Energy Unit Conversion Homework
IEER Workshop 2010
This is an optional exercise that will put you on your technical toes in time for the IEER
workshop. Try your hand at the four problem sets below, perhaps during the plane ride
for you travelers. IEER will provide the answer key and, if you wish, an IEER technical
staff person will review the answers with you one-on-one, at your request, over lunch on
Day One of the workshop. No penalty for incorrect answers – this is for learning!
Introduction
Unit conversion is the operation that allows you to convert a measurement of length, or
some other physical property of something, with one kind of measurement stick into the
same thing measured with another type of measuring stick.
For instance, a person might be 70 inches or 5.83 feet or 0.0011 miles tall
(approximately). Note that the bigger the unit measure, the smaller the number needed to
say how big something is. In other words, the same height is expressed by a smaller
number in feet than in inches.
Another example: There are 12 inches in a foot (12 inches/foot). This can be written
(i)1 foot = 12 inches
Where 12 is the conversion factor to use to go from feet into inches.
Example: If you have 3 feet and want to know how many inches that is, you will need to
multiply 3 by 12. The answer is 36 inches.
You may not know how many feet there are in 1 inch, but you can find this by dividing 1
foot by 12 inches. In this case you obtain
(ii) 1 inch = 0.0833 foot
Where 0.0833 is the conversion factor to go from inches into feet.
Example: If you have 24 inches and want to know how may feet that is, you will need to
multiply 24 by 0.0833. The answer is 2 feet (after rounding off).
Unit conversion also allows you to convert from the British unit system (foot, pound,
gallon, Fahrenheit etc. – units that Americans and British are generally most familiar
with) to the metric system (meter, kilogram, liter, Celsius) and vice versa. For example
1 gallon = 3.79 liters
or
1 liter = 0.2642 gallon
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Energy Units and Conversions
Coal, natural gas, and oil are fossil fuels. The quantities for these fuels are expressed in
different units:
The unit for coal is the short ton. 1 short ton = 0.9 metric ton
The unit for natural gas is the cubic foot (ft3).
The unit for oil is the barrel. 1 barrel = 42 gallons
Coal, natural gas and oil are used in power plants to produce electricity. The unit for the
amount of electrical energy is the kilowatt-hour.
When coal, natural gas, and oil are burned, a certain amount of energy is released. In the
United States, the BTU (British thermal unit)a is the popular unit for the amount of
energy released. Another unit of energy is the Joule.b
1 BTU = 1,055 joules
The table below gives the amount of energy (in BTU) that is released when the given
amount of fossil fuel is burned or electricity is used.
Quantity burned/used
Coal: 1 short ton
Natural gas: 1 cubic foot
Oil: 1 barrel
Electricity: 1 kWh
Energy released per unit
20,754,000 BTU/short ton coal
1,031 BTU/ft3 natural gas
5,800,000 BTU/barrel oil
3,412 BTU/kWh electricity
The problems follow on the next page. (For further practice on unit conversions, see the
practice worksheet at IEER’s Online Classroom: www.ieer.org/clssroom/unitconv.html)
a
One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree
Fahrenheit.
b
The joule is a metric system unit. 1 calorie = 4.184 joules. 1 calorie is the amount of heat necessary the
raise the temperature of 1 gram on water by 1 degree Celsius.
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Problem Set
Using the information given above, solve the 5 problems below.c
1) The United States consumed 1.1 million short tons of coal per year in 2004.d
Calculate the energy released by this amount coal in BTUs and then in joules.
2) The United States consumes about 22.3 trillion cubic feet of natural gas per year.e
Calculate the energy released in BTUs and then in joules.
3) The United States consumes about 20 million barrels of oil per day.f
a) How many barrel of oil per year are consumed?
b) What is the energy consumed in BTUs per year?
c) What is the energy consumed in joules per year?
c
For tips on scientific notation – a useful method for writing big numbers more efficiently (e.g.,
19,000,000,000,000 = 19 x 1012) – see IEER’s Online Classroom at www.ieer.org/clssroom/scinote.html.
d
Energy Information Administration, www.eia.doe.gov/emeu/cabs/Usa/Coal.html.
e
Forecasted for the year 2005 by the Energy Information Administration,
www.eia.doe.gov/emeu/cabs/Usa/NaturalGas.html
f
Average consumption rate for 2004 and for the first nine months of 2005 was 20.6 million barrels per day.
EIA, www.eia.doe.gov/emeu/cabs/Usa/Oil.html
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4) A 100-watt light bulb is on for 2 hours a day.
a) What is the energy in watt-hour (Wh) it consumes per day?
b) What is the energy it consumes per year? Give your answer in watt-hour and in
kilowatt-hour (1 kilowatt = 1000 watts)
c) What is the energy it consumes in BTUs per day and per year?
d) What is the energy it consumes in joules per day and per year?
5) Assume a 1000 MW (megawatt) nuclear power plant operates 7,000 hours in one
year. (Hint: One megawatt is one million watts or one thousand kilowatts.)
a) Calculate the energy produced by this power plant in:
i. megawatt-hours (MWh) per year
ii. kilowatt-hours (kWh) per year
b) Calculate the energy in joules. (Hint: 1 kWh = 3.6 million joules)
c) Calculate the energy in BTU.
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