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Chapter 7: Thermal and Energy Systems
243
A university's campus has 20,000 computers with cathode6ray tube monitors that
are powered up even when the computer is not being used. This type of monitor is
relatively inefficient, and it draws more power than a flat panel display. (a) If each
cathode6ray tube monitor draws 0.1 kW of power over the course of a year, how much
energy has been consumed? Express your answer in the conventional units of kW ⋅ h
for electricity. (b) At the cost of 12¢ per kW ⋅ h, how much does it cost the university
each year to keep these monitors powered up? (c) On average, a computer monitor that
has the automatic sleep feature enabled will consume 72% less energy than one that is
continually powered. What is the cost savings associated with enabling this feature on
all of the university's computers?
Approach:
A year has (365 days)(24 h/day) = 8670 h. Power is the rate of energy consumption, so the
Solution:
(a) From Equation (7.5), the energy consumption for one computer during the year is:
Discussion:
The full cost of powering all the monitors is an upper bound since they are all powered all
Chapter 7: Thermal and Energy Systems
244
When a desktop personal computer is operating, its power supply is able to convert
only about 65% of the supplied electrical power into the direct6current electricity that
the computer's internal electronic components require. The remainder of the energy is
mostly lost as heat. On average, each of the estimated 233 million personal computers
in the United States consumes 300 kW ⋅ h of energy each year. (a) If the efficiency of
the power supply could be increased to 80% by using a new type of power supply that
is under development (a so6called resonance6based switching6mode system), how
much energy could be saved each year? Express your answer in the conventional units
of kW ⋅ h for electricity. (b) The United States produced 4.1 trillion kW ⋅ h of electrical
energy in 2014. By what percentage would the nation's electricity needs decrease? (c)
At the cost of 12¢ per kW ⋅ h, what would the cost savings be?
Approach:
A computer presently consumes 300 kW ⋅ h of energy, but is able to utilize only 65%. With
Solution:
(a) With the current design of power supply, the computer uses only 65% of the energy
that is consumed:
8
0
.
rather than the present value of 300 kW ⋅ h. For 233 million computers, the energy savings
is:
(
)
(
)
hkW 243.75hkW 30010233
6
⋅−⋅×=W
= 1.311× 10
10
kW ⋅ h
Energy savings: 1.311× 10
10
kW ⋅ h
(b) In terms of the electrical generation capacity, the reduction is:
10.3111
10
⋅×
hkW
(c) The cost savings is:
10
Chapter 7: Thermal and Energy Systems
245
Discussion:
These are very rough estimations since the number of computers and the energy usage per
Chapter 7: Thermal and Energy Systems
246
Suppose that the new type of computer power supply described in P7.31 costs an
additional $5. (a) At the cost of 12¢ per kW ⋅ h, after what period of time would the cost
savings in electricity offset the power supply's added cost? (b) How often do you
estimate that individuals and companies generally upgrade their desktop personal
computers? (c) From an economic standpoint, what recommendation would you make
regarding the new type of power supply if you worked for a computer manufacturer?
Approach:
Solution:
(a) With the current design of power supply, the computer uses only 65% of the energy
that is consumed:
Discussion:
Chapter 7: Thermal and Energy Systems
247
A natural6gas6fired electrical power plant produces an output of 750 MW. By using
a typical efficiency from Table 7.6 and neglecting the small amount of power drawn by
the pump, calculate the rates at which: (a) Heat is supplied to the water/steam in the
steam generator. (b) Waste heat is spent into the river adjacent to the power plant.
Approach:
From Table 7.6, typical fossil fuel power plant efficiencies are in the range 30–40%, so use
Solution:
(a) With W
t
and Q
sg
denoting the amounts of work and heat per unit time (power), the heat
rate supplied to the boiler by burning fuel is:
MW 507
Discussion:
These heat flow estimates are only nominal values. The actual heat supplied to the
Chapter 7: Thermal and Energy Systems
248
For the plant in P7.33, 25,000 gal/s of water flow in the river adjacent to the power
plant. The river is used as the source of cooling water for the condenser. Considering
the heat transferred from the power plant to the river each second and the specific heat
of water, by what amount does the temperature of the river rise as it passes the power
plant? The density and specific heat of water are listed in Tables 6.1 and 7.4.
Approach:
Solution:
Discussion:
Chapter 7: Thermal and Energy Systems
249
Your school’s engineering library just received a set of 1000 new books, and they
have been delivered to the first floor of the library. Your group has been commissioned
to place the books on the appropriate shelves in the library. Estimate how much work is
done by your group to move the books to the proper shelf location. Next, estimate how
much internal energy was used by your group members to accomplish this task (i.e.,
how many calories were burned). Finally, using the first law of thermodynamics and
assuming other sources of energy loss are negligible, calculate the average change in
internal temperature experienced by your group members.
Notes to instructors
Clearly, there is no single correct solution to this problem, as it depends upon the
assumptions each group makes and how many group members they have. It also depends
upon the parameters of their home campus engineering library and what assumptions they
make about where the books have to be moved from and to. Regardless, you should still see
Approach:
In order to get an idea for how to approximate the amount of work done, the energy
exerted, and the average change in internal temperature of all the group members some
We next make assumptions about how the books are initially arranged and then moved to
their final destinations. Using the Engineering section of the Library at the home institution
250
1.125m high resulting in a total change in height or >h of 0.825m. Equation (7.4) is then
used to calculate the amount of work done transporting the books from the original
destination to the book stacks. Once the amount of work is calculated, we use the
conversion factor of 1J = 0.239 Cal to find the number of calories burned.
Another important assumption is that only the work done on the books will be considered,
Ckg
person
°
Solution:
The total work required to lift one of the books to the stacks is found using Equation (7.4),
m
Chapter 7: Thermal and Energy Systems
251
© 2017 Cengage Learning
®
. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
TcmQ
personperson
=
( )
T
Ckg
J
kgJ
°
=3470731044
CT
°
=
004.0
Total work done = 5220 J
Total calories burned = 1248 Cal
Average change in internal temperature = 0.004˚C
Discussion:
Given our assumptions, which limited the work calculation to only consider the change in
vertical height of the books, these answers are reasonable. The positive change in internal
Chapter 7: Thermal and Energy Systems
252
Your group has been tasked by university administration to develop upper6 and
lower6bound estimates of how much energy could be stored by taking advantage of the
foot traffic on your main campus on a weekday during the academic year. Provide clear
support for your answer, including:
• The assumptions made regarding the foot traffic (e.g., location, volume of
traffic, etc.)
• A description of what method(s) you plan to use to harness the foot traffic
energy
• A clear set of calculations and a discussion of the reasonableness of your
estimated bounds.
Notes to instructors
Clearly, there is no single correct solution to this problem, as it depends upon the
assumptions each group makes. It also depends upon the parameters of their home campus
and how they define the “campus”, and what assumptions they make about what a typical
weekday looks like on campus. Regardless, you should still see a clear description of their
Chapter 7: Thermal and Energy Systems
253
Your group has been contracted to perform a feasibility study on the use of solar
energy to power appliances or other personal electronics. You are asked to choose one
commonly used appliance or electronic consumer product (excluding a light bulb or
smart phone) that is used frequently or runs continuously throughout an entire day. You
are then asked to design a power supply system that would allow for continuous use of
your appliance or product using the minimum number of solar panels and batteries.
Determine the specifications for your solar panels, batteries, and any other components
you will need. Provide clear support for any assumptions you are making about the
power consumption of your appliance or product, including what kind of current it
requires. Show all calculations that you make to support and validate your conclusions.
As part of your discussion, also address the feasibility of scaling your solution up to
providing power for 1000 of the same appliances or products for commercial or
industrial purposes, including what barriers may exist for such scaling.
Your group should start with the following assumptions:
• This system will be used year6round within 100 km of your university and will have
to accommodate the appropriate exposure to the sun in this region.
• Any excess power that is generated and not able to be stored in the batteries or used
immediately by your appliance or product will be lost in the form of heat.
• Any battery used in your design will supply its specified voltage for the specified
number of amp6hours.
• Any connections between components are appropriately rated and have zero energy
loss.
Notes to instructors
Obviously, there is no single correct solution to this problem, as it depends upon the
assumptions each group makes, the appliance or personal electronic device they choose,
and the characteristic climate of their campus and region. While Chapter 7 of the text
includes some material on solar power generation (Example 7.11), the groups will most
likely need to do some additional research into power storage and power supply. You
should see a clear description of their approach, including their set of assumptions, a
Chapter 7: Thermal and Energy Systems
254
