Move A->B What about entropy change?

[bolly]

move A-->B ...What about entropy change?

Hi,
I have a physical question regarding entropy, temperature, internal energy and mechanical energy.
The situation is following: Two objects are located inside a one dimensional frictionless and adiabatic space where object “a” is an observer that makes object “b” to move an increment into one direction via a force. (Obviously observer “a” has to move the same increment into the opposite direction). After that process both objects shall stay at fixed places for ever.

If we calculate the change of mechanical energy that the observes has to invest to make object “b” to move an increment then the energy change is zero because the force that the observer has build up against “b” to accelerate it into one direction is completely recycled because of deceleration at the end of the increment.

However this is also the point were I am unsure because I am not able to answer whether entropy and energy do change during that process or not. I would say no because internal energy has to stay constant but I hope that someone else here could give a better explanation or a hint.

A similar question regarding this is: Did the observer requires energy to make the process working ?

Best Regards,
bolly

 

[Simon Bridge]

Obviously observer “a” has to move the same increment into the opposite direction.[/quote] - object A just has to move according to the equal and opposite force exerted by A on B.

However this is also the point were I am unsure because I am not able to answer whether entropy and energy do change during that process or not. I would say no because internal energy has to stay constant but I hope that someone else here could give a better explanation or a hint.

A frictionless adiabatic space has properties: list them.
The list of properties should go a long way to clearing up your thinking here.

A similar question regarding this is: Did the observer requires energy to make the process working ?

The list of properties should help there too. What are the obvious energy changes? Is total energy conserved in the system you described?

 

[Andrew Mason]

Hi,
I have a physical question regarding entropy, temperature, internal energy and mechanical energy.
The situation is following: Two objects are located inside a one dimensional frictionless and adiabatic space where object “a” is an observer that makes object “b” to move an increment into one direction via a force. (Obviously observer “a” has to move the same increment into the opposite direction). After that process both objects shall stay at fixed places for ever.

If we calculate the change of mechanical energy that the observes has to invest to make object “b” to move an increment then the energy change is zero because the force that the observer has build up against “b” to accelerate it into one direction is completely recycled because of deceleration at the end of the increment.

However this is also the point were I am unsure because I am not able to answer whether entropy and energy do change during that process or not. I would say no because internal energy has to stay constant but I hope that someone else here could give a better explanation or a hint.

A similar question regarding this is: Did the observer requires energy to make the process working ?

Best Regards,
bolly

Can you explain why/how the force is "recycled"? What stops the objects from moving after a applies a force to b?

AM

 

[bolly]

Hello Bridge & Mason,
Thank you very much for your responses.
Regarding Bridges hint on the properties of the space:
The properties of the space can be considered as following:
- one dimensional
- adiabatic (no energy can go in and no energy leaves)
- the space is containing two objects (the object (the observer) “a” and the observed object “b” )
- the initial situation is, that both objects stay at fixed places since the beginning of all time
We need to consider an information generator inside the observer to generate the information when to start with the moving process. This generator just produces the information without energy release. This information then triggers the force generator (which is also inside the observer) which subsequently pushes the object “b”. The force generator builds up its force to accelerate object “b” up to finite velocity and then if a short period has elapses it build up force with opposite sign to decelerate object “b”. During deceleration the observer recycles its mechanically energy initially released to accelerate object “b”.Finally both objects stay at its new places for the rest of time.
Regarding Masons hint: No there is no explanation because every real system like a spring or magnet will build up infinite oscillation. The force generator inside the observer springs into action with a Heaviside like kinetic. I mean it builds up its force instantaneously. Then after the period has elapsed the generator stops its force generation instantaneously again with a Heavyside like kinetic.


Here is a small draft of the situation
--------------A-B----------------------------- 0<t<t1
---------- A-------B-------------------------- t = t1
---------- A-------B-------------------------- t1 < t< infinity
Regarding the force generator:

+F `````*
0 ****** ***** ********* t
-F...... *

I still have no idea but I hope for more hints.

Best Regards,
bolly

 

[Simon Bridge]

During deceleration the observer recycles its mechanically energy initially released to accelerate object “b”

That is a worrying statement - how can something recycle the energy it releases?
You say you have no explanation for this - could it be you have just described a non-physical process?

You have to identify the energy change, ask where the energy comes from.

Lets make this concrete:
A and B are the same total mass.
There initial separation is large compared with their own sizes.
A has an electromagnet and a battery. A simple switch can turn it on, or off, or reverse polarity.
B has a permanent magnet.

t<0 electromagnet is off.
t=0 switch electromagnet to "repel"
... A and B experience the repulsive force, and move apart from each other, picking up kinetic energy.
Where does this energy come from?

t=t1 reverse polarity
... A and B slow down with respect to each other
... when they are stationary again:

t=t2 switch electromagnet off

The situation with energy changes and entropy should be clear to you now.
Notice that from t=0 to t=2, energy is drained from the battery - where does it go?

 

[bolly]

Hi Simon,
maybe it is not so important, which mechanism actually is causing the process to work – for me it is more important whether the information, that starts the process can influences the entropy and temperature or not.

The process has no practical sense – it’s just theoretically to think about entropy and temperature.

Possible answers to my question are:

A.) entropy & temperature stay constant for ever (but why?)
B.) the production of an information that causes the process to start causes also a change of entropy or/and temperature (but why ?)

The reason for this question/model is an exercise from an undergrad textbook. The question is: How much energy is necessary to move an object frictionless from point 1 to point 2 on an equipotential surface of earth’s gravitational field. The answer is: zero. The explanation states that the energy to accelerate the object is recycled during deceleration. This is from the mechanical point of view true but I am unsure whether this is also the case if thermodynamics is considered. I added “the observer” which makes the object to move from point 1 to point 2.
I started this discussion here with my labmates – nobody is able to proof or bust the hypothesis and I would be very happy if you or another expert could give a good hint or maybe a proof that clarifies the situation.
Best Regards,
bolly

 

[pumila]

Not sure there is any change in entropy here.

1. Energy from the mechanism providing the accelerative force is converted losslessy into kinetic energy.

2. Kinetic energy is fully recovered into non-kinetic form by the deceleration.

So provided that the recovered energy is stored in an accessible form such as an idealised battery the energy remains available for further use and there has been no change in entropy.

Is this where you are going?

 

[bolly]

@pumilla
yes this is also the statement given in the textbook I mentioned before - however since I am not the expert in thermodynamics I still have a problem to basically accept this axiom.

If we would consider an observer „a“ and e.g. 12 objects which are non randomly moved by the observer in such a kind:

situation before t1:
* * * * * * * * * * * *
situation after t1:
************

I would say that in this case – if we consider an adiabatic space – the shown process is an isentropic compression which means the temperature will increase.
In my first example we would have – depending on the direction either an isentropic expansion or an isentropic compression. This will cause an temperature change and therefore a net energy change over time which the observer has released into the space.
However the objects do not repel each other which could mean there is no compression or expansion – but I am still unsure.

Maybe you or someone else could give another hint.

Best Regards,
bolly

 

[pumila]

If you have a mechanism that creates heat then you have lost control of the energy and since heat is not a fully-recoverable energy store then entropy changes.

So where exactly do you see this heat appearing? If it appears during the initial acceleration then you will have less kinetic energy to recover. If it occurs during deceleration then you are not recovering all the kinetic energy but are losing some to heat.

 

[bolly]

@pumila

I was thinking that the process describes an isentropic compression or expansion because the distance between the objects changes. According to the carnot process an isentropic compression causes the temperature to increase and vice versa. I hope this is correct so far.

Best Regards,
bolly

 

[pumila]

Isentropic processes do not change entropy.

What is being compressed? Is there a gas involved in the problem definition? The problem as originally defined does not allow for any compressible material.

If there is some sort of sealed piston arrangement involving gas compression then yes indeed, the temperature will rise as the gas is compressed, but the gas temperature will fall again as the gas expands so provided no heat escapes from inside the piston (an idealised "reversible adiabatic process" ) the extra energy used to drive the compression energy (and stored as a pressure differential) remains fully recoverable by returning everything to its starting position hence no change in entropy. No real process is truly 100% adiabatic, but we are talking theory here.

 

[bolly]

@pumila

Thank you very much – now we conclude:
The undergrad textbook statement that inside a frictionless 1d space a shift of an object with a defined mass consumes no energy is necessarily wrong. Because if the object is moved to another position to rest there forever then mechanical energy was converted to heat or heat was back converted into mechanical energy. This is because the system requires at least one observer which provides a force to move the object. The observer can be considered to be a second object in a certain distance to the moved object. If the distance decreases after the move then there is an isentropic compression which means that the temperature increases because mechanical energy was converted into heat. Otherwise if the distance between observer and the moved object increases then there is isentropic expansion which means that the temperature of the system will decrease because heat was converted into mechanical energy.
This holds if object and observer can be considered to be particles of an ideal gas (which is theoreticaly)
The only problem is following:
Do we have a compression if the distance between the particles or atoms of an ideal gas decreases (because a force is acting on the particles) ?

 

[pumila]

In saying that "The undergrad textbook statement that inside a frictionless 1d space a shift of an object with a defined mass consumes no energy is necessarily wrong" is predicated on there being isentropic compression, which is an extension that is not part of the original working hypothesis. This assumption implies some compressible 1D working fluid is sealed between the two system components (perhaps not a valid 1d assumption as fluids exist in 3d and pressure is at least 2d); this assumption changes the experiment so that conclusions drawn from it cannot be applied to the original textbook statement. The definition does not seem to treat the system components as behaving like the molecules of an ideal gas.

Given we have added a compressible working fluid to the system, the process is defined (quite reasonably) as isentopic, so no change in entropy. Since no change in entropy, why is that statement above "necessarily wrong"? It consumes energy only to store it in reversible form. The statement can be meaningful only if we are not looking at total available energy, but only the energy the observer has expended and has not yet recovered, while the original statement refers clearly to total energy.

That's as far as I can reasonably go. The question as it stands is perhaps not meaningful in the context of a 1d system, but laying aside the fact we cannot have any realisable 3d object like a gas molecule or even pressure in a 1d system, and instead assuming that ideal gases work in 1d systems like they do in 3d systems, we can suggest that at any temperature above absolute zero we would have compression as the molecules closed together. No idea how it would actually work though.

 

[bolly]

@pumila.
Thank you – I gas you right.

The only issue I have with this is that the information regarding the alignment of the objects (observer and object) has changed without energy consumption.

In general this would mean that information can be generated or changed without energy consumption – right ?

 

[pumila]

We could indeed use a logic zero as the initial position and a logic one as the alternate position. We could apply energy to change it into logic one, and absorb it back to make a logic zero again. Then add some way of reading it (perhaps try to extract the energy and if energy is output it must have been a logic one so we restore the one and generate an output). In theory it looks possible but there is a minimum energy loss to drive the output, plus the inevitable losses of a physical realisation of such a system.

 

[bolly]

-->>We could indeed use a logic zero as the initial position and a logic one as the alternate position. We could apply energy to change it into logic one, and absorb it back to make a logic zero again.<<--

@pumila
If we consider an adiabatic space (e.g. 3d) then the energy you are speaking from must be heat.
Every change of information that goes along with moving objects means either compression or expansion depending on the change of the positions. This causes either the temperature to rise or to drop (- however I have no idea how to measure the temperature inside a vacuum that is containing an observer and an object like a box). If the observer makes all it's changes retrogressively then the observer also absorbs all energy (heat) back.


A hypothetical quantum computer made of some sort of semiconductor material that uses the spin states of electrons which can be manipulated and measured by external electrical fields would change its temperature depending on the information stored inside.

 

[Simon Bridge]

Perhaps you are thinking more that object A is reading the information (as the observer), and object A is encoding it. i.e. you are trying to include the observer in the system?

So the if initial B position is 0, and the final B position is a 1, then the original description has A change the information from a 0 to a 1 without a a net change in energy - and you expected one. Would this be what you are saying?

 

[jeffrey c mc.]

Will someone post a serious response to; 'what is a one-dimensional space?' Color me stupid yet I always thought space was occupied by a three-dimensional object. Will someone please elucidate me on that idea. How can a question postulating a one-dimensional space, be semantically valid? Please advise.

 

[Simon Bridge]

Its an abstract mathematical concept ... "space" in classical physics is usually treated as a 3-volume, with an external time axis. However, a lot of physics reduces to 1D - i.e. when we are considering the translation of the center of mass of a body along a path or the variation in the electric potential about a spherical charge distribution.

So - in practice, 1D space means that all the properties of interest vary only in one direction in space.

The words "space" in math has a very broad meaning - go look up space and "subspace" in maths, to see what I mean.

A physical "space" can have any number of dimensions which need not have units of distance.
Each dimension is, itself, a space with dimension 1.

Semantically, the English language is fluid in that words can have different uses in different contexts.
You get used to it with practice.

 

[bolly]

-----< So the if initial B position is 0, and the final B position is a 1, then the original description has A change the information from a 0 to a 1 without a a net change in energy - and you expected one. Would this be what you are saying? >----

@ Simon,
yes exactly this is what I have tried to say – thank you for finding the right words.

Regarding this issue I found also this interesting link:
http://physicsworld.com/cws/article/news/2010/nov/19/information-converted-to-energy

I would be happy if we could conclude that information is basically heat if the space that contains that information is an adiabatic one.

Best Regards,
bolly

 

[pumila]

Not sure it is heat. The energy stored and retrieved is essentially related to the pressure - that is, an increased density of gas molecules. The temperature change is a consequence of that density change.

 

[jeffrey c mc.]

Thank you Simon;
From your discussion I understand that in order to simplify the measurement, two identities are related, and then described in their relation, and that is the dimension under consideration. The relation of the two together, in the system that is under scrutiny. Which may be a subsystem of a larger set, or not. Now I will go look at the mathmaticia reference in order to get an idea of the practice as applied. Thanks for the 'clue.'

 

[Simon Bridge]

Off the description, it does appear that the information has changed with no net change of energy in the observer.
I'm not sure this is a problem exactly - after all, entropy does not decrease.

But I notice: the state of the system changes - how does the observer know the state has changed?

I'm still not sure that the situation described is a physical one - even allowing the idealizations.
Can we come up with a physical realization which would work as described if we assumed stuff like zero friction?

You've seen the magnet approach.
We could also imagine A and B are connected by a spring, and a cord, under tension, held fast by A.
A affects the state change by releasing the cord for a time.
In that case there is a net change in PE in the spring.

 

[pumila]

The problem as stated has not fully defined the nature of a state output or a control input. Without these we have a two-state device is in its own isolated universe and of no use to anyone. How is the device used?

Either the observer 'knows' the current state, or the observer does not 'know' the current state and can only try to change it. In the former case we can ask the observer at any time, in the latter case we have to query the system via the observer in some way; however, querying such a storage device in that latter case is not a problem. Some storage devices are organised in such a way that their state is unknown till they are destructively queried. Magnetic core memory, for example. To read core memory, you try and set it to '0'. If you detect a magnetic energy transition you know it was a '1', else it must have been a '0' already; if it was a '1' then you need to rewrite it to '1' to restore the data.

 

[pumila]

There is no difference in entropy between two signals with the same scope. So a logic '0' and a logic '1' have no difference in entropy because they both represent the same level of organisation - a '1' is no more 'disorganised' than a '0'.

 

[bolly]

@pumila

There is also an observer who is actually moving the object. Therefore the distance between the observer and the object changes which is from my point of view different from a situation that describes just a single object that can exists as a logical “0” or “1”. If we define the logical value by the position of the object then we have at least a two bit system, were the observer has a logical value that changes in the opposite way compared with the object. (the space is frictionless therefore both the observer and the object have to change its absolute position)
The molecule "retinal" is such a system which can exist in the two states “cis ” and “trans”. To switch from “cis” to "trans" it needs to absorb a quant therefore is absorbs energy. The back conversion happens mechanically via an enzyme. If there is no back conversion the energy of the quant stays absorbed forever.

The given solution for the original textbook exercise (see my first post) is wrong because there must be an observer who actually moves the object. If so then the observer can only recover its mechanical energy if the object is moved back into its starting position.

Regarding "retinal": http://en.wikipedia.org/wiki/Retinal