Energy and Human Ambitions on a Finite Planet, 2021a

5 <strong>Energy</strong> <strong>and</strong> Power Units 73
It is straightforward to convert back to Joules, because 1 kW is 1,000 J/s
<strong>and</strong> one hour is 3,600 s. So 1 kWh is 1 kW times 1 hr, which is 1,000 J/s
times 3,600 s, <strong>and</strong> is therefore equal to 3,600,000 J, or 3.6 MJ. A related
measure sometimes comes up: the watt-hour (Wh). In much the same
vein, this is equivalent to 1 J/s for 3,600 seconds, or 3,600 J. 9
9: A Wh is one-thous<strong>and</strong>th of a kWh, not
surprisingly.
Box 5.3: Don’t be one of those people. . .
If you ever hear someone say “kilowatts per hour,” it’s likely a
mistake, 10 <strong>and</strong> has the side effect of leading people to erroneously
think that kilowatts is a unit of energy, not a power. Kilowatts is
already a rate (speed) of energy use: 1,000 Joules per second.
10: Literally, kW/hr would be a sort of acceleration
through energy. It’s a real thing
that can happen, but it’s usually not what
people mean.
One tendency some people have is to mix up kW <strong>and</strong> kWh. 11 Kilowatts 11: Perhaps related to Box 5.3.
is a unit of power, or how fast energy is being used. Think of it like
a speedometer: how fast are you moving (through space or energy)?
Kilowatt-hours is a multiplication of power times time, becoming an
energy. It’s more like the odometer: how much have you accumulated
(distance or energy)? Just like distance is rate (speed) times time, energy
is rate (power) times time.
Example 5.4.2 We will explore kWh using a light bulb for an example.
Let’s say the light bulb is labeled as 100 W. 12 How much energy does
it use?
12: ...aninc<strong>and</strong>escent, for instance
Well, it depends on how long it’s on. If it is never turned on, it uses no
energy. If it is on for 10 seconds, it uses far less than if it’s on for a day.
The characteristic quality of the light bulb is the power it expends
when it’s on—in this case 100 W. It only has one speed. In analogy
to a car <strong>and</strong> speedometer, it’s similar to saying that a car travels at a
constant speed, 13 <strong>and</strong> asking how far it travels. Well, it depends on
how much time it spends traveling at speed.
13: ...maybe30m/s; 67 m.p.h.; 108 k.p.h.
So view kWh (energy) as an accumulated amount that increases with
time. On the other h<strong>and</strong>, kW is a rate of energy expenditure.
5.5 Calories (kcal)
A common unit for describing chemical <strong>and</strong> thermal processes is the
calorie <strong>and</strong> its siblings.
Definition 5.5.1 A calorie is defined as the amount of energy it takes to
heat one gram of water (thus also 1 mL, or 1 cm 3 , or 1 cc) by one degree
Celsius (Figure 5.3). One calorie (note the small “c”) is 4.184 J of energy.
One Calorie (note the capital ”C”) 14 is 1,000 calories, or 1 kilocalorie
14: This might win the prize for the dumbest
convention in science: never define a
unit as case-sensitive, as it cannot be differentiated
in spoken language!
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.