Chapter 3 Energy Efficiency
Goals:
To define and calculate efficiency of an energy conversion deveice.
To understand and articulate the concept entropy
To understand and explain operating principles of a heat engine.
To calculate overall efficiency from step efficiencies.
3.1 Energy Conversion Devices
3.2 Efficiency of Energy Conversion Devices
3.3 Measuring Thermal Energy
3.4 Kelvin Scale
3.5 Heat Engines
3.6 The Carnot Efficiency
3.7 Entropy and Quality of Energy
3.8 Overall Efficiency
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3.1 Energy Conversion Devices
In the first lesson, we have seen that energy can be transformed from one form to another
and during this conversion, all the energy that we put into a device comes out. However,
all the energy that we put in may not come out in the desired form.
For example, we put in electrical energy into a bulb and the bulb produces light (which is
the desired form of out put from a bulb) but we also get heat from the bulb (undesired
form of energy from an electric bulb).
Light
Electrical
Energy
Heat
Therefore, energy flow into and out of any energy conversion device can be summarized
in the diagram below:
Energy
Energy Input
Useful Energy
Output
Conversion
Device
Energy Dissipated
to the Surroundings
Energy Flow Diagram for an Energy Conversion Device
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When all forms of energy coming out of an energy conversion device are added up, it
will be equal to the energy that is put into a device. Energy output must be equal to the
input. This means that energy can not be destroyed or created. It can only change its
form.
In the case of an electric bulb the electrical energy is converted to light and heat.
Light is useful form and heat is not desired from an electric bulb. This means that the all
the energy that is put in will come out, but all of it will not be in a useful form.
More Information
Say you go to the mall with $100 and you come back with only $10. You need to
account for the $90 that you spent. After thinking about it, you come up with the follow
list:

Gas $15

Sandwich, fries and Drink $8

Lost $5

New Clothes $62
So you spent $62 dollars on something useful, the clothes, but you spent additional
money for other things that were necessary for your trip.
3
Flash activity: Identify the useful energy output and undesirable energy
output in the energy conversion devices below:
First 2 Coulmns given – students must fill out last two columns. Can we do this the same
way as the Lawnmower exercise in Lesson 1??
Input
Chemical
Energy Converter
Lawn Mower
Useful Energy
Mechanical
Chemical
Automobile
Mechanical
Undesirable Energy
Thermal (heat) and radiation
(sound)
Thermal or heat (tail pipe) and
radiation (sound)
Heat (friction) – moving parts in
the engine, tires, etc.)
Electrical
Television
Electrical
Computer
Radiation (Sound
and Light)
Radiation (Sound
and Light)
Electrical (generator, dome
lights, flood lights)
Heat from circuits
Heat from circuits (electrons
moving through system) and
Mechanical (fan to cool)
Add a hint button to the “Undesirable energy column for each:
Lawnmower – Hint: How do you know the neighbor is mowing the lawn?
Automobile – Hint: Think about: Mufflers, tires and generator.
TV – Have you ever felt the back of your TV after it had been on for a few hours?
Computer: What’s in your tower and why?
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3.2 Efficiency of Energy Conversion Devices
Efficiency is the useful output of energy. To calculate efficiency the following formula
can be used:
Efficiency 
Useful Energy Output
Total Energy Input
Illustration
An electric motor consumes 100 watts (a joule per second (J/s)) of power to obtain 90
watts of mechanical power. Determine its efficiency.
Solution:
Input to the electric motor is in the form of electrical energy and the output is
mechanical energy.
Using the efficiency equation:
Motor Efficiency 
Mechanical power
90 W

 0.9
Electrical power 100 W
Or efficiency is 90%.
Want to see another example? (Give one more example like above in pop-up
textbox.) I will get this info.
Instead of example, Sarma wants cautionary note – wants it to have the yellow
caution tape in it.
Caution! This is a simple example because both variable are measured in Watts. If the
two variables were measured differently, you would need to convert them to equivalent
forms before performing the calculation.
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Vinit’s problems – 3-1
Example for equation 3.1
Illustration:
An electric motor consumes 100 watts (a joule per second (J/s)) of power to obtain 90
watts of mechanical power. Determine its efficiency?
Now lets see the solution............
Step 1: Input to the electric motor is in the form of electrical energy and the output is
mechanical energy. Using the given formula for efficiency
Efficiency
= Useful Energy Output
Total Energy Input
= 90 W
100 W
= 0.9
= 90 %
Why dont you give it a shot now....................
An electric motor consumes 92 watts (a joule per second (J/s)) of power to obtain 83
watts of mechanical power. Determine its efficiency?
Your Answer :
Submit your answ er
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Illustration 3-1 is a very simple case because both mechanical and electrical power is
given in Watts. Units of both the input and the output have to match.
Illustration 3-2
The United States Power plants consumed 39.5 quadrillion Btus of energy and
produced 3.675 trillion kWh of electricity. What is the average efficiency of the
power plants in the U.S.?
Useful Energy Output
Total Energy Input
Total Energy input = 39.5 x 10 15 Btus and the Useful energy output is 3.675 x 10 12
kWh. Recall that both units have to be the same. So we need to convert kWh into
Btus. Given that 1 kWh = 3412 Btus,
Efficiency 
3.675 1012 kWh 3412 Btus
Efficiency 

 0.3174 or 31.74%
39.5 1015 Btus
1 kWh
I need to find an example
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Vinit’s Problem 3-2
Another Example for equation 3.1
Illustration:
The United States power plants consumed 39.5 quadrillion Btus of energy and produced
3.675 trillion kWh of electricity. What is the average efficiency of the power plants in the
U.S.?
Now lets see the solution............
Step 1: To find the efficiency, both the units of input energy and the output energy have
to be same. So we need to convert kWh into Btus.
1 kWh
= 3412 Btus
Therefore 3.675 x10^12
kWh
= 3.675 x 10^12 kWh x 3412 Btus
1 kWh
= 12539.1 x 10^12 Btus
Step 2: Use the formula for efficiency.
Efficiency
= Useful Energy Output
Total Energy Input
= 12539 x 10^12 Btus
39.5 x 10^15 Btus
= 0.3174
= 31.74 %
Why dont you give it a shot now....................
The United States power plants consumed 37 quadrillion Btus of energy and produced 2
trillion kWh of electricity. What is the average efficiency of the power plants in the U.S.?
Your Answer :
Submit your answ er
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Energy efficiencies are not 100% and sometimes they are pretty low. The table belows
shows typical efficiencies of some of the devices that are used in day to day life.
Table 3-1 Typical Efficiencies of Some of the Commonly Used Devices
Device
Electric Motor
Home Gas furnace
Home Oil Furnace
Home Coal Stove
Steam Boiler in a Power Plant
Overall Power Plant
Automobile Engine
Electric Bulb
Incandescent
Fluorescent
Efficiency
90%
95%
80%
75%
90%
36%
25%
5%
20%
From our discussion on national and global energy usage patterns in Lesson 2, we have
seen that:

About 40% of the US energy is used in power generation

About 27% of the US energy is used for transportation.
Yet the energy efficiency of a power plant is about 35%, and the efficiency of
automobiles is about 25%. Thus, over 62% of the total primary energy in the U.S. is used
in relatively inefficient conversion processes.
Why power plant and automobile design engineers allowing this? Can they do better?
There are some natural limitations when converting energy from heat to work.
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3.3 Measuring Thermal Energy
Thermal energy is energy associated with random motion of molecules. It is indicated by
temperature which is the measure of the relative warmth or coolness of an object.
A temperature scale is determined by choosing two reference temperatures and dividing
the temperature difference between these two points into a certain number of degrees.
The two reference temperatures used for most common scales are the melting point of ice
and the boiling point of water.

On the Celsius temperature scale, or centigrade scale, the melting point is taken as
0°C and the boiling point as 100°C, and the difference between them is divided into
100 degrees.

On the Fahrenheit temperature scale, the melting point is taken as 32°F and the
boiling point as 212°F, with the difference between them equal to 180 degrees.
It is important to realize, however, that the temperature of a substance is not a measure of
its heat content, but rather, the average kinetic energy of its molecules resulting from
their motions.
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Below is a 6-ounce cup with hot water and 12 ounce cup hot water at the same
temperature.
1. Do they have the same heat content?
2. Do they have the same amount of energy?
Click the play button to obtain a magnified view of what is happening. Draw your
conclusions and then check your answer below.
Ok’d
Flash: Show 6 and a 12 ounce cups (clear would be good) with thermometers in them,
show close up of thermometer and temperature (same temperature). Then show close up
of each, with molecules. The 12 ounce cup should show a lot more molecules than the 6
ounce, though both should be moving around a bit.
Answer: They do not have the same heat content. Because they are at the same
temperature the average kinetic energy of the molecules is the same; however, the water
in 12 ounce cup has more molecules than the 6 ounce cup and thus has greater motions or
heat energy.
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3.4 Kelvin Scale
When water molecules freeze at 0°C, the molecules still have some energy compared to
ice at -50°C. In both cases, the molecules are not moving, so there is no heat energy.
So what is the temperature at which all the molecules absolutely have zero energy? A
temperature scale can be defined theoretically for which zero degree corresponds to zero
average kinetic energy. Such a point is called absolute zero, and such a scale is known as
an absolute temperature scale. At absolute zero, the molecules do not have any energy.
The Kelvin temperature scale is an absolute scale having degrees the same size as those
of the Celsius temperature scale. Therefore, all the temperature measurements related to
energy measurements must be made on Kelvin scale.
Combine thermometers with an animation. Press play and observe what happens:
Animation goes here:
Show ice – thermometers show
temperature for water freezing.
Place ice into a pan on the stove and it
melts – thermometers show temperature
for melting water.
Water in ban starts to boil –
thermometers show temperature for
boiling water.
http://www.weldbend.com/Image
s/Diagrams/Technical%20Diagra
ms/Temp.gif
Based
on your observations, answer the following questions:
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At what temperature does water freeze?
___ Kelvin ____ Celsius ____ Fahrenheit
At what temperature does ice melt?
___ Kelvin ____ Celsius ____ Fahrenheit
At what temperature does water boil?
___ Kelvin ____ Celsius ____ Fahrenheit
Ok:
Add pop-up “More Information” text box with the above screen:
You can convert a temperature in Celsius (c) to Kelvin (k) with this formula:
k = c + 273.15
You can also change a temperature in Kelvin to Celsius:
c = k - 273.15
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3.5 Heat Engines
Energy conversions occurring in an automobile are illustrated below:
Chemical
Energy
Thermal
Energy
Mechanical
Energy
Energy Conversions in an Automobile
Any device that converts Thermal energy into mechanical energy - such as automobiles
or power plants - is called a heat engine. In these devices, high temperature heat (thermal
energy) produced by burning a fuel is partly converted to mechanical energy to do work
and the rest is rejected into the atmosphere, typically as a low temperature exhaust.
Animate this – An animated version is on Athena in animations folder – but needs learner
controls
Need to emphasize that the
objective is to maximize Work to
increase efficiency.
If High T increases OR Low T
decreases, the efficiency increases
Energy Flow in a Heat Engine
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A general expression for the efficiency of a heat engine can be written as
Efficiency 
Work
Heat Energy hot
We know that all the energy that is put into the engine has to come out either as work or
waste heat. So work is equal to Heat at High temperature minus Heat rejected at Low
temperature. Therefore, this expression becomes
Efficiency 
QHot  QCold
QHot
Where, QHot = Heat input at high temperature and Qcold= Heat rejected at low
temperature. The symbol is often (Greek letter eta) used for efficiency this expression can
be rewritten as

 (%)  1 

QHot
QCold

 100

The above equation is multiplied by 100 to express the efficiency as percent.
French Engineer Sadi Carnot showed that the ratio of QHighT to QLowT must be the same as
the ratio of temperatures of high temperature heat and the rejected low temperature heat.
So this equation, also called “Carnot Efficiency,” can be simplified as:

  1 

TCold
THot

 100%

This is only equation in blackboard format
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3.6 The Carnot Efficiency
The Carnot Efficiency is the theoretical maximum efficiency one can get when the heat
engine is operating between two temperatures:

The temperature at which the high temperature reservoir operates (Thot).

The temperature at which the low temperature reservoir operates (Tcold).
In the case of an automobile, the two temperatures are:

The temperature of the combustion gases inside the engine (Thot).

The temperature at which the gases are exhausted from the engine (Tcold).
Can we show a car engine? Maybe animate it? YES Here’s one from
http://auto.howstuffworks.com/engine1.htm Can we develop something similar?
The following may be best explained via audio and narration: When the exhaust is leaves
the automobile at a higher temperature, it carries more energy out so that amount of
energy is not available to be converted to work (moving piston). Therefore, we can
conclude that the higher the Tcold, the lower the efficiency. Similarly, if the Thot is
increased by increasing the temperature of the combustion gases, we can get higher
efficiencies.
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Then, why should we operate the automobiles at low efficiencies?
It is not that we cannot achieve high temperatures, but we do not have the engine
materials that can withstand the high temperature. As a matter of fact, we do not let the
engine gases go the maximum that they can go even now and instead try to keep the
engine cool by circulating the coolant.
So we are taking the heat out of the gases (thus lowering the Thot) and making the engine
operate at cooler temperatures so that the engine is protected - but lowering the efficiency
of an automobile.
More Information: It’s like Taxes. The more money you earn (heat), the more money is
taxed (cold), leaving you with less money to take home (efficiency). However, if you
could earn more money (heat) and find a way to have less taxes taken out (better engine
material), you would have more money to take home (efficiency).
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Below are temperature ranges for the heat (hot) and exhaust (cold) of a car engine.
Using the scales above, enter several combinations of numbers for hot and cold, and
observe the graph: (wants it to be like home simulations)
Hot
Cold
Efficiency
Function of 2 Temperatures
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Based on your observations of the graph:
1.
2.
3.
4.
What happens as High T increases? Answer: Efficiency Increases
What happens as High T decreases? Answer: Efficiency decreases
What happens as Low T decreases? Answer: Efficiency increases
What happens as Low T increases? Answer: Efficiency decreases
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Illustration 3-3
For a coal-fired utility boiler, the temperature of high pressure steam would be
about 540°C and Tcold, the cooling tower water temperature would be about
20°C. Calculate the Carnot efficiency of the power plant?
Solution:
Carnot efficiency depends on high temperature and low temperatures between which
the heat engine operates. We are given both temperatures. However, the temperatures
need to be converted to Kelvin
Thot = 540°C+273 = 813 K
Tcold = 20°C + 273 = 293 K
 293 K 
Carnot Efficiency  1 
 100  64%
 813 K 
I need to find an example
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Vinit’s Problem 3-2
Example for equation 3.4
Illustration:
For a coal fired utility boiler, the temperature of high pressure steam would be about 540
degrees C and Tcold, the cooling tower water temperature would be about 20 degrees C.
Calculate the Carnot efficiency of the power plant?
The solution............
Step 1: We are given the high temperature and the low temperatures between which the
heat engine engine operates which is needed to calculate Carnot efficiency. To calculate,
Convert the temperatures to Kelvin.
Thot
= 540 degrees C + 273
= 813 K
Tcold
= 20 degrees C + 273
= 293 K
Step 2: Use the formula for Carnot efficiency.
Carnot Efficiency
=(1 - Thot) x 100
Tcold
=(1- 293 K) x 100
813 K
= 64%
Why dont you give it a shot now....................
For a coal fired utility boiler, the temperature of high pressure st
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3.7 Entropy and Quality of Energy
From the Carnot Efficiency formula, it can be inferred that a maximum of 64% of the
fuel energy can go to generation. To make the Carnot efficiency as high as possible,
either T hot should be increased or T cold (temperature of heat rejection) should be
decreased.
Let’s look at the Energy conversions in a power plant:
Schematic of
a Coal fired
Power Plant
Audio with animation: Coal or oil or gas has chemical energy stored in the chemical
bonds of the fuel. When the fuel is burned, the chemical bonds in the fuel are broken and
new bonds are formed releasing thermal energy . This thermal energy is transferred to
water that turns into high pressure, high temperature steam. The high pressure, high
temperature steam turns the turbine and converts the thermal energy into mechanical
energy. The steam after turning the turbine will still have some energy but not enough to
turn the turbine. The low pressure steam is condensed into water and the water is sent
22
back to the boiler. The turbine is connected to a generator and in the generator the
mechanical energy is converted into electricity by turning a conductor in a magnetic field.
23
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Video demo goes here – will record on 12/16/04
24
The basic energy conversions in the three main components in a power plant are shown
quantitatively in the image below:
(Can we make this a little bigger?)
Chemical Energy Input (100 BTU
Boiler
)
Thermal Energy (88 BTU
Turbine
)
Mech. Energy (36 BTU
Generator
Elec. Energy Output (10.26 Wh
)
)
Energy Conversions in a Power Plant
Audio with animation: Let’s say the boiler takes in 100 Btus of chemical energy and
produces 88 Btus of useful thermal energy. The 88 Btus of thermal energy from the boiler
goes into the turbine and 36 btus equivalent of mechanical energy (movement of turbine
blades) is produced. This 36 Btus of mechanical energy is transferred to the generator
which converts it to 10.26 Wh of electrical energy.
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Same exercise as with car engine (hot, cold and graph), only use these ranges
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NEW PAGE
3.8 Overall Efficiency
Using the energy efficiency concept we can calculate the component and overall
efficiency.
Overall Efficiency 
Electrical Energy Output
Chemical Energy Input
Here the electrical energy is given in Wh and Chemical Energy in Btus. So Wh can be
converted to Btus knowing that there are 3.412 Wh in a Btu.
Overall Efficiency 
10.26 Wh
3.412 Btus

100 Btus
1 Wh

35Btus
100  35%
100 Btus
Conversionof Wh to Btus
This overall efficiency can also be expressed in steps as follows
 Thermal Energy   Mechanical Energy   Electrical Energy 
Overall Efficiency  



 Chemical Energy   Thermal Energy   Mechanical Energy 
Efficiency of the Boiler
Efficiency of theTurbine
Efficiency of theGenerator
Overall Efficiency  Boiler   Turbine  Generator 
Applying this method to the above power plant example
,
88 Btus 36 Btus 35 Btus
Overall Efficiency 


100 Btus 88 Btus 36 Btus
 0.88  0.41 0.97
 0.35 or 35%
27
It can be seen that the overall efficiency of a system is equal to the product of efficiencies
of the individual subsystems or processes. What is the implication of this?
We have been looking at the efficiencies of an automobile or a power plant individually.
But when the entire chain of energy transformations from the moment the coal is brought
out to the surface to the moment the electricity turns into its final form, true overall
efficiency of the energy utilization will be revealed. The final form at home could be light
from a bulb or sound from a stereo. The series of steps are
Need an image of this from Sarma: Production of coaltransportation to power plant 
Electricity Generation  Transmission of electricity  Conversion of electricity into
light
If efficiency of each step is known, we can calculate the overall efficiency of production
of light from coal in the ground. The table below illustrates the calculation of overall
efficiency of a light bulb.
Overall Efficiency of a Light Bulb
Step
Step Efficiency
Cumulative Efficiency or
Overall Efficiency
Extraction of coal
96%
96%
Transportation
98%
94% (0.96 X 0.98)*100
Electricity Generation
35%
33% (0.96 X 0.98 X 0.38)
Transmission of Electricity
95%
31%
Incandescent bulb
5%
1.5%
Fluorescent
20%
6.2%
Lighting
AUDIO: It can be seen that to generate 6.2 units of light from a relatively efficient
fluorescent bulb, we used up 100 units of energy from coal from the ground. This also
means that during various conversion steps 93.8 units of energy is dissipated into the
environment.
28
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A similar analysis on Automobile shown in Figure 3-7 and Table 3-3 shows that only
about 10% of the energy in the crude oil in the ground is in fact turned into mechanical
energy moving people.
Figure – missing from word document but in printed document – need to get from Sarma:
Titled “Overall Automobile Efficiency”- shows sequence of steps in converting chemical
energy in crude oil in the ground to movement of a car:
Production of crude  Transportation to refinery  Refining  Transportation of
gasoline  Engine  Transmission  Movement
Figure
Overall Efficiency of an Automobile
Step
Step Efficiency
Overall or Cumulative
Efficiency
Production of Crude
96%
96%
Refining
87%
84%
Transportation
97%
81%
Engine
25%
20%
Transmission
50%
10%
Perhaps audio to explain the above more fully??
30
OMIT ALL OF FOLLOWING - NOT IN ONLINE LESSON
BUT There is a crossword puzzle at the very end…
Selected References:
Hinrichs, R. A., “Energy,” Saunders College Publishers, Philadelphia, PA, 1992.
Aubrecht, G. L., “Energy,” Prentice Hall, Inc., Englewood Cliffs, NJ, 1995.
Fay, J.A. and Golomb, D. S., “Energy and the Environment,” Oxford University Press,
New York, NY, 2002.
Christensen, J. W., “Global Science: Energy Resources Environment”, 4th edition,
Kendall/Hunt Publishing Company, Dubuque, IA, 1996.
Questions for Review and Discussion
1. A heat engine has Carnot efficiency of 30%. Useful output from the engine
is 1000J. How much heat is wasted?
2. How can we improve the Carnot efficiency of a heat engine by changing
the hot and cold reservoir temperatures?
3. Most of the energy conversion devices that we use in our day-to-day life
can be classified as Heat Engines. Give two examples
4. The following diagram shows the energy flow to and from a furnace.
Energy input is 30,000,000 cal
Coal furnace
Heat energy
Rejected though the tail
pipe = 29,045,000 J
Calculate is the efficiency of the furnace. You need show your work very clearly
to get complete credit
31
Multiple Choice Questions
1. Approximately what percentage of
electricity does an incandescent light
bulb convert into visible light?
a) 5
b) 20
c) 40
d) 90
2. The following step efficiencies apply
to the use of gasoline in a car: Crude
production: 96%, Refining 87%,
Transportation 97%, Engine
efficiency 25%. What is the total
efficiency of the process?
a) 40%
b) 30%
c) 20%
d) 50%
3. The flame temperature in an
automobile is 1,000 °C, and the
exhaust is emitted at 70 °C. What is
the Carnot efficiency?
a) 25%
b) 65%
c) 73%
d) 33%
4. If the energy input of a system is 50
calories and the output is 25 calories,
what is the system efficiency?
a) 100%
b) 50%
c) 200%
d) 25%
5. Heat engines are inefficient because
the energy conversion is
a) From low entropy to high
entropy
b) From high entropy to low
entropy
c) From low temperature to
high temperature
d) From high temperature to
low temperature
6. Automobile engine efficiency
increases in
a) Summer
b) Winter
7. The useful output from a heat
engine is 238 cal. The energy
that is wasted is 5667 J? What
is the Carnot efficiency of the
engine?
a) 4%
b) 15%
c) 17.6%
d) none of the above
8. Three energy conversion
processes take place in
succession. The first has an
efficiency of 50%, the second is
40% efficient, and the third
5%. What is the overall
efficiency (%) of the entire
process? (2 points)
a) 10
b) 40
c) 50
d) 5
9.The turbine is the _______
efficient component in a power
plant
a) Least
b) Highest
10. The flame temperature in an
automobile is 1652 °F, and the
exhaust is emitted at 212 °F.
What is the Carnot efficiency?
a) 88.8%
b) 87.2%
c) 68.2%
d) 25%
32
11. The function of a generator in
a power plant is to convert
a) Chemical energy to
mechanical energy
b) Mechanical energy to
electrical energy
c) Thermal energy to
mechanical energy
d) None of the above
13. In a power
plant_________energy is
converted into_______energy.
a) Chemical, Mechanical
b) Chemical, Electrical
c) Mechanical, Electrical
d) Mechanical, Thermal
14. Which of the following devices
is least energy efficient?
a) Power plant
b) Electric motor
c) Light bulb
12. Which of these is False (2
points)
a)
Efficiency 
b)
Efficiency 
wastedE  usefulE
c)
Efficiency 
wastedE  usefulE
d)
Efficiency  1  wastedE  usefulE
usefulE
TotalE
Total  wastedE
usefulE
15. Most energy conversion
process produce----------- as by
product
a) Light
b) Heat
c) Sound
d) Motion
usefulE
33
Energy Basics Review Puzzle
1
3
2
4
5
6
7
8
9
10
11
12
Across
1. Conversion of chemical energy to this
form is notoriously inefficient.
3. This law states that we cannot create
or destroy energy
7. Temperature is a measure of this form
of energy
12. This source of energy supplies most
of the US energy needs
Down
2. This primary source is used for most
of the electricity generated in this
country
9. Rate at which energy is spent
4. Second largest primary source for
electricity generation
10. Ability to do work
5. Measure of disorder
11. Useful energy divided by the total
energy is called
6. Most households use this fuel for
home heating
8. The form of energy in gasoline
34