Abstract
========
This article describes a closed system that - starting at same temperature - will build up a certain temperature difference inside this system.
In this system, a simple chemical reaction occurs, but equilibrium cannot be reached in the whole system. The reason is that in addition to the chemical reaction, there is force (e.g. gravitation) which always tries to separate the reactants and the
products to different parts of the system. Therefore the reactant concentrations in these parts are different - and therefore also the product concentrations. The chemical reaction tries to reach again a chemical equilibrium in these parts. This means
that in one part of the system the rate of the forward reaction is higher than the rate of the backward reaction and on the other part it is the other way round: the rate of the forward reaction is smaller than of backward reaction. When the chemical
reaction has different energy states then one part will be cooler and the other will be heated up. But again, the force will separate the reactants and products and so on.

This idea does not violate the second law of thermodynamics states that the total entropy can never decrease. In fact, building up a certain stable temperature difference will increase the entropy in this system.
However, this system violates the Clausius statement of the 2nd law, an empirically validated postulate of thermodynamics, which states that "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at
the same time."

Setup 1
=======
Please first suppose a simple chemical reaction A + B <=> AB in a system without an external force.
Let’s define that the density of A and B should be smaller than the density of AB and that this reaction should have a quite high bond dissociation energy, so the rate of reaction is small.

+-------------------+
| A BA B BA B |
| B A AB A B |
| B A AB AB A |
| A AB A AB B |
| AB A B B AB |
+-------------------+
No gravitational field --> same concentration in all parts

Regardless of the concentrations and distribution of the reactants A and B and product AB at the starting time (and the small reaction rate), there will be established a chemical equilibrium after a certain time. The concentrations of A, B and AB will
be the same in all parts of the system. Clearly no temperature difference will be built up.

Setup 2
=======
This system is similar to setup 1, however we have now a vertical gravitational field.
Suppose that in the beginning there is a chemical equilibrium distribution, so the forward and backward reaction rate is the same in all parts. Because of the gravity, the molecules A and B with the lower density will always be pushed up, AB with the
higher density will be pushed down. If the reaction rate would be high then A, B and AB would react so fast that the distribution remains in an equilibrium.

However, in this setup the reaction rate is quite low. So many of the molecules A and B can unhindered move upwards and AB unhindered moves downwards before a reaction may occur. This means that in the upper part, there are more A and B molecules than AB,
and in the lower part there are more AB than A and B.

So at the upper part, the high concentration of the reactants A and B favors the forward reaction of A + B <=> AB. Therefore, the forward reaction rate is higher than the backward reaction rate and so kinetic energy will be converted to bond energy.

Because of the gravitation, the product AB will immediately pushed down and other reactants A and B will be pushed up again. So it is not possible to establish there a chemical equilibrium, the rate of the forward reaction will be always higher than the
rate of the backward reaction.

On the lower part, it is the other way round: AB with the high density will be pushed down. So the concentration of product AB is higher than in the chemical equilibrium. Therefore the rate of the reverse reaction will be higher than the rate of the
forward reaction. A and B will be produced, but immediately pushed up because of the gravity, and again, there is no chemical equilibrium. So in the lower part bond energy will be converted to kinetic energy.


+-------------------+
| A B B A B |
| B A AB A |
| B AB A |
| A AB AB B |
| AB AB AB AB |
+-------------------+
With gravitational field --> A, B (low density) and AB (high density) will be separated. In the upper part the forward reaction dominates, in the lower part the backward reaction


It the upper part of system the higher number of forward reactions will convert kinetic energy into bond energy. In the lower part, because of the higher number of the backward reactions, bond energy will be converted to kinetic energy. This means the
top of the system will be cooled down, the lower part will be heated. Because of the gravity, the disorder of the concentration of the chemical equilibrium never stops, so there will be always a difference of forward and backward reactions on the top and
the bottom of the system.

After a certain time, a temperature difference will be established - since the heat exchange works against the temperature split. This temperature difference will always be pursued in this system, therefore this temperature difference has the highest
possible entropy in this system.


Conclusion
==========
This post describes a system with a chemical reaction which cannot reach chemical equilibrium, since an additional force always pushes reactants and products in different directions - and so equilibrium will be prevented. Moreover in one part the forward
reaction rate dominates in the other part the backward reaction rate. Thus one part will be cooled down, the other will be heated up - which means that heat can flow spontaneously from one part to the other part - until a certain temperature difference
will be established. This happens without external work being performed on the system. Moreover, many of these arrangements can be put together to increase the heat difference.

This idea can potentially work with any liquids and gases, and any forces like gravitational or electric fields and any chemical reaction.
This arrangement violates the empirically validated postulate of thermodynamics that states “Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.” It seems that in this
arrangement building up a temperature difference until a certain amount increases the entropy.
A similar idea with a catalyst is described here: https://groups.google.com/forum/#%21topic/alt.sci.physics.new-theories/07CSjnpoLdk

Best regards, Gerhard

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