Energy Servants
Notes:
This lesson is adapted from
Global Science: Energy, Resources,
Environment, 3rd Edition, by John W.
Christensen, published by Kendall/Hunt
©1991. Used by permission. Information
about the current version of this textbook can
be obtained at the Global Science section of
the Kendall/Hunt website.
Ancient people did not have electricity or internal
combustion engines. These are products of the Industrial
Revolution that changed the way we produce our food
and the everyday goods and services that make our lives
easier. For the past 200 years or so we have relied on
motors and engines and microchips to heat or cool our
Data used in this lesson are for 1997 and
were
compiled from the following sources:
houses and our food. Every day we use hundreds of these
devices to extract juice from fruit, move us from home to
2000 World Almanac and Book of Facts
school or work, carry our burdens, and produce words on
U. S. Energy Information Administration
the page as I am doing here. So how did ancient people
U. S. Census Bureau
make their lives easier? For those who could afford them,
American Gas Association
servants or slaves were the answer. Humans can be
employed to do work if engines, computers, and light filaments are not available.
But the good life made possible through human power is quite different from that available
through electrical motors and diesel engines. For one thing, at maximum effort humans can
provide only about one-tenth the power of a good horse -- and that effort is unlikely to be
sustained for long. Even a small car has the power of over 100 horses! So each of us uses the
equivalent of many humans working as servants. An average American uses more energy every
day than the grandest Egyptian Pharaoh could have dreamed of in terms of "energy servants".
Let's see just how many...
Objectives [At the end of this lesson students will be able to...]
•
•
•
•
•
•
•
state a definition of work as a force moved through a distance, and use the results to
calculate examples of work done in specific situations.
calculate work done over an extended time based on units of work done in shorter times.
use energy conversion values to calculate work done in a variety of units and compare
these.
determine the human equivalent of energy obtained from gasoline consumed in passenger
vehicles in the U.S.
determine the human equivalent of energy obtained from natural gas consumed in U.S.
residences.
determine the human equivalent of energy in the form of electricity consumed in U.S.
residences.
determine the human equivalent of the total energy consumed by the entire U.S. and the
average number of servants equal to the average American's personal daily demand.
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Energy Servants -- Page 1 of 9
Start-up questions
1. List all of the motors in your home or apartment. Which ones do you think require the
most energy to run? How often are they on? What total energy is needed each month for
them?
2. Did you know that a man pedaling a stationary bicycle can operate a generator that
provides enough AC electrical power to operate a small black-and-white television? But
not a large color set. Would you watch the same amount of TV if someone had to pedal a
bicycle to power it?
3. How many people pedaling stationary bicycles do you think would be needed to provide
for all of your energy demands on a daily basis? What would this equal in "horsepowerhours"?
4. How much energy is wasted in your home or apartment? Why do you think this is so?
5. Since the U.S. population is growing, and each citizen wants to have "the good life" that
our culture enjoys, what does this imply for the number of electrical generating plants
needed?
The Energy Servant Calculation
Using data from 1997 on the energy demands by the U.S. population and an estimation of the
work output that an "standard human adult male" can be expected to provide, we will calculate
the number of "energy servants" required to meet U.S. energy demands. After dividing by the
number of people in the U.S, we will determine how many "energy servants" each of us requires
to provide the good life that we enjoy. [As we perform these calculations, we will make some
use of a method of problem solving often called dimensional analysis, a method that is described
some detail in Appendix D. Many people find this method to be a useful approach for solving
“word problems” such as we are asking here.]
Part 1: The work supplied by an energy servant
As mentioned earlier, we will define "energy servants" in human terms based on an
estimation of the amount of sustained energy output provided by a "standard human adult male."
When describing energy output by humans we typically use the term "work," which can be
defined as the result of moving a force through a distance that opposes the applied force. So if I
lift a weight from the floor to a table, the work I do is calculated as the distance through which
the weight moves times the weight itself. The units of work are units of energy (force units ×
distance units = energy units). Lifting a ten-pound weight off the floor through a vertical distance
of three feet requires an energy expenditure of thirty foot·pounds. Lifting ten of these weights the
same vertical distance (like loading a truck) requires 300 foot·pounds of energy.
Work or energy as described above involves no time unit. The introduction of time requires
the concept of "power", or rate of energy delivery over time. For example, if 300 foot·pounds of
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Energy Servants -- Page 2 of 9
work described above is accomplished in one second, the average power output required to
complete this work is 300 foot·pounds per second. There is a power unit that is close to this, a
"horsepower," which is 550 ft·lbs per second (or 746 watts). This unit was defined based on the
average power output that could be expected from a good horse. Humans can not sustain the
same power output as a horse. R. Buckminster Fuller estimated that the average working man,
besides carrying his own weight, does approximately 150,000 ft·lbs of work in an eight-hour
workday. This turns out to be a rather humbling average output of 5.2 ft·lbs per second, less than
one-hundredth of a horsepower! For convenience, we will note here that this converts to 7.1
watts. Before we define an "energy servant," however, there is another consideration: our energy
demands exist for 24 hours per day, but we can only expect this "energy servant" to work for 8
hours per day. Therefore, we need three energy servants over a 24-hour period to provide us with
7.1 watts throughout the day. Another way to look at this is that each energy servant provides us
an average power output of 2.4 watts (7.1 watts × 8 hours / 24 hours = 2.4 watts). Over the
course of one year, each energy servant performs 76 MJ of work.
Part 2: Personal Energy Servants
Now that we have our energy servant defined in numerical terms, if we know how much
energy we each use on a daily basis, then we can calculate the energy we consume in terms of
human effort. This tells us how many human servants we would require to meet our needs if we
were to live without electric motors, engines, and other wonders of the industrial age. This
exercise helps show why so much of the rest of the world of the 21st century envies the American
lifestyle. And why we consume so much energy per person when compared to other nations. The
figures we will use are averages, but are likely to apply to anyone taking this class. So we are not
talking about "others"; we are talking about ourselves.
In the U.S., most of our direct energy consumption comes from exploitation of three energy
sources: gasoline (used mainly when driving our cars), natural gas (used mainly for heating
water, heating homes, and cooking), and electricity (used mostly for heating and cooling homes
and for "creature comfort" electrical appliances). Electricity itself is produced by exploitation of
a variety of sources, but for simplicity is considered here as a single source. There are also many
areas of enormous indirect energy consumption, and we will get back to that, but first we will
put find the number of energy servants that would be required
to supply our direct consumption.
Personal Gasoline Servants
According to the 2000 World Almanac and the U.S. Census
Bureau, in the United States in 1997 there were about 268 million people and 129,748,704
registered passenger vehicles. These cars traveled a estimated total of 1.61 trillion miles, and
used an average of one gallon of gasoline for each 16.67 miles traveled (other fuels account for
only a very minor percentage of passenger vehicle fuel use, at least for now, and can be ignored
in this calculation). Use these data and the fact that one gallon of gasoline contains
approximately 124,240 Btu of energy to calculate the number of personal gasoline servants the
average American has. (Note: 1 Btu = 1055 J)
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Energy Servants -- Page 3 of 9
Number of miles/year
person
Number of gallons/year
person
Energy/year
person
Personal
Gasoline
Servants
miles/year
person
=
gallons
mile
=
gallons/year
person
=
J/year
person
=
×
year
365 day
×
miles/year
person
×
×
day
24 hrs
124,240 Btu
gallon
×
hr
3600 s
×
gallons/year
person
=
1055 J
J/year
person
× Btu =
W·s
J
×
Energy Servant
2.4 W
Energy Servants
person
=
Personal Natural Gas Servants
According to the U.S. Energy Information Administration, residential U.S.
customers used about 4.98 trillion cubic feet of natural gas in 1997. One cubic foot
of natural gas supplies about 1027 Btu. Given this and the 1997 U.S. population,
calculate the number of personal natural gas servants that the average American
has.
Number of cubic feet/year
person
Energy/year
person
=
Personal
Natural Gas
Servants
=
ft³/year
person
=
ft³/year
person
J/year
person
×
×
year
365 day
1027 Btu
ft³
×
day
24 hrs
×
1055 J
J/year
person
× Btu =
hr
3600 s
×
W·s
J
×
Energy Servant
2.4 W
=
Energy Servants
person
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Energy Servants -- Page 4 of 9
Personal Electricity Servants
The U.S. Energy Information Administration reports that there were about
1,030,000,000,000 kilowatt·hours of electricity sold to residential customers in
the U.S. in 1997. Use this and the 1997 U.S. population to calculate the
number of personal electricity servants that the average American has.
Number of kW·hr/year
person
Energy/year
person
Personal
Electricity
Servants
=
kW·hr/year
person
=
kW·hr/year
person
=
J/year
person
×
year
365 day
×
×
1000 W
kW
day
24 hrs
×
×
hr
3600 s
3600 s
hr
×
J
J/year
person
× W·s =
W·s
Energy Servant
X
J
2.4 W
=
Energy Servants
person
Part 3: Total Energy Servants
Now we can calculate the number of direct or personal energy servants per American by
taking the sum of these personal gasoline, natural gas, and electricity servants. But that is only
part of the story! As you can see in Figure 1, total energy consumption in the United States is
quite high. It turns out that the total energy consumption in the U.S. in 1997 as reported by the
U.S. Energy Information Administration was 94.37 quadrillion Btu, or 9.957×1019 J -- an average
power demand of 11,800 W per person! Thus, the total number of energy servants that the
average American has is:
Total
Energy
Servants
=
W
person
×
Energy Servant
2.4 W
=
Energy Servants
person
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Energy Servants -- Page 5 of 9
Figure 1: United States Energy Consumption
Graph obtained from the Annual Energy Review published by the U. S. Energy Information
Administration.
What do these other energy servants do for us? They are used to heat and cool our schools
and workplaces, mine raw materials, convert raw materials to items like clothes and cars,
transport water, harvest and transport our food, and dozens of other things done in the public,
industrial, and commercial segments of our society. They are just as essential to our lifestyle as
our personal energy servants.
Part 4: Conclusion
Energy servants can impact our environment in numerous ways. Toxic waste generation, air
and water pollution, use of nonrenewable resources, and overuse of renewable resources are
some examples. It has been estimated that the average environmental impact of a modern
American is about 250 times that of a preindustrial human being; this magnified impact is
essentially the environmental cost of our energy servants. Thus, we have the environmental
crisis, with an impact on our biosphere unimaginable just a few generations ago.
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Energy Servants -- Page 6 of 9
Our human population is growing exponentially, placing ever-greater demands on the Earth.
For now demands are being met, but this is achieved through heavy use of non-renewable
resources such as fossil fuels. Even the dramatic improvement in crop yields during the last
century (the "green revolution") has been come about largely though a major increase in the
amount of energy used to produce one unit of food, and along the way the green revolution has
added copious amounts of pollution to our environment. Exploitation of non-renewable resources
gives a false impression of the energy demand that can be sustained. Do not be deceived. As we
continue to abuse even our renewable resources, we reduce the amount and quality of resources
that will be available in the future.
Assessment questions
1. What is the relationship between power and energy? How do we convert from one to the
other?
2. How would our lives be different if energy in the U.S. were not so cheap?
Example problem
If my house used 850. kilowatt·hours of electricity in March, and I am charged $59.50 for it,
then:
a. How much do I pay for my electricity in $ per kilowatt·hour?
b. How many energy servants would it take to produce this energy?
c. If minimum wage is $9.50 per hour, how much would it cost me to pay humans to
generate my electricity during the month of March?
Solution:
a. $59.50 ÷ 850. = $0.0700/kW·hr
Average
b. Power
Demand
=
850. kW·hr
30 days
×
day
24 hr
= 1.18 kW ×
Energy Servant
2.4 W
×
1000 W
kW
= 490 Energy Servants
$9.50
Energy Servant
1000 W
c. Cost = 850. kW·hr × servant·hr ×
× kW = $3.4 million
2.4 W
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Energy Servants -- Page 7 of 9
Homework
Using the information provided on Bill Baird's home electric and gas bills for 1998, answer the
following questions. (If your browser supports this, there is also a version ready in an Excel
spreadsheet).
1. Determine and then graph the monthly electric consumption in kW·hr for each month.
a. Write a one-sentence explanation of the why the graph that you drew shows the
electricity consumption pattern that it does.
b. What was the total cost of electricity in 1998 in this house of 2400 square feet?
c. What was the total consumption of electricity in 1998 in this house?
d. What was the average cost of electricity in 1998 in $ per kW·hr for this residential
customer of Alabama Power Co. (determine this based on the total cost and total
consumption)?
e. If the use fell to zero, would the monthly bill be $0.00?
2. Determine and then graph the monthly gas consumption in 100's of ft³.
a. Write a one-sentence explanation of the why the graph that you drew shows the
natural gas consumption pattern that it does.
b. What was the total cost of natural gas in 1998 in this house?
c. What was the total consumption of natural gas in 1998 in this house?
d. What is the average cost of gas in 1998 in $ per 100 ft³ for this residential
customer of Alabama Gas Co. (determine this based on the total cost and total
consumption)?
e. If the use fell to zero, would the monthly bill be $0.00?
f. How do you think it heats its water?
3. Does this house heat its living space with gas or electricity? What evidence do you have?
4. Does this house cool its living space with gas or electricity? What evidence do you have?
5. How many "personal electricity servants" were required on average to provide the
electrical energy for Baird's house in 1998? [Convert the total consumption in 1 c. to
Joules and divide by 76 MJ per energy servant.]
6. How many "personal natural gas servants" were required on average to provide the
energy equal to the natural gas consumed in Baird's house in 1998? [Convert the total
consumption in 2 c. to Joules, using 1027 Btu per ft³ and 1055 J = 1 Btu, and divide by
76 MJ per energy servant.]
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Energy Servants -- Page 8 of 9
Residential electric consumption by month: Baird home, Auburn, AL (1998)
month
Previous (kw-hr)
Current (kw-hr)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
2554
3011
3562
4053
4447
4977
6510
8375
9825
10922
12095
12631
3011
3562
4053
4447
4977
6510
8375
9825
10922
12095
12631
13118
Energy Used (kw-hr)
Charge
$37.21
$43.30
$39.42
$33.13
$41.90
$107.16
$128.84
$101.66
$78.63
$78.47
$42.38
$39.18
Residential gas consumption by month: Baird home, Auburn, AL (1998)
month
Previous (x100 cu.ft.)
Current (x100 cu.ft.)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
995
1082
1158
1216
1235
1250
1261
1270
1278
1284
1300
1326
1082
1158
1216
1235
1250
1261
1270
1278
1284
1300
1326
1406
Gas Used (x100 cu.ft.)
Charge
$69.86
$56.26
$43.78
$22.00
$18.54
$15.75
$13.73
$12.93
$11.71
$23.88
$34.95
$64.24
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Energy Servants -- Page 9 of 9