Kendall/Hunt
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.

     Data used in this lesson are for 1997 and were compiled from the following sources:

     2000 World Almanac and Book of Facts
     U. S. Energy Information Administration
     U. S. Census Bureau
     American Gas Association


  Energy Servants

      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 houses and our food. Every day we use hundreds of these devices to extract juice from fruit, move us from home to school or work, carry our burdens, and produce words on the page as I am doing here. So how did ancient people make their lives easier? For those who could afford them, 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...]


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 "horsepower-hours"?
  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 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)


Number of miles/year
          person
=
miles/year
person



Number of gallons/year
            person
=
gallons
mile
×
miles/year
person
=
gallons/year
person



Energy/year
   person
=
gallons/year
person
× 124,240 Btu
gallon
× 1055 J
Btu
=
J/year
person



Personal
Gasoline
Servants
=
J/year
person
× year
365 day
× day
24 hrs
× hr
3600 s
× 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
=
ft³/year
person



Energy/year
   person
=
ft³/year
person
× 1027 Btu
ft³
× 1055 J
Btu
=
J/year
person



Personal
Natural Gas
Servants
=
J/year
person
× year
365 day
× day
24 hrs
× hr
3600 s
× W·s
J
× Energy Servant
2.4 W
=
Energy Servants
person


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
=
kW·hr/year
person



Energy/year
   person
=
kW·hr/year
person
× 1000 W
kW
× 3600 s
hr
×   J  
W·s
=
J/year
person



Personal
Electricity
Servants
=
J/year
person
× year
365 day
× day
24 hrs
× hr
3600 s
× W·s
J
X Energy Servant
2.4 W
=
Energy Servants
person


Figure 1: United States Energy Consumption

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


      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.

      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:

  1. How much do I pay for my electricity in $ per kilowatt·hour?
  2. How many energy servants would it take to produce this energy?
  3. 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

   b.   Average
Power
Demand
= 850. kW·hr
30 days
×   day  
24 hr
= 1.18 kW × Energy Servant
2.4 W
× 1000 W
kW
= 490 Energy Servants

   c.   Cost = 850. kW·hr ×   $9.50  
servant·hr
× Energy Servant
2.4 W
× 1000 W
kW
= $3.4 million


Homework Only -- for Printing Solution

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.
    1. Write a one-sentence explanation of the why the graph that you drew shows the electricity consumption pattern that it does.
    2. What was the total cost of electricity in 1998 in this house of 2400 square feet?
    3. What was the total consumption of electricity in 1998 in this house?
    4. 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)?
    5. 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.
    1. Write a one-sentence explanation of the why the graph that you drew shows the natural gas consumption pattern that it does.
    2. What was the total cost of natural gas in 1998 in this house?
    3. What was the total consumption of natural gas in 1998 in this house?
    4. 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)?
    5. If the use fell to zero, would the monthly bill be $0.00?
    6. 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.]