The Math of Energy

Expand/Collapse The Math of Energy


The Math of Energy series teaches math concepts through real-world situations that are based in the energy industry or fundamental energy relations. The series is targeted for high school students, but the concepts are valuable to viewers of many ages. The videos educate viewers about the importance of mathematics in the everyday world, especially with relation to energy topics.

  • The Math of Energy | Energy Efficiency

    Electricity powers many of the most important devices in our lives, including our cell phones. There are many technologies for producing electricity, such as fossil-fuel power plants, solar panels, wind turbines, and nuclear power plants. Coal-fired power plants convert the chemical energy in coal to electricity that is then transmitted to users in the electrical power grid. The energy efficiency of a coal power plant is calculated as the amount of electrical energy produced divided by the chemical energy in coal. We can calculate the overall energy efficiency by compounding the individual energy efficiencies. Using these equations we can calculate the mass of coal required to power a typical cell phone each year.

    Grades: 9-12
  • The Math of Energy | Fossil Fuel Usage

    The use of fossil fuels, which has increased steadily since the beginning of the 20th century, has enabled many advancements in the quality of life around the world.  However, fossil fuels are a limited resource and could become scarce during the 21st century.  To create projections for future global energy consumption, we can apply lines of best-fit to historical data. There are several estimates of fossil fuel reserves remaining in the earth and these estimates are continually revised.  In order to estimate when fossil fuels will be exhausted, we can equate the total fossil fuel resource base with the integral of our line of best-fit and solve for the time. The data in this episode is taken from 2012 studies on fossil fuel consumption.

    Grades: 9-12
  • The Math of Energy | Annual Energy Usage

    In 2011, the United States consumed roughly 288 billion gallons of oil, 24 trillion cubic feet of natural gas, 1 billion tons of coal, and 17 quadrillion BTUs of energy from sources such as nuclear power and renewable energy.  All of these data can be converted to common units using the chemical energy contained in each fuel and conversion factors.  315 million Americans consumed nearly 100 quads of energy in 2011.  The average annual per-capita energy consumption is defined as the total amount of energy consumed by a country in a given year divided by the population of that country.  Using these data, we calculate the average energy consumption for each American in 2011 and compare the result with the average energy consumption for a Chinese person in 2011.

    Grades: 9-12
  • The Math of Energy | Distance & Potential Energy

    With a few pieces of information, one can calculate the distance between the village of Manang and Annapurna III by setting up a camera in the Manang village and using some basic geometrical functions, including similar triangles and the sine, cosine, and tangent functions. The Annapurna III mountain is located in the Annapurna Conservation Area of Nepal. The mountain stands at 7,575 meters, which is much higher than any mountain in the United States. Additionally, using the conservation of energy, one can calculate the speed of a falling rock if it were dropped from the top of Annapurna III and relate the kinetic energy of the falling rock with the potential energy of the rock perched at the peak of Annapurna III.

    Grades: 9-12
  • The Math of Energy | Equations of Motion

    The equations of motion provide relations between a moving object’s acceleration, velocity, and distance traveled.  In this video, we use examples of a running horse to demonstrate the relationship between acceleration, velocity, and distance.  In addition, we apply the relationships to an accelerating car to assess its fuel efficiency. The maximum fuel efficiency occurs near 55 mph, the justification for the National Maximum Speed Law of 1973, which was designed to save fuel during the 1973 oil crisis.

    Grades: 9-12
  • The Math of Energy | Gasoline Prices

    The price of gasoline varies from country to country and depends on a wide range of factors including the including proximity to refineries, supply and demand conditions, import and export conditions, and taxes. This video compares the price of gasoline in several countries by converting all of the prices to common units of dollars per gallon. The gasoline prices and international currency exchange rates are from 2013.

    Grades: 9-12
  • The Math of Energy | Train Efficiency

    Energy efficiency and greenhouse gas emissions vary among different modes of transportation. The field of life-cycle assessment (LCA) has been formed, in part, to enable direct comparisons among transportation modes. In this video, life-cycle assessment is used to compare the energy efficiency and greenhouse gas impacts of a diesel-powered low-speed train with an electrically powered high-speed train. In order to make the comparison, there's a disscussion of different types of trains, describing life-cycle assessment methods, and explaining greenhouse gas emissions accounting. The results demonstrate the importance of considering energy and environmental impacts when choosing transportation. The calculations in this video are based off of numerical data gathered between 2009 and 2012.

    Grades: 9-12

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