T' = T, S' = gamma S, P'= gamma^2 P, V'= V/gamma, and U' = gamma U

Abstract

It is shown that the Lorentz invariant temperature $T^\prime=T$ and entropy $S^\prime=\gamma S$, pressure ${\cal P}^\prime = \gamma^2 {\cal P}$, volume ${\cal V}^\prime ={\cal V}/\gamma$, and energy $U^\prime = \gamma U$, where $\gamma = (1-V^2/c^2)^{-1/2}$, are the correct transformational properties of the thermodynamical quantities of the relativistic ideal gas.