In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity of the particles. However no such velocity can exceed that of light. Is there therefore an absolute upper bound to temperature as well as an absolute zero?
Answer
Temperature is proportional to the average kinetic energy, not velocity, of the particles. Kinetic energy is unbounded; it goes to infinity as velocity approaches light-speed, proportional to $(1 - v^2/c^2)^{-1/2}$.
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