Open and closed in the geometrical sense vs the thermodynamic sense

In summary: Thanks, that actually completely answers my question. Forums turn people into internet tough guys. It's all good :)
  • #1
WraithM
32
0
"Open" and "closed" in the geometrical sense vs the thermodynamic sense

Perhaps this is a silly question, but what is the relationship between the words "open" and "closed" in the geometrical sense (open, flat, closed universes) and in the thermodynamic sense (open and closed systems) in the context of General Relativity? Is there no connection at all? Is there such a thing as a closed thermodynamic system and an open geometry or visa versa? Must a closed geometry be a closed thermodynamic system and visa versa?

I have a basic understanding of GR, and I understand a lot of the math behind it, so don't be afraid to give me a technical explanation.

Thank you!
 
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  • #2


They're different ideas. Open and closed with regards to thermodynamics is just referring to whether heat can be lost (open) or if energy is internally conserved (closed).

In GR, open and closed refer to geometries of 4d space-time, depending on if the density (omega) is greater or less than 1. If the universe is closed, it will contract again (the big crunch), if its open it will continue to expand indefinitely. There are some other effects (e.g. the sum of angles in a triangle), but I think you get the idea.
 
  • #3


zhermes said:
They're different ideas. Open and closed with regards to thermodynamics is just referring to whether heat can be lost (open) or if energy is internally conserved (closed).

In GR, open and closed refer to geometries of 4d space-time, depending on if the density (omega) is greater or less than 1. If the universe is closed, it will contract again (the big crunch), if its open it will continue to expand indefinitely. There are some other effects (e.g. the sum of angles in a triangle), but I think you get the idea.

I know the definitions of both. I was looking for the connection between the two. I fully understand that they're different ideas. Perhaps I didn't make myself clear in the question, but I meant how is the geometry related to thermodynamics? As I said, is it possible for a closed geometry to be an open system and visa versa? Or must an open geometry be an open system?

I've taken a course on basic GR and thermodynamics. I've just never dealt with the cosmological aspects of GR.
 
  • #4


WraithM said:
I know the definitions of both. I was looking for the connection between the two. I fully understand that they're different ideas.

Not so sure about that. See: http://en.wikipedia.org/wiki/Homonym" [Broken]
 
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  • #5


zhermes said:
Not so sure about that. See: http://en.wikipedia.org/wiki/Homonym" [Broken]

Calm down.
 
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  • #6


Sorry, unfortunately some of the people around these forums are rubbing off on me...
What I MEANT TO SAY was, the two ideas are quite separate. I guess, one would say that both open and closed geometries are closed thermodynamic systems because they are entire 'universes' (independent entities) of sorts, but I think that's straying from what you're asking.

CORRECTION: open and closed geometries can also refer to regions of curvature (I think), in which case there is really no relation between them and thermodynamics per se.
 
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  • #7


zhermes said:
Sorry, unfortunately some of the people around these forums are rubbing off on me...
What I MEANT TO SAY was, the two ideas are quite separate. I guess, one would say that both open and closed geometries are closed thermodynamic systems because they are entire 'universes' (independent entities) of sorts, but I think that's straying from what you're asking.

CORRECTION: open and closed geometries can also refer to regions of curvature (I think), in which case there is really no relation between them and thermodynamics per se.

Thanks, that actually completely answers my question. Forums turn people into internet tough guys. It's all good :)
 

1. What is the difference between open and closed in the geometrical sense?

In geometry, open and closed refer to the shape or structure of an object. An open shape has at least one side or boundary that is not connected to another side, while a closed shape has all sides connected. For example, a circle is a closed shape because all points on the boundary are connected, while a crescent moon is an open shape because the two ends of the crescent are not connected.

2. What does open and closed mean in the thermodynamic sense?

In thermodynamics, open and closed refer to systems that exchange energy and matter with their surroundings. An open system allows both matter and energy to enter and leave, while a closed system allows only energy to enter and leave. For example, a pot of boiling water is an open system because water vapor can escape and energy is being added through heat, while a sealed bottle of water is a closed system because no matter can enter or leave, but energy can still be added or removed.

3. Can a geometrical shape also be considered open or closed in the thermodynamic sense?

No, the concepts of open and closed in geometry and thermodynamics are unrelated. While a shape may be open or closed in terms of its physical structure, it cannot be open or closed in terms of exchanging energy and matter with its surroundings.

4. How do open and closed systems affect thermodynamic processes?

Open and closed systems have different effects on thermodynamic processes. In an open system, the exchange of matter and energy with the surroundings can impact the process, while in a closed system, only the exchange of energy can impact the process. This can lead to different outcomes and behaviors, such as a closed system reaching thermodynamic equilibrium faster than an open system.

5. Can a system be both open and closed in the thermodynamic sense?

Yes, a system can be both open and closed in the thermodynamic sense. This type of system is called an isolated system, where no energy or matter can enter or leave. This is often used as an idealized concept for studying thermodynamic processes, as it simplifies the system and removes the effects of exchange with the surroundings.

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