SISL > 2012 Sustainability in Math Workshop > Activities > The True Cost of Energy

The True Cost of Energy

Dan Flath, Macalester College
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Students figure out how much coal must be burned to power a light bulb for a year, accounting for energy losses from the coal to the lamp. Cost of mining the coal and of cleaning up the pollution created by burning the coal are used to figure out an energy price under two assumptions: (1) price does not cover the clean-up cost. (2) price does cover the clean-up cost.

Learning Goals

Make students aware that their electricity bill does not cover all the costs caused by generating the power they use.

Context for Use

Students work with the units of energy and power. The project could be suitable at the precalculus and quantitative reasoning level.

Description and Teaching Materials

Students are given information on energy loss at all steps of the chain in powering a light bulb with coal generated power: burning the coal, transmission in the grid from the power plant to the home, loss in the light bulb. From this they can determine the quantity of coal required to power the bulb for a year.

Students are given monetary values for harm to air pollution, public health, and climate caused by using coal to generate electrical power.

Skill required: ability to work with units of energy and power. True Cost of Energy (Acrobat (PDF) 24kB Mar17 13)

Teaching Notes and Tips

  • Take some time to teach students the relation between energy and power and the basic units of energy and power.
  • This project could be the basis of a 1 hour lesson.


Part of the problem asks for numerical answers. The discussion component can be evaluated for quality and thoughtfulness of exposition.

References and Resources

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