Solved Problem 5.1 - Reversible Home Air Conditioner and Hot Water Heater
Recall
Problem
4.12
in which we evaluated the following
proposed heat pump system designed for summertime hot water heating
and space cooling.
Under
the conditions shown in the diagram we determined that the
Coefficient of Performance of the hot water heater (COP
HW
)
was 4.41, and that of the space cooling air conditioner (COP
AC
)
was 3.41. Assuming that this system is required to maintain the home
air at 20°C and the hot water at 50°C, we wish to determine the
maximum possible theoretical Coefficients of Performance that could
be obtained under these conditions.
a) Draw a diagram representing the heat pump system showing the flow of energy and source and sink temperatures and determine the following:
b) the maximum possible Coefficient of Performance of a hot water heater (COP HW ) that could be obtained by a reversible heat pump,
c) the maximum possible Coefficient of Performance of a space cooling air conditioner (COP AC ) that could be obtained by a reversible heat pump.
d) Comparing the actual Coefficients of Performance shown above to those of the reversible heat pump determine if the actual heat pump shown above is feasible. State the reasons for your conclusion.
Derive all equations used starting from the basic
definition of COP HW
and COP AC
and the Carnot
relations for the ratio of heats of a heat
pump.
Solution: For a), b), and c) we need to reduce the system complexity shown above to an energy flow diagram showing only the basic requirements - cool the air to 20°C and heat the water to 50°C. Given the temperature if the heat source (20°C) and the heat sink (50°C) we can evaluate the respective reversible Coefficients of Performance.
For question d) we use the accumulated knowledge that the conditions for thermal and mechanical reversibility are so difficult to realize that no practical heat pump or heat engine can attain more than 50% to 60% of the equivalent reversible (Carnot) performance. Thus comparing the actual to the reversible Coefficients of Performance we obtain:
Engineering Thermodynamics by Israel
Urieli
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