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Mining Power and Hydrocarbon Consciousness from the Monthly Electric Bill
A Classroom Project

William P. OBrien, Jr.
Physics Department
Southwestern University
Georgetown, TX

OBrien is a physics professor at SU with a B.S. from the University of North Texas and
a Ph.D. from the University of North Carolina at Chapel Hill; his research areas are
geophysics (Using satellite technology (GPS) to teach the spherical polar coordinate
system, Euro. J Phys. 24, 101-110 (Jan. 2003)) and physics pedagogy (Deconstructing
Black Box Aspects of a Computerized Physics Lab, The Physics Teacher 43, 148-152
(March 2005)). Physics Department, Southwestern University, Georgetown, TX 78626;
obrien@southwestern.edu

Key words:
Electricity, hydrocarbons and the environment
Electric bill physics class project
Residential electric energy consumption
Personal electric energy use
Methane hydrates

PACS numbers

01.40Ha
Learning Theory and Science Teaching

45.20.dh
Energy conversion

36.00
exotic atoms and molecules

INTRODUCTORY PARAGRAPH (ABSTRACT)
(first 2 paragraphs of manuscript)

Personal monthly home electric bills provided by students in my introductory
physics classes served as data for a project designed to help them develop a sense of
scale for electric energy consumption referenced to their own electric lifestyles.
We compiled the data (total kilowatt-hours (kWh) consumed, total cost in
dollars, and number of people in the household) for each class and determined per
capita averages for monthly and annual energy consumption in kWh and equivalent
tons of coal as well as power load in watts. Data from several classes (70 electric bills
total collected over several semesters) yield per capita averages:
energy use rate = 476 kWh/month = 5.71 MWh/year = 2.9 tons of coal/year,
power load = 661 W, and
energy cost = $39/month (average price = 8.4 ¢/kWh).
The derived values provide a framework for discussions about personal and societal
electric energy use and the consequent role of terrestrial hydrocarbons in sustaining
such lifestyles. Interpretation and presentation of these data could be modified for
audiences ranging from middle-school science classes to university environmental
science seminars. INTRODUCTION
Personal monthly home electric bills provided by students in my introductory
physics classes served as data for a project designed to help them develop a sense of
scale for electric energy consumption referenced to their own electric lifestyles.
We compiled the data (total kilowatt-hours (kWh) consumed, total cost in
dollars, and number of people in the household) for each class and determined per
capita averages for monthly and annual energy consumption in kWh and equivalent
tons of coal as well as power load in watts. Data from several classes (70 electric bills
total collected over several semesters) yield per capita averages:
energy use rate = 476 kWh/month = 5.71 MWh/year = 2.9 tons of coal/year,
power load = 661 W, and
energy cost = $39/month (average price = 8.4 ¢/kWh).
The derived values provide a framework for discussions about personal and societal
electric energy use and the consequent role of terrestrial hydrocarbons in sustaining
such lifestyles. Interpretation and presentation of these data could be modified for
audiences ranging from middle-school science classes to university environmental
science seminars.

ELECTRIC ENERGY
Most electricity in the US is generated
1
by burning hydrocarbons such as coal or
natural gas to create high-pressure steam which drives turbines attached to electric
generators where, according to Faraday's Law of Induction, pulsing electric currents are
induced in loops of wire forced to spin in magnetic fields. In countries such as France
and Germany, and to a lesser extent the US, nuclear fission reactors provide the
requisite heat for creating steam. Heat-driven electric generators have overall
efficiencies
2
of only about 30-35 % , about half of the 64% theoretical efficiency (Second
Law of Thermodynamics) of an ideal heat engine operating between the 540
o
C and
20
o
C temperature extremes typical of modern steam turbines. Thus electric generators
transform three units of heat energy stored in hydrocarbons into about one unit of
electric energy readily transmissible through networks
3
of wires across great distances
to homes and industries. Burning hydrocarbons for heat, unfortunately, releases carbon
dioxide (for example, burning coal
4a
releases approximately 1 kg CO
2
per kWh of
electricity produced) and other toxic combustion byproducts
4b
into the atmosphere.
Likewise, nuclear fission reactors used to produce heat also generate toxic radioactive
byproducts (4c), some with half-lives an order of magnitude greater than the age of
human civilization.

A. CLASS SURVEY OF RESIDENTIAL ELECTRIC BILLS
Students and their families comprise a plausible sample of the larger US
population of residential electricity consumers. Analysis of monthly electric bills from
groups of students provides specific energy and power data for discussions and
problems relating the joules (3.6 X 10
6
J = 1 kWh) and watts of simple DC/AC circuits to
societal-scale projections of energy use in geographically immense circuits such as
national power grids. Furthermore, collecting fresh consumer data from students
themselves invests (and implicates) them in the results of the study. Seventy students from various physics classes supplied monthly home electric
bills (February-to-April range,1996-2004). While some students lived in apartments and
reported their own consumption, most used bills from their parents' homes (generally
in Texas). We took into account only the number of people actually living in each
residence at the time of the bill. Large standard deviations (SD) for quantities reported
below reflect the highly disparate electric lifestyles reflected in the data set; for instance,
the per capita monthly energy consumption ranged by a factor of over 25 from 69 kWh
to 1814 kWh.
Summing the total monthly energy used (in kWh) for the whole data set and
dividing that sum by the total number of people served in all households yielded 476
kWh (SD = 336 kWh) for the average monthly per capita energy use (or 5.71MWh/year).
Spreading this energy evenly over a month of hours yielded an average per capita
continuous power load of 661 W (SD = 467 W) costing about $39/month (SD = $27/mo)
or $1.30 per day for electricity whose average price was about 8.4 ¢/kWh (SD = 2.1
¢/kWh). Our derived average per capita residential electric energy use (476
kWh/month) and electric energy use rate (661 W) correspond closely to 2003 statistics
5

for Texas of 458 kWh/month and 627 W, respectively; our derived average price of 8.4
¢/kWh reflects the national US 2002 average residential price
6
of 8.5 ¢/kWh.

B. VISUALIZING ELECTRIC ENERGY USE
1. ENERGY = 476 kWh/person-month
One way to visualize each person's monthly consumption of 476 kWh of electric
energy is to calculate the equivalent amount of energy in some other form: coal is an
appropriate choice since over half
1
the electricity generated in the USA comes from
burning coal. The heat energy content of coal depends on the type of coal
7
burned and
ranges from about 2 kWh/lb (lignite) to 4 kWh/lb (anthracite); for this discussion we
choose
8
3 kWh/lb. Recall that the efficiency of burning coal to create steam for a turbo-
generator is only about 30-35% (about one-third). Thus for every pound of coal (3 kWh
of heat energy) burned to generate electric energy, two-thirds (2 kWh) of the heat
energy is unavoidably wasted in the process so that only 1 kWh of electric energy is
actually generated. Hence coal has a de facto "electric" energy density of about 1 kWh/lb
while its heat-energy density is 3 kWh/lb; this a good example of the concept
9
of
transformity.
Accordingly, the monthly per capita energy use of 476 kWh costs society 476 lbs
of coal per month (or 2.86 tons of coal per person-year); thus, a standard railroad coal
car hauling 100 tons of coal
10
would supply the annual electric energy needs of 35
people. On a longer time scale, the lifetime electricity habits of one of our average
householders who lived for 70 years (Figure 2) would require the burning of two
railcars (200 tons) of coal, a process releasing about 4.0 X 10
5
kg of CO
2
into the
atmosphere.
2. POWER = 661 W/person
Our derived average per capita residential power load of 661 W quantifies the
round-the-clock burden imposed on society and the environment by each person's
electric lifestyle (hot water, cooling/heating, lights, electric and electronic tools and novelties, etc.). This power value, perhaps the most significant finding for class
discussions, can be visualized in various ways.
Most simply, the typical householder of our survey represents an electric load
approximately equivalent to seven 100 W light bulbs (Figure 1) shining (and heating)
continuously.
Next, thinking anthropocentrically (where English units rule) in terms of beasts of
burden (one horsepower (HP) = 746 W), our power load of 661 W equals about 0.9 HP.
Although horses are rarely used these days as draft animals, the image of a large
domestic animal provides a meaningful power metaphor (and English metric) since for
all history prior to the industrial revolut