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 ${\mathcal{P}}^{\prime }={\gamma }^2\mathcal{P}$, volume ${\mathcal{V}}^{\prime }=\mathcal{V}/\gamma$, 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.