1. A Carnot heat engine operates between a heat source at 1200K and the environm

Question

1. A Carnot heat engine operates between a heat source at 1200K and the environment at 300 K. The net work produced by the engine is used to power a Carnot refrigerator which removes heat from a cooled space at -20?C at a rate of 320 kJ/min and rejects itto the same environment at 300 K. Determine: a) the net work supplied to the refrigerator, b) the heat supplied by the heat source of the heat engine, c) the heat rejected by the refrigerator, and d) the total heat rejected by the engine and the refrigerator


2. A heat pump supplies heat to a house at the rate of 150 000 kJ/ h when the house is maintained at 25?C. Over the period of one month, the heat pump operates for 120 hours to transfer energy from a heat source outside the house to the inside the house. Consider two different outside sources: the first is the outside air at -3?C and the second is a lake at 7?. If electricity costs $0.06/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.


3. Determine the entropy changes of the heat sources and heat sink in problem 1. That is, the heat source for the heat engine, the heat source of the refrigerator and the atmosphere to which the heat engine and the refrigerator reject heat 1. A Carnot heat engine operates between a heat source at 1200K and the environment at 300 K. The net work produced by the engine is used to power a Carnot refrigerator which removes heat from a cooled space at -20?C at a rate of 320 kJ/min and rejects itto the same environment at 300 K. Determine: a) the net work supplied to the refrigerator, b) the heat supplied by the heat source of the heat engine, c) the heat rejected by the refrigerator, and d) the total heat rejected by the engine and the refrigerator


2. A heat pump supplies heat to a house at the rate of 150 000 kJ/ h when the house is maintained at 25?C. Over the period of one month, the heat pump operates for 120 hours to transfer energy from a heat source outside the house to the inside the house. Consider two different outside sources: the first is the outside air at -3?C and the second is a lake at 7?. If electricity costs $0.06/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.


3. Determine the entropy changes of the heat sources and heat sink in problem 1. That is, the heat source for the heat engine, the heat source of the refrigerator and the atmosphere to which the heat engine and the refrigerator reject heat

Explanation / Answer

COP = 1 / ( 300 K) / (253 K)-1 =6.12

Then power input to the refrigerator becomes in

W net = 320 kJ/min / 6.12 = 52.28kJ/min

which is equal to the power output of the heat engine, Wnet, out

The thermal efficiency of the Carnot heat engine is determined from

=1- 300/1200=0.75

. Then the rate of heat input to this heat engine is determined from the definition of thermal efficiency to be

=52.28kJ /0.75=69.70kJ / min

The total rate of heat rejection to the ambient air is the sum of the heat rejected by the heat engine (QL, HE) and the heat discarded by the refrigerator (QH,R),

Q H= 69.70 -52.28 =17.42kJ/min

Qh=320+52.28=372.28kJ/min

Q Ambient = 372.28kJ +17.42kJ =389.7kJ / s

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