Balance Equations

Abstract

This chapter presents the basic formal aspects of balance equations of continuum thermodynamics for fields with singular surfaces. Sections 3.1–3.2 deal with unspecified quantities, and treat in detail such features as the divergence theorem for fluxes with jump discontinuities, the passage from the reference to the spatial descriptions, and transport theorem for fields with singular surface. Several forms of a general balance equation are given and their relationships are explained in Sect. 3.3. After these preparations, the balances of concrete thermodynamic quantities are presented in Sections 3.4–3.7. The appealing elegance makes these balance equations acceptable without much motivation, and this is indeed the approach taken in this chapter. Only in the four chapters which follow will these concepts along with their balance equations be derived from simpler statements.