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A Carnot engine operating in reverse as a heat pump moves heat from a cold reservoir at 7°C to a warmer one at 22°C.
a. What is the efficiency of a Carnot engine operating between these two temperatures?
b. If the Carnot heat pump releases 250 J of heat into the higher-temperature reservoir in each cycle, how much work must be provided in each cycle ?
c. How much heat is removed from the 7°C reservoir in each cycle?
d. The performance of a refrigerator or heat pump is described by a “coefficient of performance” defined as K = Qc/W. What is the coefficient of performance for our Carnot heat pump?
e. Are the temperatures used in this example appropriate to the application of a heat pump for home heating? Explain.
(a)
The efficiency of the Carnot engine.
Answer to Problem 3SP
The efficiency of the Carnot engine is
Explanation of Solution
Given info:
Temperature of hot reservoir is
Write an expression to calculate the efficiency.
Here,
Substitute
Thus, the efficiency of the Carnot engine is
Conclusion:
The efficiency of the Carnot engine is
(b)
The work provided in each cycle.
Answer to Problem 3SP
The work provided in each cycle is
Explanation of Solution
Given info:
Heat released to hot reservoir is
Write an expression for work provided in each cycle.
Here,
Substitute
Thus, work provided in each cycle is
Conclusion:
The work provided in each cycle is
(c)
The heat released from cold reservoir.
Answer to Problem 3SP
The heat released from cold reservoir is
Explanation of Solution
Write an expression for heat released from cold reservoir.
Here,
Substitute
Thus, the heat released from cold reservoir is
Conclusion:
The heat released from cold reservoir is
(d)
The coefficient of performance of the heat pump.
Answer to Problem 3SP
The coefficient of performance of the heat pump is
Explanation of Solution
Write an expression for coefficient of performance of the heat pump.
Here,
Substitute
Thus, the coefficient of performance of the heat pump is
Conclusion:
The coefficient of performance of the heat pump is
(e)
The possibility of application of the heat pump for home heating.
Answer to Problem 3SP
Yes, the heat pump can be used for home heating.
Explanation of Solution
For home heating only moderate energy range is required. That will be sufficient to increase the temperature of home slightly. Here for working of the pump, only moderate range of energy is required.
Since the energy required is moderate, the energy provided by the heat pump will be adequate. The energy release will be less compared to the energy required to run the heat pump.
Conclusion:
Yes, the heat pump can be used for home heating.
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Chapter 11 Solutions
Physics of Everyday Phenomena
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