Energy and Human Ambitions on a Finite Planet, 2021a

1 Exponential Growth 10
the impossibility of our continuing exponential growth in energy. All
kinds of reasons will preclude continued energy growth, including the
fact that human population cannot continue indefinite growth on this
planet. We will address space colonization fantasies in Chapter 4.
1.3 Thermodynamic Consequences
Physics places another relevant constraint on growth rate, <strong>and</strong> that
concerns waste heat. Essentially all of our energy expenditures end up
as heat. Obviously many of our activities directly involve the production
of heat: ovens, stoves, toasters, heaters, clothes dryers, etc. But even
cooling devices are net heat generators. Anything that uses power from
an electrical outlet ends up creating net heat in the environment, with
very few exceptions. A car moving down the road gets you from place A
to place B, but has stirred the air, 13 heated the engine <strong>and</strong> surrounding
air, <strong>and</strong> deposited heat into the brake pads <strong>and</strong> rotors, tires <strong>and</strong> road.
Our metabolic energy mostly goes to maintaining body temperature.
But even our own physical activity tends to end up as heat in the
environment. The only exceptions would be beaming energy out of the
earth environment (e.g., light or radio) or putting energy into storage
(eventually to be converted to heat). But such exceptions do not amount
to much, quantitatively.
What happens to all of this waste heat? If it all stayed on Earth, the
temperature would climb <strong>and</strong> climb. But the heat does have an escape
path: infrared radiation 14 to space. The earth is in an approximate
thermodynamic equilibrium: solar energy is deposited, <strong>and</strong> infrared
radiation balances the input to result in steady net energy. As we will see
in Chapter 5,therate at which energy flows is called power,sothatwe
can describe energy flows into <strong>and</strong> out of the earth system in terms of
power. Physics has a well-defined <strong>and</strong> simple rule for how much power
a body radiates, called the Stefan–Boltzmann law: 15
P A surf σ(T 4 hot − T4 cold
). (1.8)
P is the power radiated, A surf is the surface area, T hot is the temperature of
the radiating object in Kelvin 16 (very important!), T cold is the temperature
of the environment (also Kelvin), <strong>and</strong> σ is the Stefan–Boltzmann constant:
σ 5.67 × 10 −8 W/m 2 /K 4 . 17 Note that the law operates on the difference
of the fourth powers of two temperatures.
Example 1.3.1 A table in a room in which the table <strong>and</strong> walls are all
at the same temperature does not experience net radiation flow since
the two temperatures to the fourth power subtract out. In this case,
as much radiation leaves the table for the walls as arrives from the
walls to the table. But a room-temperature object at 300 K radiates
approximately 450 W per square meter to the coldness of space.
Some time, go feel the exhaust air from an
air-conditioning unit, or the heat produced
at the back <strong>and</strong> bottom of a refrigerator.
Even though these devices perform a cooling
function, they make more heat than
cool.
13: Stirred-up air eventually grinds to a halt
due to viscosity/friction, becoming heat.
14: ...aformofelectromagnetic radiation
15: . . . leaving out something called emissivity,
not relevant for our purposes
16: Conversions to Kelvin from Celsius (or
Fahrenheit) go like:
T(K) T(C) + 273.15;
T(C) (T(F) − 32)/1.8
17: It’s actually an easy constant to remember:
5-6-7-8 (but must remember the minus
sign on the exponent).
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.