AP Environmental Science Summer Assignments

Welcome to AP* Environmental Science (APES) for the 2021-2022 school year! APES is designed to be the equivalent of a one semester, introductory college course in Environmental Science. The course is interdisciplinary, encompassing topics in chemistry, physics, geology, biology, environmental studies, and geography. It also incorporates a sociological, political, and global perspective. APES is designed to provide students with the scientific principles, concepts, and methodologies required to understand the interrelationships of the natural world, to identify and analyze environmental problems both natural and human­made, to evaluate the relative risks associated with these problems, and to examine alternative solutions for resolving and/or preventing them.

This assignment serves to help you prepare for the year ahead. To be a successful APES student, you must be willing to spend significant time outside of class preparing and completing work. Remember that this course is modeled after a college course, so both the fast pace and sheer depth of information may be new to you. This course requires dedication, commitment, and total immersion into the field of environmental science.

This assignment is to be completed independently and is DUE ON THE FIRST DAY OF SCHOOL.

Assignment Estimated time

Materials required What you need to turn in

Part 1 Introduction to APES Read Chapters 1, 2, and 20 in the textbook

2 hour+ Text Book Guided Notes

Guided Notes for Chapters 1 and 2

Part 2 Legislation

Varies *Computer with internet access

Legislation assignment

Flash Cards (digital or physical)

Part 3 Math Skills And Basic Review

3 hours+ Pencil and paper. Calculators

Answers to problems, showing all work. Bring completed on first day of school. There will be a quiz in class sometime during first two weeks of school on this material and the content from Part 1.

Part 1 Summer APES Assignment (Reading Guides)

Chapter 1: Environmental Science: Studying the State of Our Earth Vocabulary: Define the following terms in your own words.

1. Fracking 7. Environmentalist 13. Species 19.

Development 25.

Hypothesis

2. Environment 8. Environmental Indicator

14. Species Diversity 20.Sustainability 26.

Replication 3.Environmental

Science 9. Ecosystem

Services 15. Speciation 21. Sustainable Development

27. Sample Size (n)

4. Ecosystem 10.

Environmental Indicator

16. Background Extinction Rate 22. Biophilia 28. Theory

5. Biotic 11. Biodiversity 17. Greenhouse Gases

23. Ecological Footprint

29. Control Group

6. Abiotic 12. Genetic Diversity 18.Anthropogenic 24. Scientific

Method 30. Natural Experiment

Opening Story: To Frack, or Not to Frack

1. What environmental problems are fossil fuels responsible for?

2. Why is natural gas better than traditional fossil fuels?

3. Explain why initially natural gas appeared to be beneficial to the natural environment.

4. Name and explain the negative environmental effects of fracking.

5. How does fracking provide a good introduction to the study of environmental science? Module 1: Environmental Science offers important insights into our world

1. Give an example of something biotic and something abiotic within an ecosystem. Explain how these two interact.

2. Explain how fracking is part of a larger system.

3. Using the fisheries of the North Atlantic as an example, come up with a list of four systems.

4. What role do humans play in environmental systems? Give an example of 2 negative impacts humans have

had on these systems.

5. How does new technology generally impact resource use?

6. Who uses more resources per capita: a child born in Los Angeles or a child born in rural India? Why? Module 1 AP Review Questions (pg 6) 1. 2. 3. 4. Module 2: Scientists monitor natural systems for signs of stress 1. Fill out the following chart about five global environmental indicators outlined in Table 2.2 and pages 8­14.

Indicator Increasing, decreasing or staying the same

right now?

To achieve sustainability, does it need to

increase, decrease or

stay the same?

Why should you

(personally) care about

this indicator?

How does this

indicator connect to ONE other indicator?

Biological Diversity

Food production

Average Global Temperature and [CO2]

Human Population

Resource depletion

2. List and explain the 3 levels in which biodiversity occurs. 3. How many new species evolve (new species) worldwide per year? What should the extinction rate be (per million every year)? Currently how many species are going extinct?

4. Why are greenhouse gases important? 5. What are the two major sources of anthropogenic carbon dioxide? 6. What is the difference between renewable and non­renewable resources? 7. What happened on Easter Island and what should we learn from their mistakes? 8. What does an ecological footprint represent? 9. Explain how iron can be used sustainably. Do the Math (pg. 11) A particular forest is 10,000 acres. Determine its size in hectares. (1 hectare = 2.47 acres). Show all work and units. Module 2 AP Review Questions 1. 2. 3. 4. 5. Module 3: Scientific Method

1. Explain the scientific method and its application to the study of environmental problems.

2. Explain how environmental science presents unique challenges (4 reasons).

3. What is required for an idea to be considered a theory, in a scientific sense? Consider “the theory of evolution”.

4. What is the purpose of a control group in an experiment?

5. What are the goals of the environmental justice movement, and why are they relevant to achieving sustainability?

Module 3 AP Review Questions (pg 25) 1. 2. 3. 4. 5. Chapter 1 Practice Exam 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Chapter 2: Systems and Matter Vocabulary: Define the following terms in your own words.

1. Matter 9. Ionic Bond 17. Chemical Reaction 25. Energy 33. Temperature

2. Mass 10. Hydrogen Bond

18. Law of Conservation of

Matter 26. Joule 34. 1st Law of

Thermodynamics

3. Molecule 11. Polar Molecule

19. Inorganic Molecule 27. Power 35. 2nd Law of

Thermodynamics

4. Compound 12. Surface Tension

20. Organic Molecule

28. Electromagnetic

Radiation

36. Energy Efficiency

5. Isotopes 13. Capillary Action 21. Carbohydrate 29. Photon 37. Energy Quality

6. Radioactive Decay 14. Acid 22. Protein 30. Potential

Energy 38. Entropy

7. Half­life 15. Base 23. Nucleic Acid 31. Chemical Energy

39. Negative Feedback Loop

8. Covalent Bonds 16. pH 24. Lipid 32. Kinetic Energy 40. Positive Feedback Loop

A Lake of Salt Water, Dust Storms and Endangered Species

1. Where is Mono Lake and why is it unique?

2. What was the controversial plan made in 1913? What were the consequences of that plan?

3. Explain how the Mono Lake system changed due to the decline in freshwater.

4. What changed in 1994? What caused the change?

5. What does the story about Mono Lake illustrate about human interactions with complex natural systems.

Module 4: Matter comprised atoms and molecules that move along different systems

1. What is radioactive decay and why would be study it in environmental science? (see if you can come up with more than one reason).

2. What is the difference between an atom, a molecule, and compound?

3. What is a half life and why would we study it in environmental science?

4. How does carbon dating work?

5. Water has four important properties that help it support life on Earth. List the four properties and define any that you are not familiar with.

6. The pH scale is logarithmic. How much more basic is something with a pH of 10 than something with a pH of 7?

Module 4 AP Review Questions 1. 2. 3. 4. 5. 6. Module 5: Energy is a fundamental component of environmental systems

1. What is energy? Name three types of energy.

2. Explain how energy can be converted from one form to another.

3. How does the amount of energy within an ecosystem determine they type of organisms that reside there?

4. For each situation below, state whether the 1st or 2nd law of thermodynamics applies: a. In a car, only some of the energy from the gasoline is used to propel the car. The rest is lost as heat.

b. Nothing can ever be 100% efficient in terms of converting energy to work.

c. When you walk up a hill you gain the same amount of energy you will lost as you walk down.

d. Your computer, TV, and refrigerator all need a fan to keep from overheating.

e. There is no such thing a perpetual motion.

5. What is the difference between energy efficiency and energy quality?

6. What is the difference between an open and closed system? Give an example of each.

7. Label the following as a positive or negative feedback loop:

a. The baby boom resulted in lots of children therefore the US population grew. Those children grew up

and had more babies making the population continue to grow. = b. Cole takes a nap and gets a sticker when he gets up so the next day he takes a nap so that he will get

another sticker. = c. Air conditioner and thermostat = d. Compounding interest. = e. California state lottery increases so more people buy tickets.

= Module 5 AP Review Questions (pg 54)

1. 2. 3. 4. 5. 6.

Chapter 2 AP Environmental Science Practice Exam

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14.

Part 2 APES Summer Assignment Legislation Purpose: The study of Environmental Science includes an understanding of the different facets of environmental legislation. Without this background, students will not be able to fully comprehend the different legal ramifications, which are closely related with ethical and economic issues.

Flash Cards- For each topic, create a flashcard (digital or physical) that addresses the following questions: 1. Is this a law, treaty, or act (or something else altogether)? 2. In what year was this first enacted? What are dates of amendments (if any)? 3. What events or situations led to this? 4. What is the basic premise of this law/act/treaty (what does it accomplish/address)? You will be expected to know about ALL 26 environmental legislation, acts, or treaties. Environmental Legislation, Laws, and Acts: 1. Endangered Species Act 2. Convention on International Trade in Endangered Animals (CITES) 3. Federal Insecticide, Fungicide and Rodenticide Act (FIFRA) 4. Clear Air Act 5. Clean Water Act 6. Comprehensive Environmental Response, Compensation and Liability Act 7. National Environmental Policy Act 8. Safe Drinking Water Act 9. Resource Conservation and Recovery Act 10. Federal Food, Drug, and Cosmetic Act (Delaney Clause) 11. Taylor Grazing Act 12. National Wildlife Refuge System

13. Wild and Scenic Rivers Act 14. Endangered Species Act 15. Energy Policy Act 16. Desert Protection Act 17. Surface Mining Control and Reclamation Act 18. Kyoto Protocol 19. Montreal Protocol 20. Paris Agreement 2016 21. Agenda 21 22. London Dumping Convention 23. Helsinki Convention 24. Lacey Act 25. Stockholm Convention 26. Antiquities Act

Keep Up the Good WorK!!!!! One Section Left!!!!!

Part 3 Math and Concept Review The 2022 AP Environmental Science Exam will allow calculators on both the multiple choice and free-response sections. While that is good news, it is still very important for you know how to set up the steps of the calculation and how to use your calculator. You must still show all of your work, including units, to receive full credit on free-response math questions. Chemistry is a big part of environmental science. Chemistry is a prerequisite before registering for the course. In order to review some of the basic chemistry concepts, you will need to complete the following on a clean sheet of paper. This may be typed or handwritten.

1. For each of the following, write out the chemical name that goes with the symbol. CO2 CO C6H12O6 CH4 H2

N2 NO2 NO3 NH3 NH4

O2 O3 P PO43­ S

SO2 SO3 H2SO4 NaCl Pb

U Rn Hg Cl H2O

2. Answer the following to the best of your ability:

a. What is the pH scale? What does it measure?

b. How do the numbers on the pH scale compare? Example – is a pH of 4 twice as strong as a pH of 2? Hint – the pH scale is not linear!

c. What are the average pH ratings of the following common substances in the environment?

i. Blood­ ii. Rain­ iii. Freshwater (lake or river)­ iv. Ocean water­

Practice Interpreting Data: The following questions are to help you practice reading information shown on a graph. Answer each question on the separate answer sheet.

1. Identify the graph that matches each of the following

stories: a. I had just left home when I realized I had

forgotten my books so I went back to pick them up.

b. Things went fine until I had a flat tire. c. I started out calmly, but sped up when I realized

I was going to be late.

2. The graph at the right represents the typical day of a teenager. Answer these questions:

a. What percent of the day is spent watching TV? b. How many hours are spent sleeping? c. What activity takes up the least amount of time? d. What activity takes up a quarter of the day? e. What two activities take up 50% of the day? f. What two activities take up 25% of the day?

3. Answer these questions about the graph at the right: a. How many sets of data are

represented? b. On approximately what calendar date

does the graph begin? c. In what month does the graph reach its

highest point?

3. Answer these questions about the graph on

the right: a. How many total miles did the car travel?

b. What was the average speed of the car for

the trip?

c. Describe the motion of the car between

hours 5 and 12?

d. What direction is represented by line CD?

e. How many miles were traveled in the first

two hours of the trip?

f. Which line represents the fastest speed?

4. Answer these questions about the graph at the right: a. What is the dependent variable on this graph?

b. Does the price per bushel always increase with demand?

c. What is the demand when the price is 5$ per bushel?

5. The bar graph represents the declared majors of freshman enrolling at a university. Answer the following questions:

a. What is the total freshman enrollment of the college?

b. What percent of the students are majoring in physics?

c. How many students are majoring in economics?

d. How many more students major in poly sci than in psych?

6. Answer these questions about the data table:

a. What is the independent variable on this table?

b. What is the dependent variable on this table?

c. How many elements are represented on the table?

d. Which element has the highest ionization energy? Scientific Notation Environmental Science often deals with very large numbers (e.g. billions of gallons of oil) and very small numbers (e.g. contamination of an aquifer with mercury). To better manage these numbers and to decrease errors, scientists have developed a shorter method to express numbers using scientific notation which is based on powers of 10. Thus, for example, an environmental scientist calculates that 123,000,000,000 kilograms of biomass was produced in a test plot during the previous year. Example: 123,000,000,000 kg Step 1: Place a decimal after the first digit. 1.23000000000 Step 2: Count the digits after the decimal…there are 11. This will be the exponent. Step 3: Drop the zeros and write in the exponent. 1.23 x 1011 kg Writing tiny numbers in scientific notation is similar. The only difference is the decimal is moved to the left and the exponent is a negative. A tiny number written in scientific notation looks like this:

4.26 x 10-8 kg of lead in a water sample To write a tiny number in scientific notation, move the decimal after the first digit that is not a zero. Count the number of digits before the decimal you just wrote in. This will be the exponent as a negative. Drop any zeros before or after the decimal. Example: .0000000426 kg Step 1: 00000004.26 Step 2: Count the digits before the decimal…there are 8. Step 3: Drop the zeros and write in the exponent as a negative. 4.26 x 10-8 kg

Note: You do not have to use scientific notation on the AP exam, but it may be helpful to you when you have to add/subtract/multiple/divide very large and very small numbers. Problems: Convert the following numbers into or from scientific notation.

1. 678,959,000,000= ___________________________________

2. .00000004567= ___________________________________

3. 5,689,000,000= ___________________________________

4. 8,923= ___________________________________

5. .00000000456789= ___________________________________

6. 2.23 x 10-9= ___________________________________

7. 3.19 x 1012= ___________________________________

8. 4.444 x 10-4= ___________________________________

Atomic Number

Ionization Energy (volts)

2 24.46

4 9.28

6 11.22

8 13.55

10 21.47

Scientific Notation Calculations Multiplication: add exponents, multiply bases (3 x 103) (4 x 105) = 12 x 108 or 1.2 x 109

Division: subtract exponents, divide bases (5.2 x 104) / (2.6 x 102) = 2 x 102

Addition: convert both numbers to same exponent, the add bases; exponents stay the same (3000 x 106) + (14 x 105) = 3001.4 x 106

Subtraction: convert both numbers to same exponent, then subtract bases; exponents stay the same (2000 x 103) – (1000 x 102) = 1900 x 103

Problems: Calculate the result by hand or with your calculator (it is important to know how to enter exponents on your calculator if you are going to us it!)

1. (8.7 x 10-3) x (4.2 x 10-9) = ________________________________

2. (5.2 x 1018) x (8.7 x 1022) = ________________________________

3. (8.7 x 10-3) / (4.2 x 10-9) = ________________________________

4. (5.2 x 1018) / (8.7 x 1022) = ________________________________

5. (3 x 109) + (14 x 106) = ________________________________

6. (1.5 x 104) + (25 x 103) = ________________________________

7. (8.5 x 107) – (4.5 x 107) = ________________________________

8. (92 x 109) – (.15 x 106) = ________________________________

Averages and Percentages

1. Averages To find an average, add all the quantities given and divide the total by the number of quantities. Example: Find the average of 10, 20, 35, 45, and 105. Step 1: Add all the quantities. 10 + 20 + 35 + 45 + 105 = 215 Step 2: Divide the total by the number of given quantities. 215 / 5 = 43 Practice: Calculate the three averages below. You have the benefit of a calculator but if asked in an FRQ (free response question) you will have to show all of your work for credit. Please show your work for each problem below.

1. Find the average of the following numbers: 11, 12, 13, 14, 15, 23, and 29

2. Find the average of the following numbers: 124, 456, 788, and 343

3. Find the average of the following numbers: 4.56, .0078, 23.45, and .9872

2. Percentages Percents show fractions or decimals with a denominator of 100. Always move the decimal TWO places to the right go from a decimal to a percentage or TWO places to the left to go from a percent to a decimal. Examples: .85 = 85%. .008 = .8% Finding the Percent of a Given Number To find the percent of a given number, change the percent to a decimal and MULTIPLY. Example: 30% of 400 Step 1: 30% = .30 Step 2: 400 x .30 12000 Step 3: Count the digits behind the decimal in the problem and add decimal to the answer. 12000 120.00 120 Finding the Percentage of a Number To find what percentage one number is of another, divide the first number by the second, then convert the decimal answer to a percentage. Example: What percentage is 12 of 25? Step 1: 12/25 = .48 Step 2: .48 = 48% (12 is 48% of 25) Finding Percent Change Environmental scientists often analyze trends. A popular approach to communicating these trends is percentage increase/decrease over time. In calculating percentage of change, you are concerned with the difference between two numbers and how much of the first number added to or subtracted from the first number will produce the second number. The three steps are as follows: Example: 234.98 to 324.77 = _____% change Percent change = Original number - new number Original number Step 1: 234.98 – 324.77 = -89.79 Step 2: -89.79/ 234.98 = -.3821 Step 3: -.3821 x 100 = -38.21% change (the negative number indicates that it is a decrease) Finding a Total Value To find a total value, given a percentage of the value, DIVIDE the given number by the given percentage. Example: If taxes on a new car are 8% and the taxes add up to $1600, how much is the new car? Step 1: 8% = .08 Step 2: $1600 / .08 = $160,000 / 8 = $20,000 (Remember when the divisor has a decimal, move it to the end to make it a whole number and move the decimal in the dividend the same number of places. .08 becomes 8, 1600 becomes 160000.) Practice: Remember to show all your work, include units if given. Check your work with a calculator.

1. What is 45% of 900?

2. Thirteen percent of a 12,000 acre forest is being logged. How many acres will be logged?

3. A water heater tank holds 280 gallons. Two percent of the water is lost as steam. How many gallons remain to be used?

4. What percentage is 25 of 162.5?

5. 35 is what percentage of 2800?

6. 14,000 acres of a 40,000 acre forest burned in a forest fire. What percentage of the forest was damaged?

7. You have driven the first 150 miles of a 2000 mile trip. What percentage of the trip have you traveled?

8. Home prices have dropped 5% in the past three years. An average home in Indianapolis three years ago was $130,000. What’s the average home price now?

9. The Greenland Ice Sheet contains 2,850,000 cubic kilometers of ice. It is melting at a rate of .006% per year. How many cubic kilometers are lost each year?

10. 235 acres, or 15%, of a forest is being logged. How large is the forest?

11. A teenager consumes 20% of her calories each day in the form of protein. If she is getting 700 calories a day from protein, how many calories is she consuming per day?

12. In a small oak tree, the biomass of insects makes up 3000 kilograms. This is 4% of the total biomass of the tree. What is the total biomass of the tree?

13. In 2000, the level of ammonia in a river was 63 ppm (parts per million). In 2004, the level was 112 ppm. What is the percentage increase since 2000?

14. A utility’s operating costs for its electrostatic precipitator was the following: 2001= $345,000 2002= $325,000 2003= $345,000 What were the annual percentage changes?

A) 2001-2002: B) 2002-2003:

Metric Conversions

Kilo-, centi-, and milli- are the most frequently used prefixes of the metric system. You need to be able to go from one to another. You can remember the order of the prefixes by using the following sentence: King Henry Died By Drinking Chocolate Milk. Since the multiples and divisions of the base units are all factors of ten, you just need to move the decimal to convert from one to another.

Example: 55 centimeters = ? kilometers Step 1: Figure out how many places to move the decimal. King Henry Died By Drinking… – that’s six places. (Count the one you are going to, but not the one you are on.) Step 2: Move the decimal five places to the left since you are going from smaller to larger.

55 centimeters = .00055 kilometers Example: 19.5 kilograms = ? milligrams Step 1: Figure out how many places to move the decimal. … Henry Died By Drinking Chocolate Milk- that’s six places. (Remember to count the one you are going to, but not the one you are on.) Step 2: Move the decimal six places to the right since you are going from larger to smaller. In this case you need to add zeros.

19.5 kilograms = 19,500,000 milligrams

Practice: Convert all of the measurements below to the new unit given. You can report your answer in scientific notation. Check you work with a calculator.

1. 1200 kilograms = ________________________milligrams

2. 14000 millimeters = ______________________meters

3. 670 hectometers = _______________________centimeters

4. 6544 liters = ____________________________milliliters

5. .078 kilometers = ________________________meters

6. 17 grams = _____________________________kilograms

Factor-Label Calculations (dimensional analysis)

Dimensional analysis is a way to convert a quantity given in one unit to an equal quantity of another unit by lining up all the known values and multiplying. It is sometimes called factor-labeling. The best way to start a factor-labeling problem is by using what you already know. In some cases, you may use more steps than a classmate to find the same answer, but it doesn’t matter. Use what you know, even if the problem goes all the way across the page! In a dimensional analysis problem, start with your given value and unit and then work toward your desired unit by writing equal values side by side. Remember you want to cancel each of the intermediate units. To cancel a unit on the top part of the problem, you have to get the unit on the bottom. Likewise, to cancel a unit that appears on the bottom part of the problem, you have to write it in on the top. Once you have the problem written out, multiply across the top and bottom and then divide the top by the bottom. Example: 3 years = ? seconds Step 1: Start with the value and unit you are given. There may or may not be a number on the bottom. 3 years Step 2: Start writing in all the values you know, making sure you can cancel top and bottom. Since you have years on top right now, you need to put years on the bottom in the next segment. Keep going, canceling units as you go, until you end up with the unit you want (in this case seconds) on the top.

Step 3: Multiply all the values across the top. Write in scientific notation if it’s a large number. Write units on your answer.

3 x 365 x 24 x 60 x 60 = 9.46 x 107 seconds Step 4: Multiply all the values across the bottom. Write in scientific notation if it’s a large number. Write units on your answer if there are any. In this case everything was cancelled so there are no units.

1 x 1 x 1 x 1 = 1 Step 5: Divide the top number by the bottom number. Remember to include units.

9.46 x 107 seconds /1 = 9.46 x 107 seconds Step 6: Review your answer to see if it makes sense. 9.46 x 107 is a really big number. Does it make sense for there to be a lot of seconds in three years? YES! If you had gotten a tiny number, then you would need to go back and check for mistakes.

In lots of APES problems, you will need to convert both the top and bottom unit. Don’t panic! Just convert the top one first and then the bottom. Example: 50 miles per hour = ? feet per second Step 1: Start with the value and units you are given. In this case there is a unit on top and on bottom. 50 miles 1 hour Step 2: Convert miles to feet first.

Step 3: Continue the problem by converting hours to seconds.

Step 4: Multiply across the top and bottom. Divide the top by the bottom. Be sure to include units on each step. Use scientific notation for large numbers.

50 x 5280 feet x 1 x 1 = 264000 feet 1 x 1 x 60 x 60 seconds = 3600 seconds

264000 feet / 3600 seconds = 73.33 feet/second Practice: Remember to show all your work, include units if given. Free Response Math questions on the AP Exam will require you to show all work WITH UNITS to receive credit- even if you have the right answer. Wrong answers can still receive set up points and wrong answers carried through additional calculations will not be penalized if the math is done correctly. Use scientific notation when appropriate. Conversions: 1 square mile = 640 acres 1 hectare (Ha) = 2.47 acres 1 kw-hr = 3,413 BTUs 1 barrel of oil = 159 liters 1 metric ton = 1000 kg

1. 134 miles = _____________________inches

2. 8.9 x 105 tons = __________________ounces

3. 1.35 kilometers per second = _____________miles per hour

4. A city that uses ten billion BTUs of energy each month is using how many kilowatt-hours of energy?

5. A 340 million square mile forest is how many hectares?

6. If one barrel of crude oil provides six million BTUs of energy, how many BTUs of energy will one liter of crude oil provide?

7. Fifty-eight thousand kilograms of solid waste is equivalent to how many metric tons?

8. Jonesville is rural community with a population of 8,000 homes. It gets electricity from a small, municipal coal-burning power plant just outside of town. The power plant’s capacity is rated at 20 megawatts with the average home consuming 10,000 kilowatt hours (kWh) of electricity a year. Residents of Jonesville pay the utility $0.12 per kWh. A group of entrepreneurs is suggesting that the residents support a measure to install 10 wind turbines on existing farmland. Each wind turbine is capable of producing 1.5 MW of electricity. The cost per wind turbine is $2.5 million dollars to purchase and operate for 20 years.

A. The existing power plant runs 8,000 hours per year. How many kWh of electricity is the current

plan capable of producing?

B. How many kWh of electricity do the residents of Jonesville consume in one year?

C. Assuming the population of Jonesville remains the same for the next 20 years, and that electricity consumption remains stable per household, what would be the cost (expressed in $ per kWh) of electricity to the residents over the next 20 years if the decided to go with wind turbines?

Sample Problem 1 A large, coal-fired electric power plant produces 12 million kilowatt-hours of electricity each day. Assume that an input of 10,000 BTUs of heat is required to produce an output of 1 kWh of electricity.

(a) Calculate the number of BTUs of heat needed to generate the electricity produced by the power plant each day.

(b) Calculate the number of pounds of coal consumed by the power plant each day, assuming that one pound of coal

yields 5,000 BTUs of heat.

(c) Calculate the number of pounds of sulfur released by the power plant each day, assuming that the coal

contains one percent sulfur by weight.

AP* Environmental Science Mastering the Math

Part I: Dimensional Analysis (aka Factor-Label or Unit Cancellation Method)

Where to start?

Step 1: Ask yourself, “What unit of measure do I need for my answer?”

Read part (a) again. You need to answer in units of “BTUs per day”. The word “per” is code for “divided by” or

“in the denominator”. Next, translate the words into math. So, “BTUs per day” becomes BTU . day

Consider this your end goal; it is how you must express your final answer. Step 2: Am I given any numbers that are paired with the units I seek? Not exactly! That would be WAY too easy. But you can identify a “bridge” of sorts that connects "BTU" and "day". You are given “power plant produces 12 million kilowatt-hours (12,000,000 kWh) of electricity each day” AND “10,000 BTU” of heat is required to produce an output of 1 kWh of electricity”. From this we can write two equivalent sets of conversion factors for each of these tidbits of valuable information.

12, 000, 000 kWh or 1 day as well as 1 kWh or 10, 000 BTU 1 day 12, 000, 000 kWh 10, 000 BTU 1 kWh

These are called conversion factors and they are your friends! Prepositions are also your friends since they link information together as in “pieces of candy” and “at 15 °F”. Your objective is to string the conversion factors together (keeping the numbers with the units) so that the unwanted units cancel out leaving you with the desired units for your answer. In our example the desired units are BTU . The numerator and denominator of a

day conversion factor represent the same quantity, such as 12 inches or 1 foot thus we are simply multiplying 1 foot 12 inches by “1”.

1 kWh

Sample Problem 1 A large, coal-fired electric power plant produces 12 million kilowatt-hours of electricity each day. Assume that an input of 10,000 BTUs of heat is required to produce an output of 1 kWh of electricity.

(a) Calculate the number of BTUs of heat needed to generate the electricity produced by the power plant each day.

(b) Calculate the number of pounds of coal consumed by the power plant each day, assuming that one pound of coal

yields 5,000 BTUs of heat. (Pick up where you left off! Let the problem lead you!)

(c) Calculate the number of pounds of sulfur released by the power plant each day, assuming that the coal

contains one percent sulfur by weight.

Step 3: Choose the conversion factors AND structure them so that you achieve your “end goal”. Remember we were asked to solve for “BTUs per day” which in “math speak” looks like units of BTU. day It there is a “trick” to this process, it involves choosing conversion factors and arranging them so that the unwanted units cancel out leaving only the desired unit(s) on your final answer! For our example, you want BTU in the numerator of your final answer along with days in the denominator. So, you need to get rid of or cancel the kWh. How?

12, 000, 000 kWh 1 day

and 10, 000 BTU make a nice pair since they result in the desired units of BTU . Yippee! day

Step 4: Solve it! Let’s revisit our sample problem: When you have cancelled out the units you don't want and are left only with the units you do want, then you know it's time to multiply all the numerators (top numbers) together, and divide by EACH of the bottom numbers! When setting up a string of conversion factors, it is often helpful to start at the end (units of the desired answer) and work backwards as explained and demonstrated on the screencast.

Sample Problem 2 The environmental impact of washing a load of dirty dishes in an electric dishwasher differs from that of washing them in a sink by hand. A comparison of the two methods may allow consumers to spend their money more wisely. Use the assumptions in the table below to perform the calculations that follow.

All the dishes fit into a single load.

The water entering both the water heater and the sink is at 50 °F. The water heater and the dishwasher are both 100% efficient. Washing the dishes by hand requires 20 gallons of water heated to 110 oF. In one complete cycle, the electric dishwasher uses 10 gallons of water heated to 140 oF and the dishwasher also uses 0.500 kilowatt-hour of electrical energy for its mechanical operations.

(a) A British thermal unit or BTU is the amount of energy needed to raise the temperature of one pound of water 1.0 °F. Additionally, one gallon of water has a mass of 8.0 pounds. Calculate the total energy used to wash a load of dishes using the dishwasher.

(b) One kilowatt-hour is equivalent to 3,400 BTUs and the cost of electricity is $0.11 per kWh. Calculate the energy in BTU used to heat the water for washing a load of dishes by hand.

(c) Calculate the cost of electricity for each dishwashing method given that one kilowatt-hour is equivalent to 3,400 BTUs and the cost of electricity is $0.11 per kWh.

Step 1: Ask yourself, “What unit of measure do I need for my answer?” Read part (a) again. The question asks you to calculate “total energy” per load, so you need to answer in units

of “BTU per load”. Translate that to math and you get BTU load

or simply BTU. Consider this your end goal; it is

how you must express your final answer for parts (a). Next, read part (b) again. The final answer to part (b) should also be reported in BTU

load or simply BTU.

Step 2: Am I given any numbers that are paired with the units I seek? Yes! (Remember, it is a legal maneuver to “flip” any of these conversion factors as long as you keep the appropriate number with the appropriate unit!)

10 gal H2O load and 8 gal H2O

1 lb H2O

and 1 BTU

1 lb H2O • 1 °F

and note the temperature change!

Yep! That’s TWO items in the denominator of one of the conversion factors, thus twice the cancelling fun. Step 3: Choose the conversion factors AND structure them so that you achieve your “end goal”. Ask yourself “What to flip and why flip at all?” Step 4: Solve it!

Sample Problem 2 The environmental impact of washing a load of dirty dishes in an electric dishwasher differs from that of washing them in a sink by hand. A comparison of the two methods may allow consumers to spend their money more wisely. Use the assumptions in the table below to perform the calculations that follow.

All the dishes fit into a single load.

The water entering both the water heater and the sink is at 50 °F. The water heater and the dishwasher are both 100% efficient. Washing the dishes by hand requires 20 gallons of water heated to 110 oF. In one complete cycle, the electric dishwasher uses 10 gallons of water heated to 140 oF and the dishwasher also uses 0.500 kilowatt-hour of electrical energy for its mechanical operations.

(a) A British thermal unit or BTU is the amount of energy needed to raise the temperature of one pound of water 1.0 °F. Additionally, one gallon of water has a mass of 8.0 pounds. Calculate the total energy used to wash a load of dishes using the dishwasher.

(b) Calculate the energy in BTU used to heat the water for washing a load of dishes by hand.

(c) Calculate the cost of electricity for each dishwashing method given that one kilowatt-hour is equivalent to 3,400 BTUs and the cost of electricity is $0.11 per kWh.

Part 2: Determining Energy Efficiency

Energy efficiency is simply the ratio of work output to work input. If the problem states that system is less than 100 % efficient, then the energy output must be divided by the stated efficiency to determine how much energy input is needed.

Percent Efficiency = Workout

Workin × 100%

Our previous sample problem made this easy on us by telling us the efficiency is 100%. Don’t always expect that since such machines do not exist! If a machine or process is 75% efficient then you simply multiply anything you calculate as being “perfect” by 0.75 effectively reducing it to only 75% rather than leaving it at the elusive 100% efficiency. Sample Problem 3 Answer the questions below regarding the heating of a house in the Midwestern United States. Use the assumptions in the table below to perform the calculations that follow.

The house has 2,000 square feet of living space.

80,000 BTUs of heat per square foot are required to heat the house for the winter.

Natural gas is available at a cost of $5.00 per thousand cubic feet.

One cubic foot of natural gas supplies 1,000 BTUs of heat energy.

The furnace in the house is 80 percent efficient.

(a) Calculate number of cubic feet of natural gas required to heat the house for one winter. Show all the steps of your calculations, including units.

(b) Calculate the cost of heating the house for one winter.

Part 3: Scientific Notation

Scientific notation is used to communicate extremely large numbers such as the speed of light or extremely small numbers such as the radius of a blood cell.

1. Converting decimal numbers LESS THAN ONE to Scientific Notation Example: Express the number 0.00234 in scientific notation.

• Place a decimal after the first nonzero number. We refer to this as the coefficient. Coefficients need to be between 1 and 9. The coefficient is then multiplied by ten raised to an exponent, 10exponent

• Determine the exponent on the “10” by counting the number of places you move the decimal point.

If you move the decimal to the right, the exponent will be negative. If you move the decimal point to the left, the exponent will be positive.

Negative exponents tell us how many times the number has been divided by 10 Positive exponents tell us how many times the number has been multiplied by 10 So, to express the number 0.00234 in scientific notation, we move the decimal 3 places to the right: 0.00234 to give 2.34 × 10-3

What does this really mean mathematically? 2.34 or 10 ×10 ×10

2.34

103

or 2.34 1, 000

or 2.34 × 10-3

Essentially, it means the number is small. How small? In the thousandths. Why do this? For years you’ve thought 0.00234 was a perfectly good number just the way it is. Why convert it to scientific notation? BECAUSE it allows us to focus on the “order of magnitude” of measurements or quantities rather than the coefficients. Compare 2.34 × 10−3 to 2.34 × 103

It’s not that the 2.34 is the most important part of the number—it’s that the number is in the thousandths (10−3) versus the thousands (103). So, 2.34 × 103 is SIX power of ten’s (10 × 10 × 10 × 10 × 10 × 10), that’s 106, or a million times larger! We say that 2.34 × 103 is six orders of magnitude greater than 2.34 × 10−3

2. Nuances of Adding and Subtracting Numbers Written in Scientific Notation First, make sure both numbers have the same exponent on the “× 10” part. It’s easiest to convert one number to the greater exponent:

5.2 × 103 + 3.6 × 104 becomes 0.52 × 104 + 3.6 × 104 or, you may prefer it stacked

Either way, (0.52 + 3.6) × 104 becomes 4.12 × 104 All done! Subtraction works the same way.

0.52 + 3.6 4.12

× 104

× 104

× 104

Sample Problem 4 Calculate the potential reduction in petroleum consumption in gallons of gasoline per year that could be achieved in the United States by introducing electric vehicles under the following assumptions:

• The mileage rate for the average car is 25 miles per gallon of gasoline. • The average car is driven 10,000 miles per year. • The United States has 150 million cars. • Ten percent of the US cars could be replaced with electric cars.

Start with the easy simplification & translate the numbers into scientific notation: 10% of 150 million cars = 15 million cars = 1.5 × 107 cars… now on to the dimensional analysis…

3. Nuances of Multiplying Numbers Written in Scientific Notation: This is much easier! Simply, multiply the coefficients and then add the exponents on the power of 10. (4 ×

10−2) × (2 × 1010) = (4 × 2) × 10(−2 + 10) becomes 8 × 10(−2 + 10) which simplifies to 8 × 108

Division works the same way EXCEPT you subtract the exponents on the power of 10. (4 × 10−2) ÷ (2 × 1010) = (4 ÷ 2) × 10(−2 − 10) becomes 2 × 10(−2 − 10) which simplifies to 2 × 10−12

Part 4: Population Growth Rate Demography is the study of the characteristics of human populations, such as size, growth, density, distribution, and other vital statistics. In demography, population growth is used informally for the more specific term population growth rate (PGR), and is often used to refer specifically to the growth of the human population of the world. The most common way to express population growth is as a percentage, not as a rate. First, we calculate the change in a population using the difference between the crude birth and death rates. What are those? The crude birth rate (CBR) is the total number of births per year per 1,000 people and the crude death rate (CDR) is the total number of deaths per year per 1,000 people. In the formula below we simply divide by ten to report the PGR as a percentage. (We wouldn’t need to divide by 10 if the CBR & CDR were expressed per “100” instead of per 1,000.)

PGR (as a percentage) = CBR − CDR 10

Part 5: The Rule of 70

The Rule of 70 is used to calculate the time required for a doubling of a population based upon population growth rate, PGR, expressed as a percentage. Resist the urge to express the growth percentage as a decimal value, leave it as a percentage! The Rule of 70 is mathematically expressed as:

timedoubling = 70 PGR (expressed as a percentage)

How long will it take for a city with an annual population growth rate of 5% to double its population?

time 70 = 70 = 14 years

doubling PGR (expressed as a percentage) 5%

How long will it take for the same city if the growth rate were 7%?

time 70 = 70 = 10 years

doubling PGR (expressed as a percentage) 7% Sample Problem 5 The fictional country Industria is tracking its population data. In 1855, the first year vital statistics were reported for the country, the population was 1.6 million, with a crude birth rate of 43 per 1,000. At that time the population of Industria was growing quite slowly, because of the high death rate of 41 per 1,000. In 1875 the population began to grow very rapidly as the birth rate remained at the 1855 level. While the crude death rate dropped dramatically to 20 per 1,000. Population growth continued to increase in the small country into the late 1800’s, even though birth rates began to decline slowly.

In 1895 the crude birth rate had dropped to 37, and the crude death rate to 12 per 1,000. A complete census was also conducted and revealed that the population of Industria had grown to 2.5 million. By 1950 population growth gradually began to decline as the death rate remained at its 1895 level, while the birth rate continued to decline to 22 per 1,000. In 1977 vital statistics revealed that the death rate was 10 per 1,000, and that population growth had slowed even more to an annual rate of 0.4%. By 1990 Industria had reduced its birth rate to that of its now constant, low death rate, and the population transition was complete.

(a) Calculate the annual growth rate of Industria in 1950.

(b) Calculate the birth rate in Industria in 1977.

(c) Assume the population of Industria continues to maintain the population growth rate recorded for the country in 1895. Determine the year in which the expected size of the population will have quadrupled.

Sample Problem 6 Between 1950 and 2000, global meat production increased from 52 billion kilograms to 240 billion kilograms. During this period, the global human population increased from 2.6 billion to 6.0 billion.

(a) Calculate the per capita meat production in 1950 and in 2000. (b) Calculate the change in global per capita meat production during this 50-year period. Express your answer as a

percentage.

Part 6: Per Capita

Per Capita is a Latin term that translates into "by head," basically meaning "average per person." Per capita can even the place of saying "per person" in any number of statistical observances. In most cases the term is used in relation to economic data or reporting, but can also be used in most any other occurrence of population description.

Now let’s see if you can put this newly acquired set of problem-solving skills to work!

Sample Problem 7 West Fremont is a community consisting of 3,000 homes. A small coal-burning power plant currently supplies electricity for the town. The capacity of the power plant is 12 megawatts (MW) and the average household consumes 8,000 kilowatt hours (kWh) of electrical energy each year. The price paid to the electric utility by West Fremont residents for the energy is $0.10 per kWh. The town leaders are considering a plan, the West Fremont Wind Project (WFWP), to generate their own electricity using 10 wind turbines that would be located on the wooded ridges surrounding the town. Each wind turbine would have a capacity of 1.2 MW and each would cost the town $3 million to purchase, finance, and operate for 25 years.

(a) Assuming that the existing power plant can operate at full capacity for 8,000 hrs/yr, how many kWh of electricity can be produced by the plant in a year?

(b) At the current rate of electricity energy per household, how many kWh of energy does the community consume in one year?

(c) Assuming that the electrical energy needs of the community do not change during the 25-year lifetime of the wind turbines, what would be the cost to the community of the electricity supplied by the WFWP over 25 years? Express your answer in dollars/kWh.

Sample Problem 8 The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current electric hot-water heater raises the water temperature to 140o F, which requires 0.20 kWh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute.

(a) Calculate the total amount of water that the family uses per year for taking showers.

(b) Calculate the annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute of the water used is from the hot-water heater.

(c) The family is considering replacing their current hot-water heater with a new energy-efficient hot-water heater that costs $1,000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover the $1,000 initial cost?