12: Relating Energy Conversion Processes
- Page ID
- 19019
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
In the previous chapter, the concept of calculus of variations was introduced. The purpose of this chapter is to draw relationships between a wide range of energy conversion processes. Processes in electrical engineering, mechanics, thermodynamics, and chemistry are described using the language of calculus of variations. Similarities between the processes are highlighted and summarized into tables.
- 12.1: Prelude
- Energy conversion is a common topic of study and calculus of variations provides a unifying language. Open questions are more often found at the boundary between disciplines, where there is less expertise. Comparing ideas between different disciplines is useful because ideas from one discipline may answer questions in another, and challenges in one discipline may pose interesting research questions in another.
- 12.2: Electrical Energy Conversion
- We can use circuits language to describe a number of energy conversion devices. Resistors convert electrical energy to thermal energy, and thermoelectric devices convert thermal energy to or from electrical energy. A charging capacitor converts electrical energy to energy stored in a material polarization, and a discharging capacitor converts the energy of the material polarization back to electrical energy. In an inductor, electrical energy is converted to and from energy of a magnetic field.