Preliminary Knowledge and Continuum Thermodynamics

Abstract

In this chapter, some basic knowledge of elastic theory, electrodynamics, and thermodynamics which will be applied in this book are introduced. Some extensions in continuum thermodynamics are proposed. It is shown that together with the first law of thermodynamics, a physical variational principle (PVP) is also held. The physical variational principle gives a true process for all virtual possible process satisfying the geometrical constrained conditions. The physical variational principle is considered to be one of the fundamental physical principles for quasistatic system, which can be used to derive governing equations in continuum mechanics and other fields. When the temperature varies with time, the inertial entropy or inertial heat theory is proposed. This theory is consistent with current classical thermodynamic theory. From this theory, the temperature wave equation with finite phase velocity is derived in a very simple fashion. It is shown that the time arrived to equilibrium of the temperature is about 1 ns $ 1 ps when an internal heat source with a Heaviside step heat function is applied. Keywords Basic knowledge • Physical variational principle • Inertial entropy BackgroundJacques and Pierre Curie brothers discovered the piezoelectric effect in 1880 (Sun and Zhang 1984; Ikeda 1990). They found out that a mechanical stress applied on crystals such as tourmaline, quartz, and Rochelle salt could produce electrical charges, and the voltage was proportional to the stress. Piezoelectric can also work in reverse, generating a strain by the application of an electric field. Centrosymmetric classes of crystals are always not piezoelectric, but a few kinds of crystals are still not piezoelectric though lacking a center of symmetry. The pyroelectric effect was found in eighteenth century (Lang 2005), earlier than piezoelectric effect. Most ferroelectric crystals are strongly piezoelectric and pyroelectric. First applications were piezoelectric ultrasonic submarine detector and quartz clocks