The equation of state of non-relativistic energy

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Discussion Overview

The discussion centers around the equation of state for non-relativistic energy, specifically addressing the parameter w and its value of 0. Participants also explore the relationship between pressure in general relativity and its definitions in thermodynamics and statistical mechanics.

Discussion Character

  • Conceptual clarification, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why non-relativistic energy has an equation of state with w=0.
  • Another participant suggests that for normal non-relativistic matter, pressure is negligible compared to energy density, particularly in the context of an ideal gas.
  • A different participant reiterates the relationship between pressure and particle velocities, noting that significant pressure arises only when velocities are relativistic.
  • Some participants assert that the concept of pressure is the same in both general relativity and thermodynamics/statistical mechanics.

Areas of Agreement / Disagreement

Participants generally agree that the concept of pressure is consistent across different frameworks, but there is ongoing exploration regarding the implications of non-relativistic energy and its equation of state, indicating some unresolved aspects.

Contextual Notes

The discussion does not resolve the underlying assumptions about the conditions under which pressure becomes negligible or the transition from non-relativistic to relativistic behavior in gases.

Joey21
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I just have a quick question about a concept I think I haven't fully grasped from my cosmology course.

Why does non-relativistic energy have an equation of state with w=0?
Also, is the concept of pressure different in general relativity than in thermodynamics or statistical mechanics?
 
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No, it is the same concept. It is just that for normal non-relativistic matter, the pressure is negligible in comparison to the energy density. Consider an ideal gas and the pressure is going to be proportional to the temperature while the energy density is proportional to the mass of each particle. As long as the temperature is much lower than the mass, pressure is negligible (when temperature becomes comparable to mass you start reaching a relativistic gas behaving as radiation).
 
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Joey21 said:
Why does non-relativistic energy have an equation of state with w=0?
The model being used in this context is of a gas. The pressure of a gas is a function of the velocities of the individual particles that make up the gas. Those velocities have to be relativistic if the pressure is to be significant compared to the mass density.

Joey21 said:
Also, is the concept of pressure different in general relativity than in thermodynamics or statistical mechanics?
It's the exact same concept.
 
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Thanks for the quick replies! They will be a lot of help.
 

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