"Consider a dimeric gas (A2) that is susceptible to endothermic dissociation or exothermic recombination (A2 - 2A). The gas is housed between two surfaces (S1 and S2), whose chemical reactivities are distinct with respect to the gas. Specifically, let S1 preferentially dissociate dimer A2 and desorb monomer A, while S2 preferentially recombines monomers A and desorbs dimer A2. [...]

http://upload.wikimedia.org/wikipedi...SLTD-Fig1c.jpg

In 2014 Duncan's temperature paradox was experimentally realized, utilizing hydrogen dissociation on high-temperature transition metals (tungsten and rhenium). Ironically, these experiments support the predictions of the paradox and provide laboratory evidence for second law breakdown." [end of quotation]

Clearly, catalysts can violate the second law of thermodynamics by accelerating reversible chemical reactions in one direction but failing to produce the same acceleration in the opposite direction.

Pentcho Valev

Heat engines violating the second law of thermodynamics are commonplace but are extremely slow and impuissant - in our mercantile world this means that they will remain unnoticed. Three examples:

1. In the following two videos one switches the capacitor on and off and the system can repeatedly lift floating weights:

https://www.youtube.com/watch?v=aHNwvfXUYb4
Rise in Liquid Level Between Plates of a Capacitor

http://www.youtube.com/watch?v=T6KAH1JpdPg
Liquid Dielectric Capacitor

Switching the capacitor on and off involves no work done on the system so the energy for the work done BY the system (if it repeatedly lifts floating weights) can only come from the environmental heat, in violation of the second law of thermodynamics.

2. A simple perpetual-motion machine of the second kind is shown in Figure 4 he

http://www.ncbi.nlm.nih.gov/pmc/arti...00645-0017.pdf
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."

Mineral acid (hydrogen ions, H+) is added to the system and "the polymolecule contracts and lifts the attached weight through a distance ΔL". Then the acid can be removed and the macromolecule resumes its initial stretched state, ready to lift another weight. The work involved in adding and removing (electrochemically) hydrogen ions, if performed reversibly, is virtually zero, while the net work extracted from contracting and stretching is obviously positive - the system is cyclically lifting weights at the expense of heat absorbed from the surroundings, in violation of the second law of thermodynamics.

3. A perpetual motion machine of the second kind published in a prestigious journal and no reaction at all from the scientific community:

http://scitation.aip.org/content/aip...1063/1.4825269
Electricity generated from ambient heat across a silicon surface, Guoan Tai, Zihan Xu, and Jinsong Liu, Appl. Phys. Lett. 103, 163902 (2013): "We report generation of electricity from the limitless thermal motion of ions across a two-dimensional (2D) silicon (Si) surface at room temperature. [...] ....limitless ambient heat, which is universally present in the form of kinetic energy from molecular, particle, and ion sources, has not yet been reported to generate electricity. [...] This study provides insights into the development of self-charging technologies to harvest energy from ambient heat, and the power output is comparable to several environmental energy harvesting techniques such as ZnO nanogenerator, liquid and gas flow-induced electricity generation across carbon nanotube thin films and graphene, although this remains a challenge to the second law of thermodynamics..."

Pentcho Valev