Are temperature and pressure related by relativity?

In summary, the conversation discusses the relationship between temperature and pressure in a fluid's rest frame and how it is affected by Lorentz transformations. The ideal gas law is mentioned as an equation of state that relates the two properties. There is also mention of the relativistic nature of temperature and how it has been a topic of debate. Ultimately, it is concluded that Lorentz transformations do not directly relate temperature and pressure, but rather they are both related to the average energy of the fluid.
  • #1
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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  • #2
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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Likes Gerald Kaiser
  • #3
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?
 
  • #4
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.
 

Related to Are temperature and pressure related by relativity?

1. How does relativity relate to temperature and pressure?

According to relativity, temperature and pressure are fundamentally related because they are both measures of the average kinetic energy of particles in a system. This relationship is described by the ideal gas law, which states that as temperature increases, so does pressure.

2. Can relativity explain the behavior of gases at extreme temperatures and pressures?

Yes, relativity can explain the behavior of gases at extreme temperatures and pressures. It takes into account the effects of special relativity, which describes the relationship between energy, mass, and velocity, as well as general relativity, which describes the warping of space and time by massive objects.

3. How does relativity affect the measurement of temperature and pressure?

Relativity does not necessarily affect the measurement of temperature and pressure directly, but it does influence the way we interpret these measurements. For example, the observed temperature and pressure of an object can change depending on the observer's frame of reference, due to the effects of special and general relativity.

4. Is there a limit to how high pressure and temperature can go based on relativity?

Yes, there is a limit to how high pressure and temperature can go based on relativity. This limit is known as the Planck temperature and pressure, beyond which our current understanding of physics breaks down. It is approximately 1.4 x 10^32 Kelvin and 1.2 x 10^113 Pascals.

5. How does relativity explain the relationship between temperature and pressure in systems with different masses?

Relativity explains the relationship between temperature and pressure in systems with different masses by taking into account the effects of mass and energy on the behavior of particles. As the mass of a system increases, so does its potential for energy, leading to higher temperatures and pressures. This is described by the famous equation E=mc^2, where E is energy, m is mass, and c is the speed of light.

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