Miroslav Silhavý
Mathematical Institut Academy of Science of the Czech Republic

Resumo: The lecture presents a sketch of a rigorous derivation of the basic thermodynamical quantities from the formulations of the first and the second laws of thermodynamics. The basic formulations of the laws are similar inasmuch as they present conditions under which a body (thermodynamic system) can do a positive work in a cyclic process. Based on the first law, one derives the proportionality of the net work and heat exchanged in a cyclic process (Joule's relation) and the energy defined as a state function. From the second law, which can be given several formulations, one derives the existence of the absolute temperature scale and the entropy, defined in and away from equilibrium, state function, but systems with genuine memory may have infinitely many entropies that do not differ by a constant. Such is the case of viscoelastic and plastic materials. A relationship between the equation of balance of energy and the equations of motions will be also outlined.