Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 91
between them in some way. They can all have exactly 2.0 units of
energy apiece, or can have individual energies of 1.2, 1.8, <strong>and</strong> 3.0 units;
or 3.2, 0.4, <strong>and</strong> 2.4; or any other of myriad combinations adding to the
same thing. Entropy provides a measure of how many combinations 27
are possible.
27: It is far beyond the scope of this book to
detail the counting scheme, but it is perhaps
important to appreciate that energy levels
are discrete—or quantized—which prevents
an infinite number of possible energy combinations.
0:4 (1) 1:3 (16) 2:2 (36) 3:1 (16) 4:0 (1)
Figure 6.3: A box containing 4 atoms or molecules of one type (white) <strong>and</strong> 4 of another type (red) has many more configurations available
(number in parentheses) when species are equally distributed so that left <strong>and</strong> right sides both have two of each. Entropy is related to the
number of ways a system can distribute itself (at the same energy level), acting to favor disordered mixing over (improbable) orderly
separation.
Example 6.4.3 To better elucidate the connection between entropy <strong>and</strong>
disorder, imagine a box of air, containing both N 2 <strong>and</strong> O 2 molecules.
As Figure 6.3 illustrates, a thoroughly-mixed arrangement has a larger
number of possible configurations, thus the highest entropy. Nature
does not give rise to spontaneous organization in a closed system. 28
The First Law of Thermodynamics is one we already encountered as
conservation of energy:
28: It is, however, possible to see lowered
entropy in one place if balanced by an increase
elsewhere: life organizes matter, but
at the expense of increased entropy in the
wider universe.
Definition 6.4.3 First Law of Thermodynamics: the energy of a closed
system is conserved, <strong>and</strong> cannot change if nothing—including energy—
enters or leaves the system boundaries.
Now we are ready for the Second Law.
Definition 6.4.4 Second Law of Thermodynamics: the total entropy of
a closed system may never decrease.
It is entropy that governs which way heat flows (hot to cold, if left alone)
<strong>and</strong> in a deep sense defines the “arrow of time.”
Box 6.2: The Arrow of Time
Consider that if you were shown videos of a rock splashing into
water, a coffee mug shattering on the floor, or an icicle melting, you
would have no difficulty differentiating between the forward <strong>and</strong>
reverse playbacks of the video.
The reverse action, you would conclude, is preposterous <strong>and</strong> can
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.