Thermodynamic arrow of time. Equating Entropy and Disorder?

[Sorcerer]

I have been extremely confused by Stephen Hawkings broken cup analogy for years.

 

“You may see a cup of tea fall off of a table and break into pieces on the floor. But you will never see the cup gather itself back together and jump back on the table… The increase of disorder, or entropy, is what distinguishes the past from the future.”

 

How is entropy eqivalent to disorder and how is the cup gaining entropy, surely the cup is the same temperature?

A system at equilibrium has maximum entropy, a system at equilibrium is highly ordered, it is as ordered as it can get. All parts are equal. Ordered things are easy to describe, people in uniform are easier to describe than people in fancy dress.

Isn't a system where the heat is unevenly distributed is more disordered? Is something not translating from the maths to the use of english, it just seems backwards.

This analogy is terribly misleading in that it makes us think of entropy as a measure of particles positions relative to each other, surely the tea cup has just as many parts in either configuration and both are equally ordered, just in different configurations.

Is entropy only a measure of heat. How did it become a measure of order? And why does the analogy seem so backwards to me?

[swansont]

How is entropy eqivalent to disorder and how is the cup gaining entropy, surely the cup is the same temperature?

 

There are more states available for the pieces to be in when it's broken. When it's whole, there is only one state. S = k_Bln(N)

 

https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)#Boltzmann.27s_principle

[Sorcerer]

 

There are more states available for the pieces to be in when it's broken. When it's whole, there is only one state. S = k_Bln(N)

 

https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)#Boltzmann.27s_principle

I kind of see, but it is only in one of those states. However then I get confused becuase when something is in equilibrium there is only 1 state.

 

Ok, so lets make coloured balls represent particles with temperature. Lets use the classice blue ---> red scale representing heat (sure you know it).

 

So if there's 3 balls all green, sitting in the corners of a triangle, even we they're rearranged the arrangement looks exactly the same, does the possible number of states also include identicle states? In that case, doesn't the tea cup exist in all it's identical states?

 

However with 3 different coloured balls, red green blue, there is 6 possible states. Even if we count arrangements of the green balls by say numbering them 1 2 3, there's still only 6, and that's the same. Are you counting the possible states, where the red ball transfers some heat to the blue ball and there is also 3 greens, are you including possible future states? Because things only classically exist in 1 state at a time.

Edited August 3, 2015 by Sorcerer

[studiot]

You need to be very clear what is meant by both equilibrium and state.

 

There are two (thermodynamic) drivers for the future direction of a system's state.

 

Minimum Energy

Maximum Entropy

 

These two may be aligned or they may be opposed and the resulting state is then a balance between these two.

Edited August 3, 2015 by studiot

[swansont]

I kind of see, but it is only in one of those states.

 

A broken cup has many possible states. An unbroken cup has only 1.

[Sorcerer]

 

A broken cup has many possible states. An unbroken cup has only 1.

I think I get it, it's just a cup.....

 

But there's only 1 broken cup, it only broke one way. I don't get how this relates, you have to put work in to rearrange the peices of the cup that's broken if you want to create more possible states, the peices aren't going to move themselves.

[swansont]

I think I get it, it's just a cup.....

 

But there's only 1 broken cup, it only broke one way. I don't get how this relates, you have to put work in to rearrange the peices of the cup that's broken if you want to create more possible states, the peices aren't going to move themselves.

 

Available states ≠ occupied states

[Sorcerer]

Actually I think the only question I need clarifying here is why is a system (lets use a gas) at equilibrium considered to be less ordered than a system which isn't? What is the measure of "Order".

When trying to visualise it at equilibrium, I see a fairly uniform gas, all molecules moving roughly equal speeds, doing their brownian motion thing. But when not at equlibrium, I see some slow molecules being whacked by really speedy ones whizzing around, it seems much less ordered. Why isn't it?

 

Available states ≠ occupied states

oh I see, it's statistics, but the way the cup broke is deterministic..... sorry I'm getting it now, it's very unlikely to unbreak, but it's just as unlikely to spontaneously rearrange into almost all of the available states, just the few closest to it.

[MigL]

Let me see if I can help clarify.

 

Instead of a cup, lets use a book, with 100 pages.

For the book to be 'ordered', i.e. make sense, those pages have to be in sequence 1 to 100.

That is one state.

 

Now take the book, rip out the pages, and toss them in the air.

When you pick them up, how many different states can you have ?

The first page can be any one of 100.

The second, any one of 99.

The third, any of 98.

And so on ..., to the last page.

This is a possible 100! states. An extremely large number.

And that is why you will never see a book's pages fall into that one 'ordered' state.

 

And that is what physics considers 'order' and 'disorder'.

[studiot]

 

Actually I think the only question I need clarifying here is why is a system (lets use a gas) at equilibrium considered to be less ordered than a system which isn't? What is the measure of "Order

 

That's not true.

 

Did you miss my post4?

 

It is not equilibrium within the system that counts.

[Sorcerer]

Let me see if I can help clarify.

 

Instead of a cup, lets use a book, with 100 pages.

For the book to be 'ordered', i.e. make sense, those pages have to be in sequence 1 to 100.

That is one state.

 

Now take the book, rip out the pages, and toss them in the air.

When you pick them up, how many different states can you have ?

The first page can be any one of 100.

The second, any one of 99.

The third, any of 98.

And so on ..., to the last page.

This is a possible 100! states. An extremely large number.

And that is why you will never see a book's pages fall into that one 'ordered' state.

 

And that is what physics considers 'order' and 'disorder'.

No there's only 1 possible state once you've picked them up. Deterministicly there is only 1 possible state for the pages to end up in because of the way you ripped them out and all other combining factors and how you picked them up. There might be 100! possible states before you ripped them out, but it is still only in 1 state as the whole book, with !100 possible states that it's pages could be rearranged. Ripping them out will only give 1 state out of 100!-1 states, but the way that occurs determines which state it is, it is only ever that one, there is only ever 1 possible state. You could purposefully repeat and arrange them in different orders, but each time they were never possibly going to be in any other order. They were in the order you put them in. The probability doesn't make sense. It seems like a lazy way to approximate reality.

 

Or is it rather that the reality in regards to heat that it's distribution actually IS only probabalistic and not deterministic? What exactly are the peices in the analogy, with regards to heat.

 

 

That's not true.

 

Did you miss my post4?

 

It is not equilibrium within the system that counts.

Sorry I didn't understand what you were saying in #4.

 

I have been told on this forum that a system with maximum entropy is at equilibrium. And that apparently equilibrium is then the most disordered state.

 

Are you saying that there can be various types of equilibrium, and that maximum entropy isn't a requirement?

 

Let me rephrase:

 

"Why is a system with maximum entropy considered to be less ordered than a system with less entropy?"

"Why is a system uniform in heat distribution, less ordered than a system with uneven heat distribution?"

"How is it possible to rearrange something uniform in more ways than something which is uneven?"

"Why does the position or order of equal quantities of something create a new arrangement, when it is quantafiably identicle?"

Edited August 4, 2015 by Sorcerer

[MigL]

A system with maximum entropy has way more states that it can be in than a system with less entropy.

Going back to the book analogy...

The only way the book makes 'sense',( is readable and ordered ) is if the pages are sequential ( 1,2,3...100 ). That is why there is only one state.

When you pick up the scattered pages, you are picking them up randomly. The first pge you pick up may be pg 17, or pg 52. There are 100 different, possible first pages you can pick up. And 99 different, possible second pages, etc. That is why there are 100! different, possible states.

 

One is an ordered state, in a specific arrangement. The other is a randomized arrangement with maximal entropy.

You can extend this analogy to a mole of gas, but then you're talking about a million, billion, billion particles, and their particular arrangement.

[Sorcerer]

How can something which is uniform (at maximum entropy) be arranged in any other way?

[MigL]

If, by uniform you mean the same thing I mean,then you can re-arrange any of the particles making up that 'uniform' gas/system and nothing will change.

There is no potential, and no useable energy to do work with, and therefore entropy is maximized.

 

You see this with the usual example of two gases of differing temperature, in a box, separated by a partition. When the gases are separate, you have a temperature potential dfferencs, and so, can do work.

Once the separation is removed the gases quickly intermingle into a 'uniform' distribution. There is no more temperatute potential difference, no more work can be done using a temp difference, and entropy is maximized

[Sorcerer]

But when entropy is at 0 isn't it also true you can "re-arrange any of the particles making up that 'uniform' gas/system and nothing will change."?

 

Interesting you said this as I was just looking at the third law of thermodynamics. A perfect crystaline structure at absolute 0 is also uniform. There is no temperature potential difference, no work can be done, however entropy is minimised, or 0.

Am I just seeing paralelles where there are none?

[MigL]

Again,it depends on your definition of 'uniform'.

 

In any crystal, atoms/molecules are arranged in one specific pattern, ie.extremely ordered.

It may be 'uniform'but certanly not a randomized distribution.

[studiot]

At least as important as your definition of uniform is using the correct definition of order.

 

Order does not mean set out in rows and clumns like soldiers at a parade.

 

Since you asking the same question in at least three threads, I have been trying to keep the reply confined to one.

 

Perhaps you missed my last reply there?

 

http://www.scienceforums.net/topic/90143-entropy-at-maximum/

Edited August 9, 2015 by studiot

[singhsippi]

Do not confuse this with Enthalpy

In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder. According to the second law of thermodynamics the entropy of an isolated system never decreases; such a system will spontaneously proceed towards thermodynamic equilibrium, the configuration with maximum entropy. Systems that are not isolated may decrease in entropy, provided they increase the entropy of their environment by at least that same amount. Since entropy is a state function, the change in the entropy of a system is the same for any process that goes from a given initial state to a given final state, whether the process is reversible or irreversible. However, irreversible processes, increase the combined entropy of the system and its environment.

 

 

url deleted

edited by mod

 

!

Moderator Note

 

This is a direct quote from Wikipedia.

https://en.wikipedia.org/wiki/Entropy

 

Any more posts that consist of only plagiarised material and a spammy link will lead to an immediate spam-ban.

 

Edited September 3, 2015 by imatfaal
put in quote and reference

[studiot]

 

In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder

 

 

I suggest you go back to the drawing board and think again.

 

Given the above definition any finite system that included a continuum would have infinite entropy.

 

Here's a hint.

 

Wat are the units of Entropy if you look in standard entropy tables?

And what are the units of 'number of specific ways' ?

and ask yourself why they are different.

Edited September 3, 2015 by studiot

[Cuba]

Way I see it is a gas can be compared with the book analogy only with no page numbers. It makes no difference what order they are in. So regardless of how you pick up the pages it will always be uniform, and since any state is a correct state it is always at maximum entropy as there is not another state it can exist in.

 

That is what I got from reading threw this thread at least.

[Sensei]

How can something which is uniform (at maximum entropy) be arranged in any other way?

Air gas molecules in room temperature and pressure have average 340 m/s velocity.

Arrangement of particles constantly changes.

Say we have heating element in room,

electrons passing through resistor heat it,

and resistor is cooled down by air molecules, and accelerates them,

they have higher velocity, higher kinetic energy.

Then it spreads in whole room. Air molecule hits other air molecule, takes part of its kinetic energy. Repeat as many as you have molecules.

Temperature near heating element will be the highest, and the further from it, the smaller temperature.

 

Uniform temperature, uniform pressure, is just laboratory approximation, practically not existing in nature.

Walk with precise thermometer (say +-0.1 C or more precision) in hand, and you will find gradient of temperature present around us.

To have uniform temperature, to be able to precisely measure temperature in f.e. liquid scientists use magnetic stirrers.

[studiot]

 

Way I see it is a gas can be compared with the book analogy only with no page numbers. It makes no difference what order they are in. So regardless of how you pick up the pages it will always be uniform, and since any state is a correct state it is always at maximum entropy as there is not another state it can exist in.

 

That is what I got from reading threw this thread at least.

 

 

 

Why have an analogy when you can have the real thing?

 

Entropy refers to occupancy of energy states.

 

What you say about always being at maximum entropy is true if all the energy states are fully occupied.

 

But most systems are not like this.

Most systems have many more unoccupied states than occupied ones so present a huge number of possible occupancy arrangements.

[Cuba]

 

 

Why have an analogy when you can have the real thing?

 

I like teaching people that do not have a degree in physics, analogies help. I posted to see if there are any major faults in my observation and subsequent simplification.

[puppypower]

In chemistry, Entropy S is connected to Free Energy G and Enthalpy H (internal energy) by the equation. G=H-TS, where T is the temperature in degrees Kelvin. The cup is a chemical state that we call ceramic. When we give it a push off the table, we add activation energy to push it over an energy hill to take advantage of gravity; table to floor. For entropy to increase, energy needs to be made available, which is done via velocity and collision. The entropy increase will absorb energy. The TS has the units of energy/mole/K.

 

The second law or entropy will increase in the universe, is connected to the constant availability of free energy,y as the forces of nature lower potential. The sun releases heat from fusion. This heat is available to increase entropy and enthalpy. The plant will absorb energy and turn this into reduced carbon. This is connected to H or enthalpy. The cells burn this chemical energy and cause entropy to increase via the availability of energy/heat. The arrow of time, connected to entropy, is due to the availability of energy as universal potentials lower.

 

Entropy is a state variable. This means the value of entropy is fixed for a given state of matter. For example the entropy of water at 25C is 6.6177 J mol^-1 K^-1 (25 °C). This is true no matter who measures it. The water may be composed of random collisions of H2O, but these always average the same for that state to give a fixed entropy value. This is an example of random leading to order; state. If we add energy to this state, some will go into H and some into S. The entropy increase will distribute to form a new state, which will always be measured the same for all.

 

The living state is interesting in that life can induce state changes allowing a local decrease in entropy. This is sort of where the broken cup, reassembles. The most obvious example is connected to reverse osmosis, where water and ions becomes pure water by applying pressure. The new state has less entropy, while giving off the energy it once absorbed. The new state of water, with a lower entropy, can be used to assist things that need a lower entropy solvent state, to happen.

 

This may be off the basic topic, but water is unique when it comes to entropy. This uniqueness comes from the fact that the hydrogen bonds of water can be ionic or covalent. The ionic state defines higher entropy, while the covalent state defines a state of lower entropy. One hydrogen bond without ever breaking, can switch between higher and lower entropy. This is useful for life in that the hydrogen bonds of water define binary switches; memory. The cell can shift to the lower entropy state of the hydrogen bonding to get a energy releases, while not breaking any hydrogen bonds. Or it can switch back to the high entropy state. Since this needs to absorb energy, it can act like an energy siphon which can help induce chemical reactions near enzymes.

Edited October 9, 2015 by puppypower

[studiot]

puppypower you have obviously studied some thermodynamics.

 

Unfortunately you have some misconceptions mixed in there.

 

 

Enthalpy H (internal energy)

 

No, internal energy and enthalpy are different properties. Enthalpy is sometimes called the heat content.

 

 

Entropy is a state variable. This means the value of entropy is fixed for a given state of matter

 

Yes entropy is a state variable, but states are defined as equilibrium states. What if the system is not in an equilibrium state?

 

Most of the time, most of the universe is not in an equilibrium state.