Energy Sciences

CONTENTS OF CURRICULUM UNIT 13.05.05

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Background
  4. Teaching Strategies
  5. Lesson 1: Coal Mining Experiment
  6. Lesson 2: Wind Energy: Building Windmills
  7. Lesson 3: Biodiesel: Alternative Fuel
  8. Lesson 4: Energy Efficiency: Use Less, Save More
  9. Appendix A: Content Objectives
  10. Appendix B: Lesson Handouts
  11. Bibliography
  12. Teacher Resources
  13. Notes

Mathematics of Energy Efficiency: Use Less, Save More

Kenya Lawrence

Published September 2013

Tools for this Unit:

Background

When I come home, the first thing I do is flip the light switch and my lights are on, like magic. Assuming I pay the electricity bill on time, what process allows the lights to come on upon the flip of a switch? Likewise, I am able to plug in one of my various appliances and I can bake a peach cobbler, wash my clothes, or watch television. I perform these activities without regard for where the electricity comes from or the impact of my use on the environment. For many adults and students, this is their reality. The background information will answer the question "Where does our electricity come from?" The focus is in on Virginia; however, you may use some of the same resources to find information specific to your state. Then, I will provide information about the environmental effects of coal mining and some renewable energy options namely biodiesel and wind. Finally, my research will look at reasons and ways to increase energy conservation practices related to electricity and fuel usage. While I go through the background, perhaps you may get some great ideas for lessons/activities you can do beyond what is presented in the lesson plans.

My seminar, Energy Sciences, helped me to understand the scientific and social factors associated with non-renewables and renewables. Yergin describes the evolution of renewable best when he says "it is one of innovation, entrepreneurial daring, political battles, controversy, disappointment and despair, recovery and luck." 5 While the campaign for renewables has restarted after somewhat of a hiatus, it is important to recognize all primary energy sources have positive and negative impacts on the environment. We can use algebraic reasoning to model, project and verify current concerns with both types of energy sources. From a social aspect, we can consider Dr. David MacKay's comment which cleverly outlines the realistic views of the British on renewables; I imagine the sentiments are similar in the U.S.:

Wind: Not in my backyard! Wind farms? "No, they're ugly noisy things." Shallow offshore wind: Not near my birds! Offshore wind? "No, I'm more worried about the ugly power lines coming ashore than I was about a Nazi invasion." Biomass: food, biofuel, wood, landfill gas: Not in my countryside! 6

How do Virginian's obtain their electricity?

First, let's define the terms energy, power and electricity. Energy is the ability to work. There are two types of energy: kinetic, also known as working energy, and potential, also known as stored energy. Energy is in everything and comes in different forms: heat (thermal), light (radiant), motion (kinetic), electrical, chemical, nuclear and gravitational. Power is the measure of energy used over time; power, P, varies directly with energy, E, and inversely with time, t, P = E/t. Electricity is the flow of an electrical power or charge through a conductor. It is actually a secondary source of energy or energy carrier because it is the result of the conversion of primary sources of energy such as coal, wind, solar energy, etc.

image 13.05.05.01

Figure 1. Breakdown of Virginia's energy sources 7

Coal and natural gas make up 57% of the primary energy sources of Virginia's total electricity production. The rest is nuclear power and renewables. Virginian's pay an average retail price of 8.87 cents per kilowatt-hour and are ranked 23 rd lowest cost in the U.S. The unit will specifically look at the production and consumption of coal.

Dominion Virginia Power runs Chesterfield Power Station in Chesterfield, VA, about 15 miles south of Richmond on the James River. It is the largest fossil-fueled power station in the state and generates 1,600 megawatts (MW). The average daily consumption of coal is 8,400 tons. Nevertheless, Virginia imports more electricity than any other state except California and the demand keeps growing. 8

Coal is plant material buried deep in the earth many years ago, subjected to high temperatures and pressures which caused physical and chemical changes, altering the plant material into peat and then into coal. Coal reserves are discovered through geological explorations which include creating a geological map of the area, conducting geochemical and geophysical surveys, and then, drilling. The area will become a mine if it is large enough and of sufficient quality so the coal can be retrieved at a reasonable cost. Coal is mined in two ways: surface (which includes mountain top mining) and underground mining (which includes strip mining). Once mined, coal is washed of its impurities, treated depending on its intended use and arrives at the power station by truck, train or ship.

So, how is coal, a primary energy source, processed to get electricity, a secondary energy source? It is placed into a hopper where it is crushed into small chunks and the conveyor belt moves the coal to the coal pile which holds a 30-day supply. From the coal pile, the conveyor belt moves the coal to the station and feeds it into a pulverizer that grinds the coal into fine pieces, like baby powder. Coal contains potential chemical energy and is combustible, which means it can catch on fire and burn easily. The powdered coal is blown into the combustion chamber of a boiler where it instantly combusts and releases kinetic thermal energy. The walls of the boiler are lined with tubes which contain purified water. The heat turns the water into high pressure steam which is used to turn the turbine, a massive drum with propeller like blades. This transforms kinetic thermal energy into kinetic motion energy. The turbine turns a magnet wrapped in copper coil to produce electricity in the generator, turning kinetic motion energy into kinetic electrical energy. Electricity is sent to a transformer that increases the voltage to 30,000-400,000 volts (like you increase water pressure). Before the power can be delivered to your homes, the electricity is lowered to safer voltage at an electrical substation where a transformer reduces the voltage to 100-250 volts (like you decrease water pressure). Finally, the electricity moves over distribution lines to your home. 9 Flip the light switch and the lights come on. Surprisingly, while living things are able to store energy from the sun, mankind has yet to find an efficient way to store electricity, so the national grid must balance supply and demand on a minute-by-minute basis.

Coal Mining Experiment

Coal mining companies are often the largest employers in the area which makes their existence essential to the families in the area. On the other hand, their existence means large areas of land are disturbed. This creates environmental challenges including soil erosion, dust, noise and water pollution, removal of all vegetation, and release of greenhouse gases such as methane and carbon dioxide. As a result, the coal industry is charged with rehabilitation, also called reclamation, of coal mine lands during and after use. Power companies are also charged with reducing release of pollutants and greenhouse gases such as such as mercury and sulfur when burning coal. New technologies are constantly developed to reduce the environmental impact of both coal mining and burning. 10

Students will simulate mountain top coal mining and its effect on the surrounding land. They will use algebraic models to describe the effects of production and consumption of coal on our environment using greenhouse gas emissions data from the Energy Information Administration (EIA). Problems may contain conversions depending on how the data are presented.

Wind Energy: Building windmills

Wind is air in motion created by the unequal heating of the earth's surface by the sun's radiant energy. Think of the power exhibited by the wind speeds of a hurricane or a tornado. Imagine we are able to harness this energy, a renewable source, to power communities. In fact, this idea is not so novel. In the mid-west of the U.S., windmills are used to grind grain, pump water and provide electricity. The wind's velocity, which can be measured with an anemometer, is a factor in calculating the amount of electricity wind turbines can generate. Wind power, P, varies jointly with half of air density,Ρ, area swept by the turbine blades, A, and the cube of the velocity, V, P = (1/2)ΡV 3. Air density is the mass per unit volume of earth's atmospheric gases and measures 1.25 kg/m 3 at sea level and 68 °F. Windmills are tall, and the air density decreases at higher altitudes and higher temperatures. The air density decreases by 3% for every 1000 additional feet in height and 1% for each additional degree in temperature. 11

On June 25 th, President Obama introduced his Climate Action Plan. The document lays out his vision to slow the effects of climate change. Wind energy plays a significant role in this endeavor. 12 The Department of Energy is planning to build a research facility off the Virginia coast near Virginia Beach, Va. The intent of the research facility is to test technologies such as remote sensing designed to determine the potential power of offshore winds. Researchers hope the results of their findings will lead to increased capital from investors by providing valid data, thus, increasing production of wind plants, also called wind farms. 13 Virginia has a strong wind resource off the coast. Preliminary research completed by Virginia Coastal Energy Research Consortium showed almost 10% of our electrical power can come from wind energy. Onshore, Dominion Virginia Power is currently developing the Bluestone River Wind Project in Tazewell County, southwest Virginia, which could produce nearly 80 MW. 14 If Dominion is successful, Bluestone River Wind Project will provide electricity to approximately 80,000 people, that is one megawatt per 1,000 people. 15

Significant environmental benefits to wind energy include no release of harmful greenhouse gases and it does not interfere with agriculture. Another significant benefit is the ability to produce power in remote locations all over the world. There are generators transforming the wind's kinetic energy into electrical energy for people who otherwise would not have access to electricity. However, like coal production and consumption, there are negative environmental impacts of wind farms. For example, other than the coast, most of the windy areas in Virginia are in national parks, like Blue Ridge Parkway. 16 This is an obvious conflict of interest; after all, national parks were established "to conserve the scenery and the natural and historic objects and the wild life therein and to provide for the enjoyment of the same in such manner and by such means as will leave them unimpaired for the enjoyment of future generations." 17 Other impacts include the consistency of wind power, as it is not always windy which makes it difficult to implement into existing power grids (recall energy supply and demand must be balanced by the minute), the aesthetics to the landscape or ocean view, the harm to birds and bats, and, in some cases, the noise. In addition, there is a large transportation cost because the majority of wind turbines are mass-produced in Europe or in the Midwest. Hence, there is a large need for skilled workers to support the development of a wind energy supply in our region. 18

Students will build a device that can measure wind speed and a windmill that can do work by picking up an item. Students will then calculate the amount of work and power needed to pick up the weight. Work is the measure of the weight lifted through height; Work, W, varies jointly with mass, m, acceleration of gravity, g, and height, h, W = mgh. Students will also calculate the wind energy created by a fan set on different speeds: low, medium and high.

Biodiesel: Alternative Fuel

Have you heard the story about the guy who ran his car on Canola oil? Too good to be true, right? Correct, that guy did a little more to the composition of the Canola oil than just putting it into his fuel tank. The simple chemistry involved using oil, methanol and sodium hydroxide. The product is biodiesel and glycerol which separates well with biodiesel on top and glycerol, a heavier substance, at the bottom of the container. Methanol and sodium hydroxide are dangerous substances. Glycerol is then removed because it will damage engines. Water is used to wash it out of the fuel, leaving biodiesel only. With no engine modifications, biodiesel can be used to power any diesel engine.

Biodiesel is a renewable fuel produced from vegetable oils, animal fats or recycled restaurant grease. In the early 1900's, Dr. Rudolf Diesel demonstrated the diesel engine and ran it with peanut oil. Diesel engines were marketed to farmers with the notion they could grow their own fuel. Indeed, farmers ran their large trucks, tractors and machinery on vegetable oil until the arrival of low cost and convenient petroleum diesel. Since 2004, West Point, VA has housed a biodiesel plant built by Pacific Biodiesel that uses soybeans made in Virginia. 19 Governments back the manufacturing of biofuel due to concerns about the environment and security of oil. Using biofuels instead of gasoline reduces carbon emissions, creates jobs and keeps money within the community. 20 While biodiesel is good for your vehicle because it provides increased fuel lubricity and extends the life of the engine, there are some concerns. Biodiesel gels like petroleum diesel does in cold temperatures. This can be avoided by purchasing biodiesel treated for winter use. There is also a conflict with the food industry because of increasing demand on the industry to supply both food and fuel to the world. The U.S. Department of Agriculture expected world grain use to reach 20 million tons in 2006, 14 million tons for the fuel industry in the U.S. and 6 million tons to supply the world's food necessities. 21 As a result, the price of food is up and it is the highest it has been in 20 years, since almost everything we eat can be used to create biodiesel. 22 The World Bank is concerned about high prices putting an additional 44 million people into poverty. 23 Moreover, most governments do not have measures in place to limit the amount of land used for biofuels as not to compete with the food industry, thus, strengthening hunger in impoverished countries.

Students will make biodiesel from old and new oil then perform titrations to determine if the biodiesel has the correct pH. Students will use compound inequalities to describe the acceptable range of pH, fuel efficiency of biodiesel, crop production and sales, and oil content of crop. Students will evaluate the sustainability of a crop by calculating the energy return on energy investments to ensure that the energy input is significantly less than the energy output. Students will also use systems of equations to model and solve problems related to the production and production cost of biodiesel.

Energy Efficiency: Use Less, Save More

image 13.05.05.02

Figure 2. Breakdown of how energy is used in Virginia 24

Dominik Saner, researcher with the Institute of Environmental Engineering in Switzerland, says residential and private transportation energy use accounts for more than 70% of carbon dioxide emissions. 25 The energy Virginians use in the residential and transportation sector make up 57% of the total energy generated. The future of energy in Virginia requires a comprehensive approach that combines efficiency programs with renewable energy sources. Many of us are not in situations where we can construct a windmill for our individual use. So, we are left to think of ways to make our current non-renewable primary energy sources last longer by decreasing the demand for energy. If we are doing our part at similar commitment levels, the ratio of consumption described could stay the same, but the total amount of consumption is reduced.

There are a variety of ways to conserve on the road that does not include converting your car to a diesel engine and making your own fuel. If you need incentive, gas in New Haven, Connecticut is currently $3.93/gallon. Gas in Virginia is about sixty cents cheaper, temporarily. So, until there are significant changes in the manufacturing of automobiles, we are faced with the high gasoline prices. One way to beat the cost is to drive at slower constant speeds and accelerate/decelerate at a slower rate when merging into traffic on a highway or local road. We waste gasoline driving at higher speeds due to rolling and internal vehicle friction and drag force. Also, turn off your car instead of idling; restarting your car takes the same amount of gas used in 0.2 seconds of idling. Finally, keeping your tires properly inflated will save money and make your gasoline last longer. 26

Like your car, there are a variety of ways to save in your home. Dominion's website has many practical energy conservation tips customers can implement during the winter and summer months. Some tips are simple and require no investments, while others require an investment which will pay for itself within months, sometimes weeks. Some examples of low to no cost energy conservation tips include: setting your thermostat a few degrees higher in summer and lower in winter, keeping your shades closed when the air conditioner is on and opening your shades during the winter to let the sun's radiant energy heat your home, cleaning/replacing filters, washing dishes or clothes in the early morning or late evening, using cold water to wash dishes and clothes, sealing air leaks at entrances, grilling meals outside, unplugging appliances not in use and turning off lights not in use. Examples of higher cost investments include: using more efficient appliances, installing ceiling fans, using a tankless-water heater and replacing lighting with more efficient bulbs. Local power companies also offer energy calculators on their website to evaluate electrical usage in your home and business facilities; understanding specific energy use by location can reduce consumption and save money. 27 If preferred, the power company will do a standard residential in-home energy audit as well. The power company also offers approved programs that help families conserve energy conveniently and offer an incentive. Some of the teachers in my seminar benefit from programmable thermostats that provide indicators of critical peak times. The most popular, or rather the most visible, program is ENERGY STAR®. In fact, there are mortgage loan incentives for having a home run by appliances under ENERGY STAR® guidelines. 28

Students will perform an energy audit of their home, write a proposal to their caregiver making suggestions and create a flyer describing 10 things we can do to conserve energy. We will use the formula: C = WNHDP/1000, where W is the power in Watts consumed by a device, N is the number of devices in use, H is the number of hours per day the device is in use, D is the number of days in a year when the device is in use, P is the price of electrical service in dollars per kilowatt-hour ($0.0887), and C is the total cost in dollars per year for using the device. We divide by one thousand to convert Watts to kilowatts. This formula accounts for other factors that simpler energy formulas do not take into account.

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