Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of 6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in dollars) between the refrigerators to freeze the water. Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would consume if it ran for 1 hour. Therefore, 1 kWh = 3.60x106 J, as evident in the following unit conversion: 1 kWh x 1000W J/s 3600s X X h(hour) KW W = 3,600,000 J Hint: The cost difference will be a very small amount. Enter your answer using three significant figures. Hint cost difference = $
Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of 6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in dollars) between the refrigerators to freeze the water. Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would consume if it ran for 1 hour. Therefore, 1 kWh = 3.60x106 J, as evident in the following unit conversion: 1 kWh x 1000W J/s 3600s X X h(hour) KW W = 3,600,000 J Hint: The cost difference will be a very small amount. Enter your answer using three significant figures. Hint cost difference = $
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
![EXERCISE
Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of
6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in
dollars) between the refrigerators to freeze the water.
Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would
consume if it ran for 1 hour. Therefore, 1 kWh = 3.60x106 J, as evident in the following unit conversion:
1 kWh x
1000W J/s 3600s
h(hour)
X
kW
W
X
= 3,600,000 J
Hint: The cost difference will be a very small amount. Enter your answer using three significant figures.
Hint
cost difference = $](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccae5729-7489-41ed-a32a-24cdd49b7598%2F41a2f083-96de-4472-a150-81c239ea7aa7%2Fqk1kteb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISE
Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of
6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in
dollars) between the refrigerators to freeze the water.
Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would
consume if it ran for 1 hour. Therefore, 1 kWh = 3.60x106 J, as evident in the following unit conversion:
1 kWh x
1000W J/s 3600s
h(hour)
X
kW
W
X
= 3,600,000 J
Hint: The cost difference will be a very small amount. Enter your answer using three significant figures.
Hint
cost difference = $
![Freezing Water
A certain refrigerator has a COP of 5.00. When the refrigerator is running, its power input is 500 W. A sample of water of
mass 700 and temperature 20.0°C is placed in the freezer compartment. How long does it take to freeze the water to ice
at 0°C? Assume all other parts of the refrigerator stay at the same temperature and there is no leakage of energy from the
exterior, so the operation of the refrigerator results only in energy being extracted from the water.
SOLUTION
Conceptualize Energy leaves the water, reducing
its temperature and then freezing it into ice. The time interval
required for this entire process is related to the rate at which energy is withdrawn from the water, which, in turn, is related
to the power input of the refrigerator.
Categorize We categorize this example as one that combines our understanding of temperature changes and phase
changes from Chapter 20 and our understanding of heat pumps from this chapter.
Analyze
Use the power rating of the refrigerator to find the time interval required for the freezing process to occur. (Use the
following as necessary: P and W.)
W
P =
At
The COP for a freezer is
Δt =
→ At =
COP = 1QcI/W = 1Qcl/ (P At)
Use Q = mcAT and Q = LAm to substitute the amount of energy IQ that must be extracted from the water of mass m.
(Use the following as necessary: L₁, Am, and AT.)
At =
W
P
mcAT +
At =
LAm
✓
P(COP)
Recognize that the amount of water that freezes is Am = -m because all the water freezes. (Use the following as
necessary: L₁, m, c and AT.)
- m( | CAT+L₁ | x )|
ΔΤ
P(COP)
Substitute numerical values to find the time interval. (Enter your answer in seconds. Assume the specific heat of water is
4,186 J/(kg . °C), and the latent heat of fusion of water is 3.33 x 105 J/kg.)
✓
S
Finalize In reality, the time interval for the water to freeze in a refrigerator is much longer than this, which suggests that
the assumptions of our model are not valid. Only a small part of the energy extracted from the refrigerator interior in a
given time interval comes from the water. What other sources of energy must be extracted by the refrigerator? (Select all
that apply.)
O Energy must also be extracted from the container in which the water is placed.
O Energy from the environment must be extracted into the refrigerator.
O Energy that continuously leaks into the interior must be extracted.
EXERCISE
Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of
6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in
dollars) between the refrigerators to freeze the water.
Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccae5729-7489-41ed-a32a-24cdd49b7598%2F41a2f083-96de-4472-a150-81c239ea7aa7%2Fgbi8uun_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Freezing Water
A certain refrigerator has a COP of 5.00. When the refrigerator is running, its power input is 500 W. A sample of water of
mass 700 and temperature 20.0°C is placed in the freezer compartment. How long does it take to freeze the water to ice
at 0°C? Assume all other parts of the refrigerator stay at the same temperature and there is no leakage of energy from the
exterior, so the operation of the refrigerator results only in energy being extracted from the water.
SOLUTION
Conceptualize Energy leaves the water, reducing
its temperature and then freezing it into ice. The time interval
required for this entire process is related to the rate at which energy is withdrawn from the water, which, in turn, is related
to the power input of the refrigerator.
Categorize We categorize this example as one that combines our understanding of temperature changes and phase
changes from Chapter 20 and our understanding of heat pumps from this chapter.
Analyze
Use the power rating of the refrigerator to find the time interval required for the freezing process to occur. (Use the
following as necessary: P and W.)
W
P =
At
The COP for a freezer is
Δt =
→ At =
COP = 1QcI/W = 1Qcl/ (P At)
Use Q = mcAT and Q = LAm to substitute the amount of energy IQ that must be extracted from the water of mass m.
(Use the following as necessary: L₁, Am, and AT.)
At =
W
P
mcAT +
At =
LAm
✓
P(COP)
Recognize that the amount of water that freezes is Am = -m because all the water freezes. (Use the following as
necessary: L₁, m, c and AT.)
- m( | CAT+L₁ | x )|
ΔΤ
P(COP)
Substitute numerical values to find the time interval. (Enter your answer in seconds. Assume the specific heat of water is
4,186 J/(kg . °C), and the latent heat of fusion of water is 3.33 x 105 J/kg.)
✓
S
Finalize In reality, the time interval for the water to freeze in a refrigerator is much longer than this, which suggests that
the assumptions of our model are not valid. Only a small part of the energy extracted from the refrigerator interior in a
given time interval comes from the water. What other sources of energy must be extracted by the refrigerator? (Select all
that apply.)
O Energy must also be extracted from the container in which the water is placed.
O Energy from the environment must be extracted into the refrigerator.
O Energy that continuously leaks into the interior must be extracted.
EXERCISE
Compare the cost to make 48 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of
6.00. Electricity costs $0.10 per kWh. Using the same assumptions given in the example, find the cost difference (in
dollars) between the refrigerators to freeze the water.
Note: A kilowatt-hour [kWh] is a unit of energy. It is the amount of energy an appliance rated at 1 kW (1000 W) would
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