Heat Gain in a Fridge Experiment

[Jacob87411]

The following is an experiment I have to do:

Using a thermometer, measure the temperature of the main food compartment of your refrigerator, and check if it is between 1 and 4°C. Also, measure the temperature of the freezer compartment, and check if it is at the recommended value of -18°C. Using a timer (or watch) and a thermometer, conduct the following experiment to determine the rate of heat gain of your refrigerator. First make sure that the door of the refrigerator is not opened for at least a few hours so that steady operating conditions are established. Start the timer when the refrigerator stops running and measure the time Dt1 it stays off before it kicks in. Then measure the time Dt2 it stays on. Noting that the heat removed during Dt2 is equal to the heat gain of the refrigerator during Dt1 + Dt2 and using the power consumed by the refrigerator when it is running, determine the average rate of heat gain for your refrigerator, in W. Take the COP (coefficient of performance) of your refrigerator to be 1.3 if it is not available.
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I'm a little confused...So is the temperature change over t1+t2 equal to the heat gain? and then to find the average do I divide it by the time?

 

[marcusl]

No, the heat gain Pg is related to the temperature difference from outside to inside, across the insulating walls. If Ta is room temperature,
Q = (Ta - Tm) * A1 / R1 + (Ta + T2) * A2 / R2
where A1,A2 are the surface areas of the main,freezer compartments and R1,R2 are the mean surface resistivities or "R-values" of the corresponding insulating walls.

You don't need to use any of that, however, nor do you really need to know the temperatures of the compartments. You know (or will look up) the power consumption when the motor is running. The fraction of electrical power converted to heat power is found by dividing by COP, then multiply that by the duty cycle Dt2/(Dt1 + Dt2) to find the average heat power gain. Does that make sense?

 

[HoanCai]

Where does a thermometer come into place in this experiment then?