Energy and Human Ambitions on a Finite Planet, 2021a

5 <strong>Energy</strong> <strong>and</strong> Power Units 75
formula, but we implicitly create the formula on the fly by recognizing
that the amount of energy required should scale with the mass of water
<strong>and</strong> with the amount of temperature increase. Hopefully, this approach
leads to a deeper underst<strong>and</strong>ing of the concept, while printing a formula
on the page might short-circuit comprehension.
This would be an excellent opportunity
to create your own formula to
capture the idea, like an expert!
5.6 British Thermal Unit (Btu)
Why would we waste our time talking about the arcane British thermal
unit (Btu)? It’s because data provided by the U.S. <strong>Energy</strong> Information
Administration on global energy use is based on the Btu. More specifically,
country-scale annual energy expenditures are measured in units of
quadrillion (10 15 ) Btu (see Box 5.4). Also, heating appliances in the U.S. 18
are rated in Btu/hour—a unit of power that can be converted to Watts.
Definition 5.6.1 The Btu is the Imperial analog to the kcal. 19 One Btu is
the energy required to heat one pound of water one degree Fahrenheit.
We need to cover the unit in this chapter in
order to be energy-literate in the U.S., <strong>and</strong>
because it will come up later in this book.
18: . . . hot water heaters, furnaces, air conditioners,
ovens <strong>and</strong> stoves
19: Recall that 1 kcal is the energy it takes
to heat one kilogram of water by 1 ◦ C.
In terms of Joules, 1 Btu is about 1,055 J, or not far from 1 kJ.
We can make sense of the conversion to Joules in the following way: a
pound is roughly half a kilogram <strong>and</strong> one degree Fahrenheit is approximately
half a degree Celsius. So a Btu should be roughly a quarter of a
kcal. Indeed, 1,055 J is close to one quarter of 4,184 J.
Box 5.4: Quads: qBtu
The U.S. uses quadrillion Btu to represent country-scale annual
energy expenditures. It is denoted as qBtu, or informally “quads.”
One qBtu is approximately 10 18 J. 20
The U.S. uses about 100 quads per year. Since a year is about 3.16×10 7
seconds, 21 dividing energy in Joules by time in seconds tells us that
the U.S. power is about 3 × 10 12 W (3 TW), working out to about
10,000 W per person as a per-capita rate of energy use.
20: 1.055 × 10 18 J, more precisely.
21: A cute <strong>and</strong> convenient way to remember
this, approximately, is π × 10 7 seconds per
year.
Example 5.6.1 For appliances characterized by Btu/hr, we can relate
to power in Watts via 1 Btu/hr as 1,055 J per 3,600 s, working out to
0.293 W.
Thus, a hot water heater rated at 30,000 Btu/hr is effectively 8,800 W.
Let’s also pause to underst<strong>and</strong> how long it will take to heat a shower’s
worth of hot water at this rate. We’ll do it two ways:
1. Heating 15 gallons 22 (125 pounds) from a cool 68 ◦ F toahot 22: Typical shower flow is about 2 gallons,
131 ◦ F at 30,000 Btu/hr will take how long? We must put in or ∼8 L, per minute.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.