Chapter 6: Problem 7
What are the characteristics of all heat engines?
Chapter 6: Problem 7
What are the characteristics of all heat engines?
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Get started for freeA heat pump with a COP of 3.2 is used to heat a perfectly sealed house (no air leaks). The entire mass within the house (air, furniture, etc.) is equivalent to \(1200 \mathrm{kg}\) of air. When running, the heat pump consumes electric power at a rate of \(5 \mathrm{kW}\). The temperature of the house was \(7^{\circ} \mathrm{C}\) when the heat pump was turned on. If heat transfer through the envelope of the house (walls, roof, etc.) is negligible, the length of time the heat pump must run to raise the temperature of the entire contents of the house to \(22^{\circ} \mathrm{C}\) is (a) \(13.5 \mathrm{min}\) (b) \(43.1 \mathrm{min}\) \((c) 138 \min\) \((d) 18.8 \mathrm{min}\) \((e) 808 \mathrm{min}\)
Cold water at \(10^{\circ} \mathrm{C}\) enters a water heater at the rate of \(0.02 \mathrm{m}^{3} / \mathrm{min}\) and leaves the water heater at \(50^{\circ} \mathrm{C}\). The water heater receives heat from a heat pump that receives heat from a heat source at \(0^{\circ} \mathrm{C}\). (a) Assuming the water to be an incompressible liquid that does not change phase during heat addition, determine the rate of heat supplied to the water, in \(\mathrm{kJ} / \mathrm{s}\) (b) Assuming the water heater acts as a heat sink having an average temperature of \(30^{\circ} \mathrm{C}\), determine the minimum power supplied to the heat pump, in \(\mathrm{kW}\)
It is commonly recommended that hot foods be cooled first to room temperature by simply waiting a while before they are put into the refrigerator to save energy. Despite this commonsense recommendation, a person keeps cooking a large pan of stew three times a week and putting the pan into the refrigerator while it is still hot, thinking that the money saved is probably too little. But he says he can be convinced if you can show that the money saved is significant. The average mass of the pan and its contents is 5 kg. The average temperature of the kitchen is \(23^{\circ} \mathrm{C},\) and the average temperature of the food is \(95^{\circ} \mathrm{C}\) when it is taken off the stove. The refrigerated space is maintained at \(3^{\circ} \mathrm{C}\), and the average specific heat of the food and the pan can be taken to be \(3.9 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C} .\) If the refrigerator has a coefficient of performance of 1.5 and the cost of electricity is 10 cents per \(\mathrm{kWh}\) determine how much this person will save a year by waiting
Somebody claims to have developed a new reversible heat-engine cycle that has the same theoretical efficiency as the Carnot cycle operating between the same temperature limits. Is this a reasonable claim?
What are the two statements known as the Carnot principles?
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