Energy Models

To support decisions about our energy systems, we must make quantitative estimates in systems that are too complex to gather complete information.

Constructing a model is the initial mental exercise we perform before a calculation. In a model we determine the relationships and assumptions.

  • If we are estimating energy what is it proportional to?
  • What existing data can we base our estimate on?
  • What simplifying assumptions are we making?

Common Energy Conversions

  • 1 BTU = 1055 J
  • 1 kWh = 3.6 MJ

Strategy

Making an energy estimation is a skill that is honed through practice. The following is a good checklist to use as you develop this skill.

  • Main question
    • What are you trying to estimate and why is it important?
  • Model
    • What model, quantities, and/or tools will provide a plausible estimate?
    • Check that you understand the basic physical steps you are modeling.
    • This is an approximation but is still useful.
  • Quantities
    • Gather the quantities you need to estimate using your model.
  • Dimensions
    • Check that your model will provide the correct dimensions.
  • Units
    • Check that your model will provide the correct units.
  • Calculate
    • Compute your estimate paying special attention to your calculator syntax and scientific notation.
  • Implications
    • Determine the importance of the estimation result to your original question.

Simple Warmup Models

If you need 2 cups of sugar for 25 cookies, how much sugar for 100 cookies?

If you are traveling at an average speed of 60 miles an hour for 3 hours, how far will you travel?

More important estimations of energy quantities are more complex, but use the same basic ideas as the two models above.

Links between models, tools, and reality

Keep in mind that each of these quantities above represent a straightforward physical fact.

You already know that coal burns and that coal must be burned to create electricity. The next step in your mastery is to realize that an energy density describes this fact.

You know now that a coal-fired power plant takes heat energy and turns it into electrical energy. Knowing that an energy efficiency quantifies this fact will help you build your models.

Model Outputs

Models help us make decisions. We may want to use a model to help us estimate the amount of energy being used for a certain use if we don’t have a direct measurement.

We might use a model to predict the amount of energy saved by adopting a certain energy strategy. Even with imprecise estimates of some quantities, we may be able to say that the strategy should be adopted or rejected. Another possibility is that we require more study.

Accuracy and Communication

Your models should be computed in a way that makes it more likely for you to arrive at the correct answer.

When you present your models to someone else, they should be presented in a way that is most likely for your audience to understand quickly.

These methods may not be the same, but it will be more efficient if they are at least close.

Gasoline Usage in the United States

Imagine that we did not have the US Energy Information Administration compiling statistics of gasoline usage. If we needed to make an estimate of gasoline usage to support a decision about the speed limit of fuel consumption how would we make it?

Carbon Intensity of Electricity

These are averages for electricity power plants.

Fuel Source Carbon Intensity
Coal 2249 lb CO2/MWh
Natural Gas 1135 lb CO2/MWh
Proposed EPA Limit ~ 1100 lb CO2/MWh