Second Law of Thermodynamics versus Maxwell's demon.

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Nicolaas Vroom

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Oct 30, 2022, 9:02:11 PM10/30/22
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For an introduction of Second law of Thermodynamics read this:
https://en.wikipedia.org/wiki/Second_law_of_thermodynamics
If you want to study any subject you must first define what you
mean. There are two definitions:
1) One simple statement of the law is that heat always moves from
hotter objects to colder objects (or "downhill"), unless energy is
supplied to reverse the direction of heat flow.
(Text copied from Wikipedia)
2) The second definition starts from an experiment:
We start with an empty container. We place a divider in the container.
One half we fill with hot water and one half with cold water.
We remove the divider. We measure with a thermometer the water
and we observe what happens.
Initial the water temperature on one side is higher than on the
other side, but slowly this difference decreases and after a certain
time this difference disappears and the temperature becomes in
equilibrium. What is also possible that there after the average
temperature of the container slower drops.
This process we call the Second Law of Thermodynamics.
The physical explanation is that two water molecules in close contact
exchange heat from the hotter molecule towards cooler molecule, such
that the hotter one becomes cooler and the cooler one becomes hotter.

Someone could claim that the result of both definitions is the same.
That is true. But the second definition is more complete; you
should always start with an experiment.

With an experiment you can also establish the following rules.
When you want to increase the average temperature, you have to add
more hot water.
When you want to decrease the average temperature, you have to add
more cold water.

For an introduction of Maxwell's demon read this:
https://en.wikipedia.org/wiki/Maxwell%27s_demon
Also, in this case there are two definitions:
1) In the thought experiment, a demon controls a small massless
door between two chambers of gas. As individual gas molecules
(Or atoms) approach the door, the demon quickly opens and closes
the door to allow only fast-moving molecules to pass through in
one direction, and only slow-moving molecules to pass through
in the other.
Etc. the demon's actions cause one chamber to warm up and the
other to cool down.
2) The purpose of the experiment to cool down chamber A
and to heat up chamber B. To do that the experimenter has to take
two actions:
A1) To select the molecule with the highest temperature in chamber A
and transport this molecule to chamber B.
A2) To select the molecule with the lowest temperature in chamber B
and transport this molecule to chamber A
Both these molecules have to be exchanged 'simultaneous'.
As a result of this action the average temperature in chamber A will
decrease and in chamber B will increase.
B1) The two actions should stop when in (A1) the temperature of the
molecule with the highest temperature in chamber A is lower than
the average temperature in B.
B2) The same when in (A2) the temperature of the molecule with the
lowest temperature in chamber B is higher than the average
temperature in A.
The problem is that as part of the two actions A1 and A2 each time
it becomes more difficult to decide which molecules to select.
To state this more realistic: that more energy is involved.
Each of the two actions requires energy.

The conclusion of this experiment is in contradiction with
definition 1 of maxwell's demon.

When you combine the two experiments the situation becomes:
Considering two chambers with different temperatures, combining
these two gives one chamber with the average temperature.
This process evolves without 'any' effort.
In a second phase, trying to go back to the original situation
costs a lot of effort. This is because specific molecules in
A have to be selected to be transported to B and vice versa.
This process will stop before the original situation is reached.
To reach the original situation extra energy is required.

https://www.nicvroom.be/wik_Second_law_of_thermodynamics.htm
https://www.nicvroom.be/wik_Maxwell's_demon.htm

Nicolaas Vroom

Thomas Koenig

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Nov 1, 2022, 4:15:51 AM11/1/22
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Nicolaas Vroom <nicolaa...@pandora.be> schrieb:
> For an introduction of Second law of Thermodynamics read this:
> https://en.wikipedia.org/wiki/Second_law_of_thermodynamics
> If you want to study any subject you must first define what you
> mean. There are two definitions:
> 1) One simple statement of the law is that heat always moves from
> hotter objects to colder objects (or "downhill"), unless energy is
> supplied to reverse the direction of heat flow.
> (Text copied from Wikipedia)
> 2) The second definition starts from an experiment:
> We start with an empty container. We place a divider in the container.
> One half we fill with hot water and one half with cold water.
> We remove the divider. We measure with a thermometer the water
> and we observe what happens.

If you look at the macroscopic of phenomenological thermondynamics,
the second law is easy:

dS/dT >= q

where S is the entropy of a (closed) system, T the temperare
and q the heat exchanged across the system's boundary.

(There is a quick question to see if people you're discussing
the Second Law and entropy knows what they are talking about.
Ask them how to decrease the entropy of a glass of water.
If they answer "This is not possible, because entropy always
increases", they are caught in a misconception promoted by
popular science. If they answer sometething like "put it in the
fridge" or "empty it", they know what they are talking about).

Nicolaas Vroom

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Nov 2, 2022, 10:08:19 AM11/2/22
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Op dinsdag 1 november 2022 om 09:15:51 UTC+1 schreef Thomas Koenig:
> Nicolaas Vroom <nicolaa...@pandora.be> schrieb:
> > For an introduction of Second law of Thermodynamics read this:
> > https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

> If you look at the macroscopic of phenomenological thermodynamics,
> the second law is easy:
>
> dS/dT >= q
>
> where S is the entropy of a (closed) system, T the temperature
> and q the heat exchanged across the system's boundary.

If you want to know something about entropy read this:
https://en.wikipedia.org/wiki/Entropy#Reversible_process
Entropy change dS is defined as dS= dQ/T
In my text I did not mention Entropy.

> (There is a quick question to see if people you're discussing
> the Second Law and entropy knows what they are talking about.
> Ask them how to decrease the entropy of a glass of water.
> If they answer "This is not possible, because entropy always
> increases", they are caught in a misconception promoted by
> popular science. If they answer something like "put it in the
> fridge" or "empty it", they know what they are talking about).

?
My understanding is, that entropy is more important related
to the Carnot cycle which I did not discuss.

In Maxwell's demon what the 'demon' tries to do is:
1. To select the coldest water molecule from the left chamber
and move this to the right chamber and
2. At the same time to select the hottest water molecule from
the right chamber and move this to the left chamber.
This will increase the average temperature of the left chamber
and decrease the average temperature of the right chamber.
The demon should stop until T of the coldest water molecule from
the left chamber is higher than the Average T of the right chamber.

You can also claim that the result is that the Entropy of the
left chamber has increased and of the right chamber has decreased.
You could also claim that the overall Entropy stays the same(?)

I have a general problem with this whole exercise, because the
selection and transport of the water molecule also costs energy.
This has nothing to do with the concept entropy.

https://www.nicvroom/be/
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