Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 90
boiler
high pressure
turbine
generator
steam
electricity
pump
condenser
steam
return
pump
heat source, T h
cold water source, Tc (river, ocean, or cooling towers)
Figure 6.2: Generic power plant scheme, in which some source of heat at T h generates steam that flows toward the condenser—where the
steam cools <strong>and</strong> reverts to liquid water, by virtue of thermal contact to a cool source at T c provided by a body of water or evaporative
cooling towers. Along the way, the rushing steam turns a turbine connected to a generator, exporting electricity. This basic arrangement is
employed for most power plants using fossil fuels, nuclear, solar thermal, or geothermal sources of heat.
6.4.1 Entropy <strong>and</strong> Efficiency Limits
A deep <strong>and</strong> powerful piece of physics intervenes to limit how much
useful work may be extracted out of a flow of heat from a hot source at
temperature T h to a cold source at temperature T c . That piece is entropy.
You don’t need to fully grasp the deep <strong>and</strong> subtle concept of entropy
in order to follow the development in this chapter <strong>and</strong> underst<strong>and</strong> the
role entropy plays in limiting heat engine efficiency. All the same, it is a
stimulating topic that we’ll dip a toe into for some appreciation.
Definition 6.4.2 Entropy is a measure of how many ways a system might
be organized at the microscopic level while preserving the same internal
energy. 25
This definition may be an obscure disappointment to those expecting
entropy to be defined as a measure of disorder. 26 Consider a gas maintained
at constant pressure, volume, <strong>and</strong> temperature—thus fixing the
total energy in the gas. The atoms/molecules comprising the gas can
arrange into a staggeringly large number of configurations: any number
of positions, velocities, rotational speeds <strong>and</strong> axis orientations, or vibrational
states of each molecule, for instance—all while keeping the same
overall energy.
25: E.g., at constant temperature, pressure,
volume.
26: Entropy is indeed related to disorder, in
that there are many more ways to configure
matches in a mess than there are ways to
neatly stack them.
Example 6.4.2 To illustrate, consider a tiny system containing 3
molecules labeled A, B, <strong>and</strong> C, having a total energy of 6 units split
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.