1). I am a solar cell designer and made a cell with an efficiency
of 25%. The solar power on it is 1,000. W/m2.
(A) I find that I can use electricity from the cell to heat 15,000.
grams of water from 25oC to 99oC in one hour. What
is the surface area of the panel? (Specific heat of water is exactly 1
cal/gm/oC)
(B) What is the new surface area of the panel if in one hour energy
from it is able to heat 15,000 grams of water from 25oC to 100.oC
and then vaporize half of the water? (Latent heat of vaporization of water
is 540. cal/gm)
2). I am doing a remodeling job at home which requires electrical wiring. I am using a copper wire with a diameter of 2.00 mm and 250. feet long. The electrical resistivity of copper is 1.72x10-8W-m. However I find that this wire is too small (in cross sectional area of course) for what I need. I need the resistance to be less than 0.0400 W. How many such copper wires do I have to connect in parallel to satisfy my requirement?
3). Given the equation for resistance as a function of resistivity,
length and cross-sectional area of a conductor is
R = r L / A
(A) Write a plain English sentence describing the relationship among
resistance, length, and cross-sectional area of a conductor. Do not use
words like "divided by" or "over" or "numerator" or denominator" in your
sentence. In other words, we want a scientific description of this relationship.
(B) Which of the terms in the above equation are/is intrinsic properties
and which are/is extrinsic properties?
(C) Calculate the cost of a LONG copper wire with a 0.500 inch diameter
to be used to carry current from Brown’s Ferry Nuclear Power Plant to Auburn
(a distance of 215 miles) if the density of copper is 555 pounds per cubic
foot and the price of copper is $1.60 per pound. There are 5,280 feet in
one mile and the resistivity of copper is 1.72x10-8W-m.
4). I have a piece of radiator material with an unknown emissivity
value. However, I do know that at 700. K, its radiation loss rate is 1.09
x 104 W/m2.
(A) What is its emissivity?
(B) What is its radiation loss rate at 900. K?
(C) However much energy can be dissipated from one side of a panel
with an area measuring 2.00m by 3.00m in one day at 900. K?
5). The R-value of a certain thickness of fiberglass is found
to be 3.40 m2K/W.
(A) What is the R-value in units of ft2Fohr/Btu?
Use dimensional analysis and show all your work.
(B) If the k-value of fiberglass is 0.0470 W/m-K, what is the thickness
of this fiberglass in inches? Show all your work.
(C) Is the k-value an intrinsic or extrinsic property of fiberglass?
Is the R-value an intrinsic or extrinsic property of fiberglass?
6). I am a farmer who lives in a very remote area where I have
no city water and no electricity from Alabama Power Company. I have a well
for all my water supply. I use a motor to operate a well pump and I use
a solar photovoltaic panel to generate the electricity for the motor. The
pump is rated at 2.00 HP (needs 2.00 HP of electricity from the solar panel
to operate) and it is 90.0% efficient in pumping water. My solar cells
are 10.0% efficient and provide sufficient power to operate the pump when
the power density of the sun is exactly at 500 W/m2.
(A) What is the size of my solar panel?
(B) If my pump runs at 120.V, how much current does it need?
(C) As I mentioned, my pump is 90.0% efficient in pumping water and
my well is 100. m deep, how many kilograms of water can it pump up in exactly
1 hour? (You may like to know that potential energy of a substance is related
to mgh, mass times gravitational constant times height)
7). I am an engineer working for Toyota to develop electric cars
driven solely by batteries. I have twenty 12.0V batteries in the car and
each battery has a 100.A-h rating. In my experiments on the test track,
I found that my range is 120. miles on the highway if the car is driven
at a constant speed of 60.0 mph.
(A) How much energy is stored in my twenty batteries? (I will accept
any energy unit)
(B) At 60.0 mph, how long will the batteries last?
(C) What is the power (in unit of kW) drawn by my motor when I run
my car at 60.0 mph?
(D) However, the range dropped to 100. miles if the speed is at 70.0
mph. What is the power (in unit of kW) drawn by my motor when I run my
car at 70.0 mph?
(E) If my motor runs at 20.0 kW at 80.0 mph, what is the range at 80.0
mph?
8). I am very energy conscious and I build my house with very
well insulated walls. My walls have an insulating brick (2" thick) on the
outside with a 6" thick fiberglass insulation and then a 1" thick sheetrock.
(A)What is the effective R-value of the wall?
(B) The winter temperature outside is 0oC and I want to
maintain my inside temperature at 23oC. The total wall area
is 5.0x104 sq. ft. What is the minimum
power rating of my heater (in units of Watts) if the only heat loss is
through my walls?
9). In a home energy system design, it is necessary to remove
1.00 x 105 W of waste power using a 10m
x 2.0m radiator panel. I find that at when the power going to the panel
is 1.00 x 105 W, the panel is at a temperature
of 648 K.
(A) What is its emissivity?
(B) What will the panel temperature be if the power to the panel is
2.00 x 105 W?
10). Note: material in this problem not included on 1999 final exam.You are very energy conscious and you use energy efficient double pane windows in your home. One of your windows measure 2.0m by 2.0m. It has two panes of energy efficient glass (5.0mm thick each) with a thermal conductivity of 0.2 W/m-K. The two panes are separated by a 10.mm gap giving a convection heat transfer coefficient h of 5 W/m2-K. If the amount of heat flow through this particular window measures 100W, what is the temperature difference between the outside and the inside?
11). I have a piece of radiator material with an unknown emissivity value. However, I do know that at 700. K, its radiation loss rate is 10,890 W/m2. (a) What is its emissivity? (b) What is its radiative power density at 900. K? (c) However much energy can a panel with an area measuring 2.00m x 3.00m dissipate in one day at 900. K?
12). I am a hydroelectric power generator designer living in Idaho. In one of my projects, the water flow rate in my hydroelectric generator is 1.00 x 105 kg/second. The water enters the generator at a velocity of 10.0 m/s and my generator is 50.0% efficient with a output rating of 500. kW (kilowatt). What is the exit velocity of my water? (Kinetic energy is 0.5mv2)
13). I am doing a remodeling job at home which requires electrical wiring. I am using a copper wire with a diameter of 1.0mm and 100. feet long. Unfortunately, the job requires 150. feet of wire and the only other wire I have is 1.4mm diameter aluminum wire. If I connect the two types of wires end to end to form the long wire that I need, what is the resistance? (Room temperature resistivity of copper is 1.72x10-8 W-m and that of aluminum is 2.63x10-8 W-m)
14). There is an unknown electrical conducting cable which has an electrical resistance of 10.0 W at 100.oC and 11.0 W at 200.oC, what is its temperature dependent coefficient of resistance (ao)?
15). The table below gives the (Alabama Power) power consumption
rate at three-hour intervals for Dr. Baird's house in the summer for one
day (midnight to midnight). Alabama Power has a program to encourage power
usage at night where the rate is $0.08/kW-hr from 6 am to 9 pm everyday
and $0.04/kW-hr from 9 pm to 6 am. How much does Alabama Power charge Dr.
Baird for the 24-hour period?
|
|
Consumption (kW) |
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| Midnight - 3am |
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| 3 am - 6 am |
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| 6 am - 9 am |
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| 9 am - noon |
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| noon - 3 pm |
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| 3 pm - 6 pm |
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| 6 pm - 9 pm |
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| 9 pm - midnight |
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16). I have a natural gas burner which I use to heat a special oil mixture. This oil mixture has a specific heat of 3.00 cal/gmoC and I find that it takes 10.0 cubic feet of natural gas to heat 10.0 kg of this oil mixture from 25oC to 100.oC. What is the efficiency (in unit of %) of this burner?
17). I am an Alabama Power Company electrical engineer. My boss
asks me to design a cable made of copper (room temperature resistivity
of copper is 1.72x10-8 W-m)
to carry electricity from the power station to his private cottage. The
length of the cable is 10.0 km (10.0 kilometer) and its resistance must
not exceed 1.00 W for the entire length.
(A) If the cross section of the cable is a square, what is the size
of the side of the cable?
(B) Is this a maximum or minimum value (in other words, can the size
be larger or smaller than this value)?
(C) If I pass 1000. amps through this cable, what is the voltage drop
across it?
(D) Under the condition of passing 1000. amps through the cable, how
much power is generated in this cable?
(E) How much electrical energy would the cable consume under the 1000.
amps condition in one day?
18). I am building a house and I have decided to use aluminum as my wiring material. The resistivity of aluminum at exactly 0oC is 2.63x10-8 W-m. I have a segment of the wire which is rectangular in cross section (measuring 1.00 mm by 2.00 mm) and it is 100.0 m long. I find that when I pass 30.0 amps of electrical current through, the temperature increases to 100.oC. If the resistance temperature coefficient (ao) is 5.00 x10-3/oC, what is the resistance of the wire when it is carrying 30.0 amps?
19). I am a hydroelectric power generator designer living in
the state of Oregon. In one of my projects, the water flow rate in my hydroelectric
generator is 1.0x105 kg/second. The water
enters the generator at a velocity of 10.0 m/s and the water exits the
generator at a velocity of 5.00 m/s. The output power of my generator is
1.0x103 kW (kilowatt).
(A) What is the efficiency of my generator?
(B) If I work extremely hard and get the efficiency to 100.%, what
is the output power of my generator? (Assume all other conditions remain
unchanged).
20). I am remodeling my home and find that one section of my
electrical wiring has two different wires tied end to end. Evidently the
previous owner ran out of proper wires and was too cheap to buy more. The
total resistance of the long wire is 1.00 W.
One section of it is made of copper and it is 1.00 mm in diameter and 100.
feet long. The second section is made of aluminum and but it has a rectangular
cross section measuring 1.0 mm x 2.0 mm. (and that of aluminum is 2.63x10-8
W-m)
(a) What is the length of the aluminum section?
(b) If under operating condition, the voltage drop across the first
section (copper) is 1.0 V, what is the current throught the wire?
(c) If under operating condition, the voltage drop across the first
section (copper) is 1.0 V, what is the voltage drop across the aluminum
section?
(d) Under the conditions of (b) and (c) above, what is the heat generated
in the total wire?
21). I recently bought an electric car (powered solely by battery)
from Ford. It uses a single battery at 100. V and the battery is rated
at 50. A-h. According to Ford, the range of the vehicle is 200. miles if
it is driven at a constant speed of 30.0 mph (miles per hour).
(a) How much energy is stored in the battery?
(b) What is the power of the motor (in unit of Watts) when it is driven
at 30.0 mph?
(c) Unfortunately I have a slow leak (or drain) in the electrical circuit.
The current leak (or drain) is exactly 1 Ampere at all times. If I fully
charge my battery and then unplug and park it somewhere, how long does
it take to completely drain my battery?