A comprehensive understanding of energy is crucial to succeeding on the AP® Environmental Science exam. On the APES exam, you will encounter problems that will require you to solve problems related to solar energy, fossil fuels, power plant operation, and other energy concepts. In this crash course review, we’ll cover what you need to know about energy and a sample free response question involving energy calculations. Let’s get started.

What is Energy?

Energy is the ability to do work. Energy cannot be created, it must come from somewhere, this is the first law of thermodynamics. Energy can be transferred to different forms, but some of it becomes unusable at each step in the process, this is the second law of thermodynamics. Energy comes in many forms, kinetic, potential, mechanical, etc., but all forms of energy have the ability to do work.

Measuring Energy

In physics, work is defined as force times the distance through which the force acts. From this definition, we get the idea that energy is the property that allows one to move objects and thus accomplish some physical labor or work. Thus, all forms of energy must be reducible to these units.

There are two systems of measurement: The United States Customary System used in the US and the metric system (SI) which is used everywhere else. The metric system is used in science and a specific subset of the system centimeter-gram-second, is particularly relevant for the APES exam. The following table exhibits how force and energy are measured in the major measurement systems.

Units in Energy Calculations

In order to effectively calculate energy on the APES exam, there are several specialized units that you will need to know. We will break down these units and how they are used below.

The Newton

The newton is named after Isaac Newton and is a unit of force. It is capitalized when it is abbreviated, but not when used in measurement (e.g. N). In the above table, it can be seen that one newton is equal to 1 \text{ kg}\times { 1 \text{ m}}/{ { \text{s} }^{ 2 } }, about 0.225 lbs. It is a common mistake to think one newton equals one kilogram, but it is important to note that that is not the case.

The Joule

The joule (J), named for Sir James Prescott Joule, a British energy scientist, is an energy unit and is defined as the work completed by the force of one newton acting at a one-meter distance. One joule is very small, but it remains the unit of energy most often used in science.

The Calorie

The calorie was also discovered by Sir James Prescott Joule and is the heat needed to raise one gram of water one degree Celsius. His discovery of the calorie demonstrated that mechanical energy and heat are equivalent. There is also the kilocalorie or Calorie (note the capital c). A kilocalorie will raise one kilogram of water by one degree. Calories in food are always kilocalories.

1 \text{ calorie} = 4.184 \text{ Joules}

The calorie can be used to determine a fuel’s energy content. The fuel is burned to exhaustion, the heat is transferred, and the temperature difference is measured, allowing the ability to calculate, in calories, the energy content of the fuel which can then be converted to Joules.

The BTU

The BTU is a common unit for heat energy that you will see on the AP® Environmental Science exam. One BTU is the amount of heat required to raise a pound of water by one degree Fahrenheit.

Using \dfrac{ 2.2\text{ lbs} }{ 1 \text{ kg} } and \dfrac{ 1.8 ^{\circ} \text{ Fahrenheit}}{ 1^{\circ} \text{ Celsius}} , it can be found that:

1 \text{ BTU} = 252 \text{ calories} = 1055 \text{ Joules}

BTUs are used to rate air conditioners, furnaces, and water heaters in the form of BTUs/hour, which refers to the amount of heat a unit can produce per hour. Sources of fuel are rated in BTUs per unit in weight, usually a ton.

The Therm

Another unit of measure you will encounter both on the AP® Environmental Science exam is the therm or thermal unit, which is used by gas companies to measure how much natural gas you use. 1 \text{ therm} = 100{,}000 \text{ BTU} One cubic foot of natural gas has a heat value of 1030{ \text{ BTU}}/{ { \text{f}}^{ 3 } } at normal temperature and pressure, meaning that one therm is approximately equal to 100 cubic feet of natural gas.

Gas companies also use different terminology where c stands for 100 and where m stands for 1000. They are used as numerical prefixes and are not capitalized due to the potential for confusion with SI units. For example, 2ccf is equal to 200 cubic feet. This may seem confusing at first, but it is usually pretty obvious when this notation is being used.

Power

Power, the term that describes energy flow, is defined as the time rate of work and is measured in joules per second. One Watt is equal to one joule per second. There is no unit to measure power in the cjs system. In USCS system, horsepower is the unit used for power and one horsepower equals 550 ft-lbs per second, equivalent to 0.75 kW or 746 watts.

It is easy to confuse power and energy when in dealing with watts. A useful analogy for thinking about this is to think about buying gas. You pay based on the amount of gas you put in your car, not how fast you put the gas in your car.

When you pay your electric bill, the electricity you use will be measured in kilowatt hours or \text{ kW} \cdot \text{h}. One kilowatt will power ten 100-watt light bulbs for one hour. Kilowatt hours can easily be converted to joules as seen below. This is the energy you are paying for on an electric bill.

1 \text{ kW} \cdot \text{h} = 1{,}000 \text{ J/s} \times 3{,}600s = 3.6 \times { 10 }^{ 6 } \text{ J}

Electric Power Plants

You will also likely see questions about electric power plants on the AP® Environmental Science exam. Electric power plants are rated based on their output capacity. For example, a large electric power plant may be rated at 1,000 MWe where the e is electric and reminds you that this signals the output of the plant as opposed to the input. Input is measured in terms of the heating value of the fuel that the power plant uses. If you know the output capacity of a power plant and the level of efficiency, you can calculate the amount of fuel needed to power the plant or the energy input. For example, with an efficiency rating of 40% the calculations would be as follows:

\dfrac { 1{,}000 \text{ MW}}{ 0.40 } =2{,}500 \text{ MW}

\dfrac { 2{,}500 \times 106 \text{ J/s} \times 3{,}600 \text{ s/h}}{ 1054 \text{ J/BTU}} = 8.54 \times { 10 }^{ 9 } \text{ BTU/hr}

To calculate tons of fuel needed per hour, you would divide the above number by the heating value of the fuel that power plant uses. You will see problems similar to this on the AP® Environmental Science exam.

Solar Energy

Another energy calculation that you will run into on the APES exam is solar energy. The rate at which sun is received on the surface is called solar flux. At the Earth’s orbit, this value is the solar constant 1{,}400{ \text{ W}}/{ { \text{ m}}^{ 2 } }. The atmosphere absorbs about half this amount, leaving 700{ \text{ W}}/{ { \text{ m}}^{ 2 } }. Averaging for day and night, seasons, and all latitudes, this number is further reduced to 240{ \text{ W}}/{ { \text{ m}}^{ 2 } }, but this amount varies some by location. Greenland, for example, gets less solar flux, than Brazil.

Solar energy is especially important in AP® Environmental Science because it is a renewable energy source. Unlike fossil fuels, solar energy will be around for years to come. Additionally, solar energy is also important for calculations such as how much biomass will grow in one area compared to another.

Energy Calculations on the AP® Environmental Science Exam

You will encounter questions about energy calculations on the AP® Environmental Science exam in both the multiple choice and free response sections of the exam. In the multiple choice section, questions will typically require less math and be simpler to perform. In the free response section of the exam, you will need to make more involved calculations and show your work in order to receive credit. To help you prepare for the free response section of the exam, we will cover an energy calculation question from a previous exam.

Battery electric vehicles (BEVs) have been introduced to consumers as an alternative way to reduce the environmental effects caused by use of internal-combustion engine (ICE) vehicles. A comparison of both vehicle types can help determine whether the use of BEVs would be beneficial in the future. Where calculations are required, show your work.

(a) Identify THREE strategies that the federal government could implement to encourage the use of BEVs.

(b) Assume that the fuel efficiency of the ICE vehicle is 25 miles per gallon (mpg) and that gasoline costs $3.75 per gallon (gal). Calculate the cost of gasoline per mile.

(c) The charger supplies energy to the BEV battery at an average rate of 4.0 kilowatts (kW) and fully charges the BEV battery in 7.0 hours. The car will run for 100 miles on a full charge. The cost of electricity is $0.11 per kilowatt-hour (kW\cdoth).

i. Calculate the cost of the electricity to fully charge the battery. Assume that the battery is not charged to begin with.

ii. Calculate the cost of electricity per mile to drive the BEV.

When it is driven 100 miles, the ICE vehicle contributes 72.8 pounds (lb) of { \text{CO}}_{ 2 } from the burning of the gasoline. The drilling, refining, and transportation costs of getting the gasoline to the gas station add an additional 17.7 lb of { \text{CO}}_{ 2 } per 100 miles. The BEV does not emit any { \text{CO} }_{ 2 } itself, but the extraction, transportation, and combustion of the coal that produced the electricity at the power plant add 63.6 lb of { \text{CO}}_{ 2 } for the same 100 miles.

(d) Calculate the difference in the amount of { \text{CO}}_{ 2 } that would enter the atmosphere if both cars were driven 100 miles.

(e) Describe TWO economic impacts (excluding costs related to climate change resulting from { \text{CO}}_{ 2 } emissions or the cost of gasoline at the pump) that result from an increased number of BEVs on the road.

As you can see, this question deals with power, and the kilowatt-hour unit we discussed above. Part (a) of this question is worth three points, one for each strategy that could be implemented. This part does not require calculations and has many possible answers. You might cite increasing taxes on diesel and gasoline, creating restrictions for ICE vehicles, increasing the accessibility of charging stations, creating tax incentives for purchasing BEVs, or other possible incentives.

In part (b) of this question, two points are available and energy calculations are required. The first point is for setting your work up correctly and including units, the second is for getting the right answer. Your work should look something like this.

\dfrac {\$3.75} {25 \text (miles)} = (\$0.15) \text (mile)

In part (c)(i), two points are available and energy calculations are required. One point is for setting your work up correctly including units and the second is for getting the right answer. Your answer should look like something like this.

7 \text{ hours} \times 4 \text{ kW} \cdot \text{h} \times \dfrac { 11 \text{ cents}}{ \text{kW}\cdot \text{h}} = \$3.08

In part (c)(ii), one point can be earned for the correct answer and work is not required, but it is still good practice to include your work. Your answer should look like this.

\dfrac { \$3.08 }{ 100 } = \$0.03 \text{ per mile}

Part (d) of this question requires some basic addition and is worth one point with work shown. Your answer should look something like this.

72.8 \text{ lb} + 17.7 \text{ lb} = 90.5 \text{ lb}

90.5 \text{ lb} - 63.6 \text{ lb} = 26.9 \text{ lb}

In part (e) of this question, you can earn two points, one for each correct impact. Possible correct answers include the fact that BEV drivers will save money that can be spent elsewhere, increased jobs in the electrical industry, and increased jobs and profit for manufacturing and repairing BEVs.

Wrapping Up Energy Calculations

This AP® Environmental Science reviewed all the energy calculations and units you will need to know to be successful on the APES exam. By carefully reviewing these units and calculations, you will be able to apply them to any energy question you encounter on the APES exam.

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