Question

You place your lunch leftovers in the refrigerator. Suppose the refrigerator needs to remove 2.4280E+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 3.2787E+4 J of thermal energy that it expels into the kitchen as a result.

a.) What is the total work done by the compressor motor in the refrigerator? (Ignore any thermal loses due to friction in the motor.)

b.)What is the Coefficient of Performance for the refrigerator?

c.)Your 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?

d.)It takes electricity to run the motor on the refrigerator. If your cost of electricity is 11 cents per kilowatt*hour, how much does it cost (in cents - do not enter units) to cool your lunch down?

Answer 1

a)Workdone by the compressor,

W = Q_hot - Q_cold

= 3.2787*10^4 - 2.4280*10^4

= 8407 J <<<<<<<<<-----------------Answer

b) COP = Q_cold/Workdone

= 2.4280*10^4/8407

= 2.890 <<<<<<<<<-----------------Answer

c)

Power = Q_hot/time taken

time taken = Q_hot/power

= 3.2787*10^4/(2.7*10^3)

= 12.1 s <<<<<<<---------Answer

d) Workodne by the motor = 8407 J

= 8407/(3.6*10^6) kWh

= 0.002335 kWh

so, cost = 0.002335*11

= 0.02568 cents <<<<<<<---------Answer