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Dear Chris!

As you surely know, we define temperature in thermodynamics as the
derivative of energy with respect to entropy. There's no physical reason
why this derivative should be somehow limited. Although the *velocity*
of all particles in a gas is bounded by the velocity of light, there is
no limit to their *kinetic energy*, which really constitutes the
internal energy of a gas and therefore its temperature.

Maybe you are confused by the fact that in ideal gas calculations one usually uses the nonrelativistic energy-momentum relation E=p^2/2m, and with p=mv energy should be limited due to the limitation in v. But as you heat a gas to higher and higher temperatures, this relation is no longer valid but must be replaced by the relativistic equation E^2=m^2c^4+p^2c^2 with p=mv\gamma. Here \gamma is the well-known gamma factor 1/\sqrt{1-\beta^2}. So there is no limit to the kinetic energy.

Adopting the relativistic energy-momentum relation makes the formulae look slightly different, but a glance into any good textbook on thermodynamics and statistics will tell you at once that nothing fundamental changes.

Hope that helps,

Georg

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