12: Relating Energy Conversion Processes
- Page ID
- 19019
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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
- This page discusses the application of calculus of variations in science and engineering, focusing on energy conversion across disciplines. It emphasizes the value of interdisciplinary analysis for uncovering insights and new research opportunities. Through examples like mass-spring and capacitor-inductor systems, it derives key physics laws, including conservation and thermodynamics.
- 12.2: Electrical Energy Conversion
- This page compares circuits language and electromagnetics language in electrical system analysis, focusing on charge, voltage, magnetic flux, and current. It introduces calculus of variations to describe energy conversion, emphasizing the interrelationship between circuit parameters and electromagnetic fields. The application of Gauss's laws in analyzing energy storage in dielectrics and magnetic materials is discussed.
- 12.3: Mechanical Energy Conversion
- This page covers the application of calculus of variations in energy conversion devices, highlighting energy storage in mechanical systems like springs and flywheels, with tables summarizing key parameters. It discusses constitutive relationships in mechanics, linking physical quantities and motion through equations, including connections between mechanical and electromagnetic fields via Maxwell's equations.
- 12.4: Thermodynamic Energy Conversion
- This page covers fundamental thermodynamic properties—volume, pressure, temperature, and entropy—and their importance in energy conversion. It details how these properties interact using calculus of variations, exemplified through sensors and devices. Additionally, it explores the second law of thermodynamics, linking temperature and entropy while focusing on entropy conservation and its dual nature (positive or negative).
- 12.5: Chemical Energy Conversion
- This page explores the calculus of variations in relation to energy storage systems such as batteries and fuel cells. It distinguishes between macroscopic systems characterized by charge density and redox potential, and microscopic systems defined by electron number and chemical potential. Two methodologies for each system type are presented, highlighting diverse generalized paths and potentials.
- 12.6: Problems
- This page covers the materials and characteristics of electronic devices, categorizing them as conductors, dielectrics, or semiconductors. It features exercises to match devices with their common materials, such as cadmium telluride in photovoltaic devices, and discusses key physical effects like the electro-optic effect and the Seebeck effect. The page also defines various devices based on their energy conversion mechanisms, including photovoltaic and thermoelectric devices.