You place your lunch leftovers in the refrigerator. Suppose the refrigerator nee

Question

You place your lunch leftovers in the refrigerator. Suppose the refrigerator needs to remove 2.1860E+4 J of thermal energy from your lunch to cool it to the temperature of the inside of the refrigerator. In the meantime, this means the refrigerator produces 2.9176E+4 J of thermal energy that it expels into the kitchen as a result. What is the total work done by the compressor motor in the refrigerator? (Ignore any thermal loses due to friction in the motor.)

What is the Coefficient of Performance for the refrigerator? Y

our refrigerator actually acts like a heater in your kitchen. Suppose you have a small electric space heater that has a power output of 2.7kW. How long would this heater have to run to produce the same amount of heat as the refrigerator produced while cooling your leftovers?

It takes electricity to run the motor on the refrigerator. If your cost of electricity is 7 cents per kilowatt*hour, how much does it cost (in cents - do not enter units) to cool your lunch down?

Explanation / Answer

Here, low temp body is the refrig and its contents, the high temp body is the room, and the work done W is supplied to the compressor.
So the question says that (refer the image again) Q2 is 2.186E3 J, and Q1 is 2.9176E4 J. W is to be calculated.
From the Law of Conservation of Energy, Q1 = Q2 + W
or 29176=21860+W or W = 7316 J

Coefficient of Performance, or CoP = (Desired Effect)/(Work Input Required)
Here the desired effect is to cool the lunch ie remove 21860 J from the system. The work input to be provided is already calculated above ie W=7316 J
CoP=21860/7316 = 2.99

Output of heater = 2.7kW = 2700W = 2700 J/sec
Heat expelled by refrigerator = 29176 J
Time taken by heater = (Total heat to be generated = Heat expelled by the refrig)/(Heat expelled in one second) = 29176/2700 = 10.81 sec

Energy used, E = Work input = 7316 J
Cost per unit = 7c/kWh = 7c/3600000J (because 1kWh = 3600000J) or 0.00000194444 c/J
Total cost = (Cost per unit)*(No of Units) = 0.00000194444*7316 = 0.014225556 cents

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