Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 89
characterize burning fuel as a purely thermal action, since what transpires
within the cylinder of a gasoline-burning internal combustion engine
seems like more of a little explosion than just the generation of heat. This
is not wrong, but neither is it the whole story. The process still begins as
a fundamentally thermal event. When the fuel-air mixture ignites, the
temperature in the cylinder increases dramatically. To appreciate what
happens as an immediate consequence, we turn to the ideal gas law:
PV Nk B T. (6.1)
P, V <strong>and</strong> T are pressure, volume, <strong>and</strong> temperature (in N/m 2 ,m 3 , <strong>and</strong>
Kelvin). N is the number of atoms or molecules, <strong>and</strong> k B 1.38×10 −23 J/K
is the Boltzmann constant, which we will see again in Sec. 13.2 (p. 199).
The temperature rise upon ignition is fast enough that the cylinder
volume does not have time to change. 23 Eq. 6.1 then tells us that the
pressure must also spike when temperature does, all else being held
constant. The increase in pressure then pushes the piston away, increasing
the cylinder volume <strong>and</strong> performing work. 24 But it all starts thermally,
via a sharp increase in temperature.
In the most general terms, thermal energy tries to flow from hot to
cold—out of a pot of hot soup; or into a cold drink from the surrounding
air; or into your feet from hot s<strong>and</strong>. Some part of this flow can manifest
as physical work, at which point the system can be said to be acting as a
heat engine.
This is the physicist’s version, which looks
a little different than the chemist’s PV
nRT. For a comparison, see Sec. B.4 (p. 381).
23: The moving piston allows the volume
to change, but on slower timescales.
24: Work is measured as pressure times the
change in volume. Pressure is force per unit
area, so the units work out to force times
distance, as they should given the definition
of work.
Definition 6.4.1 A heat engine is loosely defined as any system that turns
heat, or thermal energy into mechanical energy: moving stuff.
Example 6.4.1 Example heat engines: when heat drives motion.
1. Hot air over a car’s roof rises, gaining both kinetic energy <strong>and</strong>
gravitational potential energy;
2. Wind is very similar, in that air in contact with the sun-heated
ground rises <strong>and</strong> gains kinetic energy on an atmospheric scale;
3. The abrupt temperature increase in an internal combustion
cylinder drives a rapid expansion of gas within the cylinder;
4. Steam in a power plant races though the turbine because it is
flowing to the cold condenser.
The last example deserves its own graphic, as important as this process
is in our lives: almost all of our electricity generation—from all the
fossil fuels <strong>and</strong> even from nuclear fission—follows this arrangement.
Figure 6.2 illustrates the basic scheme. Table 6.2 indicates that 98%
of our electricity involves turning a turbine on a shaft connected to a
generator, <strong>and</strong> 84% involves a thermal process as the motive agent for
the turbine—most often in the form of steam.
Table 6.2: Schemes for electricity generation.
Most are thermal in nature, <strong>and</strong> nearly
all employ a turbine <strong>and</strong> generator. Data for
2018 from Table 8.2a of [34].
Source
% elec.
in U.S.
therm. turb./
gen.
Nat. Gas 35.3 ̌ ̌
Coal 27.3 ̌ ̌
Nuclear 19.2 ̌ ̌
Hydroelec. 7.0 ̌
Wind 6.6 ̌
Solar PV 2.2
Biomass 1.5 ̌ ̌
Oil 0.6 ̌ ̌
Geotherm. 0.4 ̌ ̌
Sol. Therm. 0.09 ̌ ̌
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.