 A household refrigerator with a coefficient of performance of 1.2 removes heat from the refrigerated space at a rate of 60 kilojoules per minute. Determined first, the electrical power consumed by the refrigerator, and then the rate of heat transfer rejected to the kitchen air. After that, I want to know what is the theoretical maximum coefficient of performance that could occur if the refrigerator was operating between temperatures of 2 degrees Celsius and 22 degrees Celsius. While I recognize from the problem statement that I have a refrigeration cycle, I am consuming work to move heat transfer in a way that it would not naturally be driven from a cool refrigerated space to a warmer kitchen environment. I know that the high temperature side, which is the kitchen air, is 22 degrees Celsius, and I know that the inside of the refrigerator is about 2 degrees Celsius. So you can think of the low temperature side as being the refrigerator box itself, and the high temperature side as being the ambient kitchen air. The refrigeration cycle sits on the back of the device and pushes heat from the inside of the refrigerator to the kitchen air. I know that the coefficient of performance of this system is 1.2, and because it's operating in a cooling mode, that's going to be a COPR, because the cooling side of it is the side that I care about. Remember, I could take the same cycle and stick it out my patio door and make it operate as a heating system. I mean if the door of the fridge were open and it were taking up the entire patio door and the inside section of the fridge were pointed out and the back of the fridge were pointed into my kitchen, I mean theoretically it is operating as a heating device. It is pulling heat out of the outside air, pushing it into my kitchen. Granted, it's a terrible heater, but it is a heater. Also, with a coefficient of performance of 1.2, it's also a terrible fridge, but that's besides the point. I know that my coefficient of performance of a refrigeration cycle operating in refrigerating mode is the proportion of heat transferred in to the network in, and I know that it is removing heat from the refrigerated space at a rate of 60 kJ per minute. So that's giving me Q.in. The first thing I asked was the electric power consumed by the refrigerator. So that's asking for network in. To figure that out, I can take Q.in divided by COPR. That number again was 60 kJ per minute, and my COPR was 1.2. I didn't ask for a specific unit in this example problem, but let's say that I wanted to know the electrical power in kilowatts. Well, a kilowatt is a kilojoule per second, so I have to convert from seconds to minute. There are one minute in 60 seconds. So if I take 60 divided by 60 and take that result, which is 1 divided by 1.2, I will get my electrical power, which is 0.833 kilowatts. The next question asks, what is the rate of heat transferred to the kitchen air? Well, if I'm pulling in electrical power at a rate of 0.83 kilowatts, and I'm pulling in heat at a rate of 60 kJ per minute, and the only place that that can go is heat transfer out, then my heat transfer out is going to be the network in plus the Q.in. That comes from an energy balance on the kitchen refrigerator itself. I didn't ask for a unit again, so just to be antagonistic, let's say that I wanted to know the rate of heat transferred to the kitchen air at a rate of kJ per minute. So now I have to take our shiny new kilowatts and convert that back into kJ per minute. A kilowatt is a kJ per second, and there are 60 seconds in one minute, then I add 60 to that number, and I get 110. The last thing I asked for was the theoretical maximum coefficient of performance that could occur if this refrigerator was acting between a 2-degree refrigerated space, so TL is 2 degrees, and a 22-degree Celsius kitchen, so TH is 22 degrees. Well, we can use that equation we came up with earlier, COPRmax, which comes from when we treat the refrigeration cycle as a Carnot refrigerator, is going to be 1 over TH over TL minus 1. So we're plugging in 22 degrees Celsius for TH, again we have to convert that to Kelvin, and 2 degrees Celsius refrigerated space, and we get a theoretical maximum of 13.75. So the theoretical maximum coefficient of performance that could occur if a perfect device were operating between these two temperatures is 13.758. Because our actual COP is less than the theoretical maximum, that means that our device is possible, we can also conclude that there are a lot of opportunities for improvement. This is not a very good refrigeration system.