Question 14 (a) An air conditioning system is used to cool a house during summer and maintain it at 18°C when the outdoor air temperature is 40°C. The house gains heat through the walls and the windows at a rate of 2000 kJ/min while the heat generated within the house from people, lights, and appliances amounts to 150 kJ/min. The second-law efficiency of this system is 40%. The price of the electricity is £0.2 per kWh. Determine i. the COP of this air conditioning system. [4] ii. the costs of electricity consumption per day. [£] [8] iii. the rate of heat rejection to the outdoor air by the system. [kJ/min] [3] (b) A heat engine receives heat from a heat source at 950°C at a rate of 1200 kJ/min and rejects heat at 80°C. The second law efficiency of this engine is 45%. The rejected heat is recovered by a central heating system. The entire power output of the heat engine is used to drive a heat pump to extract heat from outdoor air at 0°C to supply heat to the same central heating system at 80°C. Determine i) the thermal efficiency of the engine [%]. [2] ii) the maximum rate of heat received by the central heating system. [kJ/min] [8]
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The COP (Coefficient of Performance) of the air conditioning system is given by: COP = (cooling effect)/(work input) The cooling effect is the amount of heat removed from the house, which is equal to the heat gained through the walls and windows plus the heat Show more…
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A heat pump is a type of heater that uses electricity to do the work of pulling thermal energy out of cold air. This is done to heat a home in winter. It's a "backwards" engine where work is converted to heat, rather than the other way around. If the heat pump produces 1500 J of thermal energy for the home while wasting 500 J of energy, what is the efficiency of the heat pump? (enter the percentage as number between 0 and 100) How much electricity is input into the system during this process (in J)? If this is a Carnot heat engine, what happens to the entropy of this system during this process? a. it increase or stay the same b. it increase c. it decrease or stay the same d. it stays the same e. It decrease 200 J of the waste energy is thermal losses: the part of the heat pump that is outside gives off heat to the environment. When the heat pump is turned off, it is at temperature of 80 degrees C. Gradually, it is cooled by 0 degree C air to an equilibrium temperature of 3 degrees C. During this cooling process, which of the following happens to a system that includes the heat pump and the air? (mark all that are true): the system becomes more ordered the entropy of the system stays the same the system produces work the system becomes less able to produce usable work the system becomes more disordered
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20.42. Heat Pump. A heat pump is a heat engine run in reverse. In winter it pumps heat from the cold air outside into the warmer air inside the building, maintaining the building at a comfortable temperature. In summer it pumps heat from the cooler air inside the building to the warmer air outside, acting as an air conditioner. (a) If the outside temperature in winter is $-5.0^{\circ} \mathrm{C}$ and the inside temperature is $17.0^{\circ} \mathrm{C}$ , how many joules of heat will the heat pump deliver to the inside for each joule of electrical energy used to run the unit, assuming an ideal Carnot cycle? ( b) Suppose you have the option of using electrical resistance heating rather than a heat pump. How much electrical energy would you need in order to deliver the same amount of heat to the inside of the house as in part (a)? Consider a Carnot heat pump delivering heat to the inside of a house to maintain it at $68^{\circ} \mathrm{F}$ . Show that the beat pump delivers less heat for each joule of electrical energy used to operate the unit as the outside temperature decreases. Notice that this behavior is opposite to the dependence of the efficiency of a Carnot heat engine on the difference in the reservoir temperatures. Explain why this is so.
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