Concept explainers
A Carnot heat pump is to be used to heat a house and maintain it at 25°C in winter. On a day when the average outdoor temperature remains at about 2°C, the house is estimated to lose heat at a rate of 55,000 kJ/h. If the heat pump consumes 4.8 kW of power while operating, determine (a) how long the heat pump ran on that day; (b) the total heating costs, assuming an average price of $0.11/kWh for electricity; and (c) the heating cost for the same day if resistance heating is used instead of a heat pump.
FIGURE P6–111
(a)
The actual running time of the heat pump in a day.
Answer to Problem 111P
The actual running time of the heat pump in a day is
Explanation of Solution
Determine the coefficient of performance of the Carnot heat pump depends on the temperature limits in the cycle.
Here, the temperature inside the house is
Determine the total amount of heat lost by the house.
Here, the rate of heat gain per unit degree is
Determine the work input of a Carnot heat pump.
Here the power input required by heat pump is
Determine amount of time the heat pump ran.
Here, the rate of work input of a Carnot heat pump is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the actual running time of the heat pump in a day is
(b)
The total heating cost that day.
Answer to Problem 111P
The total heating cost that day is
Explanation of Solution
Determine the total heating cost that day.
Conclusion:
Substitute
Thus, the total heating cost that day is
(c)
The amount of cost if resistance heating is used instead of heat pump.
Answer to Problem 111P
The amount of cost if resistance heating is used instead of heat pump is
Explanation of Solution
Determine the amount of cost if resistance heating is used instead of heat pump.
Conclusion:
Substitute
Thus, the amount of cost if resistance heating is used instead of heat pump is
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Chapter 6 Solutions
Thermodynamics: An Engineering Approach