Question

Using a timer (or watch) and a thermometer, conduct this 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 to make sure that steady operating conditions are established. Start the timer when the refrigerator stops running, and measure the time \(\Delta t_{1}\) it stays off before it kicks in. Then measure the time \(\Delta t_{2}\) it stays on. Noting that the heat removed during \(\Delta t_{2}\) is equal to the heat gain of the refrigerator during \(\Delta t_{1}+\Delta t_{2}\) and using the power consumed by the refrigerator when it is running, determine the average rate of heat gain for your refrigerator, in watts. Take the COP (coefficient of performance) of your refrigerator to be \(1.3\) if it is not available. Now, clean the condenser coils of the refrigerator and remove any obstacles in the way of airflow through the coils. Then determine the improvement in the COP of the refrigerator.

Short answer

Answer: To determine the improvement in the COP after cleaning the condenser coils, follow these steps: 1. Measure the time the refrigerator stays off and on before cleaning the coils. 2. Calculate the heat removed during the on time and the heat gain during the total time. 3. Determine the average rate of heat gain, in watts, before cleaning the coils. 4. Clean the condenser coils and remove obstacles in the airflow. 5. Measure the time the refrigerator stays off and on again and calculate the new average rate of heat gain. 6. Calculate the improvement in COP by comparing the old and new average rates of heat gain.

Step-by-step solution

Measure the Time the Refrigerator Stays Off and On

Place a timer or watch near the refrigerator and make sure the door has not been opened for a few hours to establish steady operating conditions. Start the timer when the refrigerator stops running, and measure the time \(\Delta t_{1}\) it stays off before it kicks in. Then measure the time \(\Delta t_{2}\) it stays on.

Calculate the Heat Removed and Heat Gain

The heat removed during \(\Delta t_{2}\) is equal to the heat gain during the total time \(\Delta t_{1}+\Delta t_{2}\). Let \(P\) be the power consumed by the refrigerator when it's running (given in watts). The heat removed during \(\Delta t_{2}\) can be written as: Heat removed = COP \(\times\) P \(\times \Delta t_{2}\) Assuming the COP value of 1.3 (if not available), the heat gain can be calculated as: Heat gain = Heat removed = 1.3 \(\times\) P \(\times \Delta t_{2}\)

Determine the Average Rate of Heat Gain

To determine the average rate of heat gain, we need to first calculate the total time (\(\Delta t_{1}+\Delta t_{2}\)) the refrigerator was either off or on. Then, divide the heat gain by this total time: Average rate of heat gain = \(\frac{\text{Heat gain}}{\Delta t_{1}+\Delta t_{2}} = \frac{1.3 \times P \times \Delta t_{2}}{\Delta t_{1}+\Delta t_{2}}\)

Clean the Condenser Coils and Remove Obstacles

Now that we have determined the average rate of heat gain, we need to improve the COP of the refrigerator by cleaning the condenser coils and removing any obstacles in the way of airflow through the coils. This step doesn't require calculations, but it involves physically cleaning the coils and inspecting for any obstacles.

Determine the Improvement in COP

After cleaning the condenser coils and removing the obstacles, perform the same measurements for \(\Delta t_{1}\) and \(\Delta t_{2}\) and calculate the new average rate of heat gain using the formula from Step 3: New average rate of heat gain = \(\frac{1.3 \times P \times \text{New } \Delta t_{2}}{\text{New } \Delta t_{1}+\text{New } \Delta t_{2}}\) Finally, calculate the improvement in the COP by comparing the old average rate of heat gain with the new one: Improvement in COP = \(\frac{\text{New average rate of heat gain}}{\text{Old average rate of heat gain}}\) This value indicates the improvement in the efficiency of the refrigerator after cleaning the condenser coils and removing the obstacles in the airflow.