Are temperature and pressure related by relativity?

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Discussion Overview

The discussion revolves around the relationship between temperature and pressure in the context of relativity, particularly focusing on gases and fluids. Participants explore how these properties are defined in different frames of reference and the implications of Lorentz transformations on their relationship.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that since temperature relates to average molecular energy and pressure to average molecular momentum, a Lorentz transformation might connect the two.
  • Another participant explains that temperature and pressure are defined in the fluid's rest frame and are connected through equations of state like the ideal gas law, noting the role of the energy-momentum tensor.
  • A later post clarifies that the discussion pertains to local temperature and pressure in non-equilibrium fluids and questions whether these should be computed in the local rest frame, acknowledging the controversial nature of relativistic temperature.
  • One participant concludes that pressure depends on the average of molecular velocities and is proportional to average energy, while also stating that the relationship between temperature and pressure is not derived independently but relies on the equation of state.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Lorentz transformations to relate temperature and pressure, with some suggesting a connection while others clarify the definitions and contexts in which these properties are considered. The discussion remains unresolved regarding the consensus on the relativistic character of temperature.

Contextual Notes

The discussion highlights the complexity of defining temperature and pressure in non-equilibrium states and the implications of different frames of reference, without reaching a consensus on the relativistic treatment of these properties.

Gerald Kaiser
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Since the temperature of a gas is related to its average molecular energy and the pressure to the average molecular momentum, it would seem that a Lorentz transformation would somehow relate the two. Does anyone know of related work?
 
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The temperature and pressure of a fluid is related to those properties in the fluid's rest frame. The temperature and pressure are related via an equation of state such as the ideal gas law. Lorentz transformations mix pressure and energy density with the off diagonal components of the energy-momentum tensor (of which kinetic energy of course gives a contribution to the energy density).
 
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Thanks. I should have added that I meant the LOCAL temperature and pressure in a fluid that's not necessarily in (global) equilibrium. Would those be computed in the local rest frame? I understand the the relativistic character of temperature has been a controversial topic. Has some consensus developed around it?
 
OK, I figured it out. Due to its isotropy, p depends only on the average of v^2 and is, in fact, proportional to the average energy. The expression for the temperature in terms of the average energy is not derived independently but uses the equation of state to show that it, too is proportional to the average energy (at least for an ideal gas). So I was wrong to think Lorentz transformations would relate the two. Thanks for the help.
 

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