 # 1. Consider three reservoirs that are TH = 473.2 K, TL = 293.2 K an...

## Question

1. Consider three reservoirs that are TH = 473.2 K, TL = 293.2 K and T1 = 277.2 K. A Carnot heat engine can be reversed and used as either a heat pump or a refrigerator. In the case of a heat pump the heat flow to the higher temperature reservoir is the desired output and it is used to heat a room or building. In the case of the refrigerator the desired energy flow is the heat in from a region to be cooled. For the heat pump or refrigerator, the work input is provided by electricity. For this information answer the following questions:

a) Calculate the Carnot Efficiency of a heat engine that operates between TH and TL
b) A room is maintained at a constant temperature of 20 C and has a heat loss of 20,000 W. Consider this room for a period of 3 hours. The surroundings are at a temperature of Ti. In one option the room is heated using resistive heaters that are operated with electricity.
b1) Determine the electrical energy input to these heaters.
b2) Determine the efficiency of this heating system.
b3) Determine the entropy production for this this heating system. In this case you should include the entropy production of the heat loss process to Ti.
b4) The cost of electricity is \$0.237/kWh. What is the cost to heat the room for 3 hours?
c) For the same conditions described in part b, consider using a Carnot heat pump to supply the heat to the room. The low temperature reservoir in this case is T1 and the high temperature reservoir is the room temperature.
c1) Determine the electrical energy input to the Carnot heat pump.
c2) Determine the Coefficient of Performance (COP, the efficiency) of this heating system.
c3)Determine the entropy production for this this heating system. In this case you should include the entropy production of the heat loss process to Ti.
c4) The cost of electricity is \$0.237/kWh. What is the cost to heat the room for 3 hours?
d) Compare the performance of these two options. Which would you recommend? Why?
e) A region is to be cooled to a temperature of 277 K using a Carnot refrigerator. The heat that must be removed is 15,000 W. The heat rejected from the refrigerator is to a heat reservoir at TH. Consider the cooling for a period of 3 hours.
e1) Determine the electrical energy input to the Carnot refrigerator.
e2) Determine the Coefficient of Performance (COP, the efficiency) of this cooling system.
e3) Determine the entropy production for this this cooling system. In this case you should include the entropy production of the heat loss process from 277 K and to TH.
e4) The cost of electricity is \$0.237/kWh. What is the cost to cool the room for 3 hours?
f) A region is to be cooled to a temperature of 277 K using a heat powered Carnot refrigerator. The heat that must be removed is 15,000 W. The heat rejected from the refrigerator is to a heat reservoir at TL The heat input to this device is from a reservoir at TH. This is a Carnot model of an absorber refrigeration system. In it a Carnot heat engine operates between reservoirs at TH and TL The work output from this Carnot heat engine is the input to a Carnot refrigerator that operates between Ti and TL. Consider the cooling for a period of 3 hours.
f1) Determine the heat energy input to this Carnot refrigerator.
f2) Determine the Coefficient of Performance (COP, the efficiency) of this cooling system.
f3) Determine the entropy production for this this cooling system. In this case you should include the entropy production of the heat loss process from T1, TL and TH.
f4) The cost of the fuel to operate this system is \$0.075/kWh. What is the cost to cool the room for 3 hours?
g) Compare options e and f. Which would you recommend? Why? In problem 2, consider the source of electricity is a green source, such as solar photovoltaic or wind energy.

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