Principles of Thermodynamics#
In this chapter, the principles of classical thermodynamics, along with the relevant concepts and mathematical formalism, are introduced. The principles of thermodynamics are presented for closed systems, and subsequently extended to open systems.
The principle of conservation of mass - Lavoisier’s principle, valid in classical mechanics and summarized by the formula “nothing is created, nothing is destroyed, but everything is transformed”, states that in a closed system, the mass is constant,
\[d M = 0 \ .\]The first law of thermodynamics provides the general form of the total energy balance of a closed system, recognizing the work done by external forces \(\delta L^{ext}\) and the heat \(\delta Q^{ext}\) exchanged between the system and the external environment as the causes of the variation of the total energy of the system.
\[d E^{tot} = \delta L^{ext} + \delta Q^{ext} \ .\]The work of Gibbs provides the necessary concepts and a rigorous mathematical formalization of classical thermodynamics. The concepts of internal energy, state variables, and Gibbs’ phase rule are introduced; additionally, some phase diagrams for representing the state of a system and thermodynamic transformations are presented, which will be used in subsequent chapters.
The second law of thermodynamics describes natural tendencies: the dissipation of macroscopic mechanical energy and the transfer of heat from a hot body to a cold body, in a principle expressible in terms of entropy,
\[d S \ge \frac{\delta Q}{T} \ .\]Finally, the balance of physical quantities for open systems is derived by modifying the balance equations for closed systems, introducing terms for the flux of physical quantities due to the transport of matter across the system’s boundary.