A biology laboratory is maintained at a constant temperature of 7.00ºC by an air conditioner, which is vented to the air outside. On a typical hot summer day, the outside temperature is 27.0ºC and the air-conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having a coefficient of performance (COP) equal to 40.0% of the COP of an ideal Carnot device. (a) At what rate does the air conditioner remove energy from the laboratory? (b) Calculate the power required for the work input. (c) Find the change in entropy of the Universe produced by the air conditioner in 1.00 h. (d) What If? The outside temperature increases to 32.0ºC. Find the fractional change in the COP of the air conditioner.
(a)
The rate of removal of energy by the air conditioner.
Answer to Problem 22.70AP
The rate of removal of energy by the air conditioner is
Explanation of Solution
Given info: The temperature of laboratory is
The formula for Carnot efficiency of cooling is,
Here,
Substitute
Solve the above expression for
The coefficient of performance at
Substitute
The rate of emission of energy outside is the sum of rate of removal of energy and input work required to do so.
Rearrange the above expression for
The formula to coefficient of performance is,
Here,
Substitute
Solve the above expression for
Substitute
Substitute
Conclusion:
Therefore, the rate of removal of energy by the air conditioner is
(b)
The power required for the input work.
Answer to Problem 22.70AP
The power required for the input work is
Explanation of Solution
Given info: The temperature of laboratory is
As calculated in equation (2) of the above part,
So the work input is
Conclusion:
Therefore, the work input required for the input work is
(c)
The entropy change of universe produced by air conditioner in
Answer to Problem 22.70AP
The entropy change of universe produced by the air conditioner in
Explanation of Solution
Given info: The temperature of laboratory is
The formula to calculate change in entropy is,
Substitute
Solve the above expression for
Conclusion:
Therefore, the entropy change of universe produced by the air conditioner in
(d)
The fractional change in
Answer to Problem 22.70AP
The fractional change in
Explanation of Solution
Given info: The temperature of laboratory is
The formula to calculate
Here,
Substitute
The formula for the percentage is,
Here,
Substitute
Conclusion:
Therefore, the fractional change in
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Chapter 22 Solutions
Physics For Scientists And Engineers, Technology Update, Loose-leaf Version
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