> gif 'bjbj .P&&iiiii}}}}TT}B%%%%%{B}B}B}B}B}B}B$D\GlBiBii%%ByyyFi%i%{By{ByyN=A%b}6o?0gBB0B?GG`AGiAy".SBBjBG& /: Energy Calculations Tutorial
Every AP Environmental Science Exam has one calculation problem in the free response section. In addition to population calculations, you may be confronted by energy calculations. It is very important for you to know how to set up these types of problems. The method that I will show you here is called the Factor-Label Method.
Lets start with a ridiculous problem no you wont be required on the APES Exam to figure out how much money a farmer made on selling canaries, but the steps are the same, when we do a real problem. Well just change the word canary to joule, well change pigs to kilowatts, and so on.
Problem: A farmer started with 5 goats. She traded all of her goats for sheep at an exchange rate of 3 sheep for 1 goat. She then traded her sheep for pigs at a rate of 1 sheep for 2 pigs. Next, she traded her pigs for canaries. For every 3 pigs, she received 27 canaries. She then sold all of the canaries for a rate of $3.25 per canary. How much money did the farmer make on her canaries?
Step 1: Write an equal sign.
=
Step 2: Ask yourself, what units do I want to end up in? Pigs? Canaries? Sheep? Nope, I want to end up in dollars. So put the dollar sign to the right of the equal sign. It will look like this now:
= $
Step 3: Now ask yourself, what did the problem start me off with? Did the farmer start with canaries? Pigs? Nope, she started with 5 goats. So, way to the left of the equal sign, put 5 goats over 1. It will look like this now:
5 goats = $
1
Step 4: See the word goats above? You have to get rid of that word because you want to be in dollars when you finish. So put the word goats in a fraction so that it will cancel with the goats in the first factor. All factors get multiplied. It will look like this now:
5 goats x _______ = $
1 goats
Step 5: Now ask yourself, What do I know about goats? Do I know something about goats and canaries? Do I know something about goats and sheep? Nope. I do know that the farmer traded his goats for sheep, at a rate of 3 sheep for 1 goat. At this point, put a 1 in front of goat and put 3 sheep as the numerator. Notice the word goats cancel. It will look like this:
5 goats x 3 sheep = $
1 1 goats
Step 6: Now you are in sheep. You need to get rid of sheep. Where will you put it in the next factor? It should now look like this:
5 goats x 3 sheep x _______ = $
1 1 goats sheep
Step 7: What do you know about his trading sheep? It should look like this:
5 goats x 3 sheep x __2 pigs_ = $
1 1 goats 1 sheep
Step 8: Now get rid of pigs
5 goats x 3 sheep x __2 pigs_ x 27 canaries = $
1 1 goats 1 sheep 3 pigs
Step 9: Youre almost done. Now you can get rid of the canaries. Remember from the problem that the farmer received $ 3.25 for each canary. Remember to put canary in the denominator to cancel, leaving only one unit left dollars.
5 goats x 3 sheep x __2 pigs_ x 27 canaries x _$ 3.25_ = $
1 1 goats 1 sheep 3 pigs 1 canary
Step 10: You are now in $. That is what you want to be in. Now, stop and do the math.
= $ 877.50
Like measuring length, there are a variety of ways to measure energy. A few examples:
BTU (British Thermal Units) amount of energy required to raise one pound of water by one degree Fahrenheit
Quad one quadrillion BTU
calories the amount of energy it takes to raise one gram of water by one degree Celsius (SI system)
Calorie 1000 calories
Joule small unit of energy in SI system
Watts measure of power defined as joules per second (SI system)
Area (square feet) space to be heated/cooled/powered
Degree days (DD) Computed by taking the average temperature (F) for the day and subtracting it from 65F if it is positive, they are heating degree days, if it is negative they are cooling degree days.
You also may need to remember the following prefixes:
PrefixKilo-Mega-Giga-Terra-Multiply by10001,000,0001 x 1091 x 1012
Energy Problem Set #1
Use the Factor-Label Method to solve the following problems:
1) A large, natural gas-fired electrical power facility produces 15 million kilowatt-hours of electricity each day it operates. The power plant requires an input of 13,000 BTUs of heat to produce 1 kilowatt-hour of electricity. One cubic foot of natural gas supplies 1,000 BTUs of heat energy.
Showing all steps in your calculations, determine the
(i) BTUs of heat needed to generate the electricity produced by the power plant in 24 hours.
(ii) Cubic feet of natural gas consumed by the power plant each hour.
Note: Begin this problem by stating the information that is provided to you in a restatement. This will get rid of a lot of the words and allow you to just focus on the facts needed to solve the problem. Show work on separate paper as need.
Work at the next question you will see one just like it on the next test!!!!!!!
2) A large, coal fired electric power plant produces 18 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 kilowatt-hour of electricity.
Showing all steps in your calculations, determine the number of
BTUs of heat needed to generate the electricity produced by the power plant each day.
Pounds of coal consumed by the power plant each day, assuming that one pound of coal yields 5,000 BTUs of heat.
Pounds of sulfur released by the power plant each day, assuming that the coal contains one percent sulfur by weight.
Energy Problem Set #1 Answers
Note: Begin this problem by stating the information that is provided to you in a restatement. This will get rid of a lot of the words and allow you to just focus on the facts needed to solve the problem.
Restatement:
Gas-fired electrical power plant
15,000,000 kW-h of electricity every 24 hours (1 day)
Plant requires 13,000 BTUs of heat to produce 1 kW-h of electricity
1 ft3 of natural gas supplies 1000 BTUs of heat energy
(i). Calculate BTUs of heat needed to generate electricity produced in 24 hours.
Start with an equal sign
=
Next, write down the units you want to be in
= BTUs
Next, what did they give you to start with, or what were you limited to? The answer to this question is 15 million kW-h every 24 hours (1 day).
1.5 x 107 kWh = BTUs
24 hours (1 day)
Note: We are now in kW-h and we have to end up in BTUs. Was there any information regarding kW-h and BTUs? The answer is yes. 13,000 BTUs are required for every 1kW-h.
1.5 x 107 kW-h x 1.3 x 104 BTUs = BTUs
day 1 kW-h
At this point your in BTUs. That is what you want to be in. So stop and do the calculations.
1.95 x 1011 BTUS per day
(ii) Calculate the number of cubic feet of natural gas consumed by the power plant each hour.
This time, I am just going to set up the problem without walking you though each step.
1.95 x 1011 BTUs x __1 ft3 natural gas x 1 day = ft3 natural gas/hour
1 day 1,000 BTUs 24 hours
= 8.1 x 106 ft3 natural gas/hour
Now, take out a couple of sheets of paper and go back to the question. The important thing is to be able to do all parts of this question correctly. If you have to peek back at the answers, thats OK for now. Remember, the answers to the essays go far beyond what most students can do under limited time conditions. What you want to work for is getting most of the material that I provide you, but dont stress if you dont get it all.
Question # 2: Work at this one!!!!!!!!
1.8 x107 kWH x 1.0 x 104 BTUs = 1.8 x 1011 BTUs/day
day kWH
b. 1.8 x 1011 BTUs x ___1lb coal____ = 3.6 x 107 lbs coal/day
day 5.0x103 BTUs
3.6 x 107 lbs coal x 0.01 lb sulfur = 3.6 x 105 lbs sulfur/day
day 1lb coal
A
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