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
Want to see more full solutions like this?
Chapter 6 Solutions
Thermodynamics: An Engineering Approach
- A dealer advertises that he has just received a shipment of electric resistance heaters for residential buildings that have an efficiency of 100 percent. Assuming an indoor temperature of 21°C and outdoor temperature of 10°C, determine the second-law efficiency of these heaters.arrow_forwardAn inventor claims to have developed a heat engine that receives 700 kJ of heat from a source at 500 K and produces 300 kJ of net work while rejecting the waste heat to a sink at 290 K. Is this a reasonable claim? Why?arrow_forwardA Carnot heat engine operates between a source at 1000 K and a sink at 300 K. If the heat engine is supplied with heat at a rate of 800 kJ/min, determine the power output of this heat enginearrow_forward
- A heat pump is used to heat a house and maintain it at 24°C. On a winter day when the outdoor air temperature is –5°C, the house is estimated to lose heat at a rate of 80,000 kJ/h. Determine the minimum power required to operate this heat pump.arrow_forwardA heat engine working with a thermal efficiency of 35% receives 2 kW of heat from a furnace. The waste heat rejected from the engine isarrow_forwardA heat pump is used to maintain a house at T1°C by extracting heat from the outside air on a day when the outside air temperature is T2°C. The house is estimated to lose heat at a rate of Q kJ/h, and the heat pump consumes 5 kW of electric power when running. Is this heat pump powerful enough to dothe job?arrow_forward
- A steam power plant receives heat from a furnace at a rate of 280 GJ/h. Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is transferred to the cooling water at a rate of 165 GJ/h, determine the thermal efficiency of this power plant.arrow_forwardA heat engine operates between two reservoirs at 8000 C and 200 C. One-half of the work output of the engine is used to drive a Carnot heat pump that removes heat from the cold surroundings at 20 C and transfers heat to a house maintained at 220 C. If the house is losing heat at a rate of 62,000 kJ/h, determine the minimum rate of heat supply to the heat engine required to keep the house at 220 C.arrow_forwardDefine the thermal efficiency of a power plant, which is of primary interest in thermodynamicsarrow_forward
- A steam power plant receives heat from a furnace at a rate of 280 GJ/h. Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is transferred to the cooling water at a rate of 165 GJ/h, determine net power output.arrow_forwardDoes a refrigerator that has a higher COP necessarily have a higher second-law efficiency than one with a lower COP? Explain.arrow_forwardA Carnot heat engine receives heat from a reservoir at 900°C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27°C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at –5°C and transfers it to the same ambient air at 27°C. Determine the total rate of heat rejection to the ambient air.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY