  A description of thermodynamics for continuum mechanical systems is presented
in the coordinate-free language of exterior calculus. First, a careful
description of the mathematical tools that are needed to formulate the relevant
conservation laws is given. Second, following an axiomatic approach, the two
thermodynamic principles will be described, leading to a consistent description
of entropy creation mechanisms on manifolds. Third, a specialisation to
Fourier-Navier-Stokes fluids will be carried through.
