# Entropy and volume

1. Feb 19, 2009

### sirchasm

In a closed system (which has no constructible physical reality), heat and work are distinct.

There are two paths a closed system can take, to reach the same point.

But, do both paths result in the same changes to the entropy-volume?

this question got trashed in another 'syince forum' - does any one have a pointer?

2. Feb 19, 2009

### Mapes

Does "reach the same point" mean "reach the same state" or "reach the same energy"? If the former, then the entropy per unit volume is changed identically; entropy and volume are state variables. If the latter, then not necessarily; adding 10 J, say, by heat will change the entropy per unit volume in a different way then adding the same amount by work.

EDIT: I should explain the difference between the two endpoints. If you're assuming the two systems are brought to the same final state, this implies that the temperatures, volumes, pressures, energies, entropies, etc. are equal. Both heat and work must be applied to both systems to satisfy this condition, but there is no requirement on the order. The final entropy and entropy per unit volume will be identical. If you're assuming the two systems are brought to the same energy only (by heating one and doing work on the other) and the pressures, volumes, etc. can be different, then the total entropy will be higher in the system that was heated.

Last edited: Feb 19, 2009
3. Feb 21, 2009

### sirchasm

OK, if you're considering the volume of the physical gas, then entropy (thermodynamic) is a state variable = 'total energy'.

Work is 'energy per unit of time', thermodynamic entropy is 'global energy over time'.
Any physical work is a derivative of energy content, measurable as pressure (a deformation of volume) and temperature (a derivative of volume in pressure units); then "volume" of the physical gas is a diffusion which is positive or negative, according to entropy content; work is a measure of energy flow, and temperature is a measure of energy flow rate.

What about dimensionless information entropy? Does it have a volume or pressure? The units are (0,1), so what does information entropy correspond to in a gs?

4. Feb 21, 2009

### Mapes

Except for "work is a measure of energy flow," this is mostly incorrect. It looks like you're just stringing technical terms together. I don't know what you're talking about.

When you say "Any physical work is a derivative of energy content," for example, does this correspond to the common definitions of work, derivative, and energy, and if so, how?

5. Feb 21, 2009

### sirchasm

Except for your misunderstanding of "work is a derivative", what prompted you to claim "this is mostly incorrect"?

Why is it mostly incorrect? (I got 'work = measure of flow', correct, huh?)

P.S. I appreciate being corrected if I am in fact, incorrect. I don't see the point of being told "that's incorrect", and waiting around for an explanation when there isn't one.

But, I suppose I should also appreciate that someone has bothered to at least post a response of some kind.
Yo' gets what yo' can in de big worl'

6. Feb 21, 2009

### Mapes

Yes, "work is a measure of energy flow," is a statement resembling consensus physics (more accurately, we would say that "work is energy in transit," because power, not work, is a measure of energy flow per unit time). A similarly worded statement can be found in textbooks. It's compatible with the definitions of work and energy, and the units match (work and energy are measured in joules).

"Any physical work is a derivative of energy content" doesn't make any sense to me. Saying that temperature is "a derivative of volume in pressure units" doesn't make any sense to me. Perhaps they're misinterpretations of something you read. But personal theories are not appropriate for this forum; that's why I asked whether you are using standard scientific definitions. Can you provide a reference for these statements?

7. Feb 21, 2009

### sirchasm

Ok, just to see if we're on the same page, or if the page really exists, can you explain the equivalence between thermodynamic entropy, and information entropy?
What does work equal, in informational terms? Or power?

Any physical work, is derived from (physical) energy, energy and entropy are related (with no entropy volume, there is no energy). Therefore work is derived from entropy, or more exactly, from changes in entropy volume.
Even though thermodynamic work doesn't 'change' thermodynamic entropy...?

8. Feb 21, 2009

### Mapes

OK, got it. By "derivative" you didn't mean differentiation, you just meant that they're related. Makes sense.

And what about the reference for saying temperature is "a derivative of volume in pressure units"?