Question

You place your lunch leftovers in the refrigerator. Suppose the refrigerator needs to remove 1.5990E+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 2.1449E+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.) Tries 0/10 What is the Coefficient of Performance for the refrigerator? Tries 0/10 Your refrigerator actually acts like a heater in your kitchen. Suppose you have a small electric space heater that has a power output of 2kW. How long would this heater have to run to produce the same amount of heat as the refrigerator produced while cooling your leftovers? Tries 0/10 It takes electricity to run the motor on the refrigerator. If your cost of electricity is 8 cents per kilowatt*hour, how much does it cost (in cents - do not enter units) to cool your lunch down?

Answer 1

Suppose work W is supplied to the compressor of refrigerator.

Now, the refrigerator needs Q2 to remove thermal energy inside of the refrigerator.

And, Q2 = 15990 J

Energy produced by the refrigerator, Q1 = 21449 J

Now, from the Law of Conservation of Energy, Q1 = Q2 + W
=> 21449 = 15990 + W

=> W = 5459 J

So, work done by the compressor motor in the refrigerator = 5459 J

Coefficient of Performance, or CoP = (Desired Effect)/(Work Input Required)
Here the desired effect is to cool the lunch ie remove 15990 J from the system. The work input to be provided is already calculated above ie W = 5459 J

Therefore, coefficient of performance (CoP) = 15990 / 5459 = 2.929

Now, output of heater = 2.0 kW = 2000 W = 2000 J/sec
Heat expelled by refrigerator = 21449 J
Time taken by heater = (Total heat to be generated = Heat expelled by the refrig)/(Heat expelled in one second) = 21449 / 2000 = 10.72 s

Energy used, E = Work input = 5459 J
Cost per unit = 8c/kWh = 8c/3600000J (because 1kWh = 3600000J)
Total cost = (Cost per unit)*(No of Units) = (8c/3600000J)*5459 = 0.01213 cents