  The relativistic continuity equations for the extensive thermodynamic
quantities are derived based on the divergence theorem in Minkowski space
outlined by St\"uckelberg. This covariant approach leads to a relativistic
formulation of the first and second laws of thermodynamics. The internal energy
density and the pressure of a relativistic perfect fluid carry inertia, which
leads to a relativistic coupling between heat and work. The relativistic
continuity equation for the relativistic inertia is derived. The relativistic
corrections in the Euler equation and in the continuity equations for the
energy and momentum are identified. This relativistic theoretical framework
allows a rigorous derivation of the relativistic transformation laws for the
temperature, the pressure and the chemical potential based on the relativistic
transformation laws for the energy density, the entropy density, the mass
density and the number density.
