Energy Resources and Consumption - Environmental Science - page 111

Here's how to solve a math problem using dimensional analysis:
1. Read the question to determine the final units.
2. Set the final units at the end of a dimensional analysis equation.
These desired final units are the only units that will not "cancel." All other units will be used to convert
from starting units toward the desired ending units.
3. Check that the problem is set up so that starting units are converted into ending units.
To cancel units, you need the unit on one top numerator and one bottom denominator of the dimensional
analysis equation. Units should cancel the same way numbers would cancel.
4. Simplify the math, cancel out zeros, and simplify the numbers.
5. Solve the math.
6. Rewrite the answer including the units.
Indicate that this is the final answer.
EXAMPLE:
Several AP Environmental Science teachers were sitting around a table discussing the full coal cars head-
ing east to several big cities and the empty coal cars returning to the mines in the west. The teachers were
wondering how much energy was in each coal car and how long the coal would last. In addition, they dis-
cussed the environmental impact of mining and transporting the coal across these distances.
A large, coal-fired power plant produces 48 million kWh of electricity each day. Assume the following:
10,000 BTUs are required to produce 1 kWh of electricity; 1 pound of coal produces 5,000 BTUs of heat;
each coal car can hold 120 tons; 1 ton is 2,000 pounds.
A. How much heat in BTUs is needed to operate the coal plant for one day?
B. How many coal cars will be needed to operate the power plant for the day?
C. How many trains will be needed to power the plant for a day if the train pulls 100 coal cars?
Follow the steps listed earlier:
1. Read the question to determine the final units.
The first question asks how much heat in BTUs is needed to produce the power for one day.
2. Set the final units at the end of a dimensional analysis equation.
Using the information provided, days should be on the bottom and BTUs on the top (BTUs/day). kWh/
day, is included in the statement "48 million kWh are produced in one day." Write this first. Next, it
states that 10,000 BTUs are used to produce 1 kWh of electricity, so place BTUs/kWh second in the
analysis. Now, with kWh on the top and kWh on the bottom, the units cancel.
3. Check that the problem is set up so that starting units are converted into ending units.
4. Simplify the math, cancel out zeros, and simplify the numbers.