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

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