Understanding and maybe even solving problems in energy conservation, energy transduction and global warming depend in part on advances in chemical thermodynamics. But chemical thermodynamics is an old and difficult branch of mathematical science. My book on mathematical mechanics tries to take baby steps towards a categorical chemical thermodynamics. For example, there exists a monoidal functor ("Hess's Law") which assigns enthalpy of formation to mixtures and enthalpy of transformation to reactions. One-, two-, or three-dimensional bodies are connected by bodies that conduct certain substances, and which may themselves be connected by bodies conducting other substances. Substances include chemicals, charge, volume, momentum, and entropy, and any flowing substance carries energy. The theory of substances is an axiomatic theory including an Energy Axiom ("First Law of Thermodynamics") and an Entropy Axiom ("Second Law of Thermodynamics"). In my dreams a grown up categorical chemical thermodynamics may invoke higher-dimensional categories and other areas of current seemingly abstract research. Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]