Heat Machines and Cycles—Internal Energy

The relevance of heat machines and cyclic processes in the analysis of thermal behaviour is addressed. The mathematical properties of cycles are presented, particularly Green’s theorem. Another important quantity—work—is introduced; volume work is stressed. The First Axiom, stating the equivalence of energy transfer by heat and work in the cycle, is formulated and its historical background is given. The First Axiom naturally leads to a function of temperature and volume called internal energy. The latter term is explained as well as the associated naming of the first law of thermodynamics, which is derived from the first axiom.