Direct Energy, 2018a

12 RELATING ENERGY CONVERSION PROCESSES 269
12 Relating Energy Conversion Processes
12.1 Introduction
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.
This chapter illustrates how to apply calculus of variations ideas to disparate
branches of science and engineering. Electrical engineers typically
use current and voltage to describe circuits. Chemists use temperature,
pressure,entropy,and volume when describing chemical reactions. Engineers
and scientists in each discipline have their own favorite quantities.
However,energy conversion is a common topic of study. Calculus of variations
provides a unifying language. Scientists and engineers typically specialize,becoming
experts in a particular area. However,open questions are
more often found at the boundary between disciplines,where there is less
expertise. Comparing ideas between dierent 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.
By studying the mass spring system of Sec. 11.5,the resulting equation
of motion was Newton's second law. By studying the capacitor inductor
system of Sec. 11.6,the resulting equation of motion was Kircho's voltage
law. In this chapter we identify the equation of motion for multiple
other systems. Through this procedure,we encounter some of the most
fundamental laws of physics including including Gauss's laws,conservation
of momentum,conservation of angular momentum,and the second law of
thermodynamics.
The discussion in this chapter is necessarily limited. Entire texts have
been written about each energy conversion processes discussed. Additionally,the
idea of applying calculus of variations to these energy conversion
processes is not novel. Other authors have compared electrical,mechanical,
and other types of energy conversion processes too [168] [169].
Some rather drastic assumptions are made in this chapter. We assume
energy is converted between one form and another with no other energy
conversion process occurring. For example in a mass spring system,energy
is converted between kinetic energy and spring potential energy while ignoring
heating due to friction,energy conversion due to gravitational potential
energy,and so on that might occur in a real system.