4. DETAILS PREVIOUS ANSWERS SERPSE10 21.AE.002. MY NOTES PRACTICE ANOTHER Freezing Water A certain refrigerator has a COP of 5.00. When the refrigerator is running, its power input is 500 W. A sample of water of mass 500 g and temperature 20.0°C is placed in the freezer compartment. How long does it take to freeze the water to ice at 0°C? Assume all other parts of the refrigerator stay at the same temperature and there is no leakage of energy from the exterior, so the operation of the refrigerator results only in energy being extracted from the water. SOLUTION Conceptualize Energy leaves the water, reducing its temperature and then freezing it into ice. The time interval required for this entire process is related to the rate at which energy is withdrawn from the water, which, in turn, is related to the power input of the refrigerator. Categorize We categorize this example as one that combines our understanding of temperature changes and phase changes from Chapter 20 and our understanding of heat pumps from this chapter. Analyze Use the power rating of the refrigerator to find the time interval required for the freezing process to occur. (Use the following as necessary: P and W.) - At = At P P Use Q = mcAT and Q = LAm to substitute the amount of energy 1Q. that must be extracted from the water of mass m. (Use the following as necessary: L, Am, and AT.) mcAT At = P(COP) Recognize that the amount of water that freezes is Am = -m because all the water freezes. (Use the following as necessary: L, m, c and AT.) m cAT – L; At = P(COP) Substitute numerical values to find the time interval. (Enter your answer in seconds. Assume the specific heat of water is 4,186 J/(kg · °C), and the latent heat of fusion of water is 3.33 x 10° J/kg.) At = 83.34 Finalize In reality, the time interval for the water to freeze in a refrigerator is much longer than this, which suggests that the assumptions of our model are not valid. Only a small part of the energy extracted from the refrigerator interior in a given time interval comes from the water. What other sources of energy must be extracted by the refrigerator? (Select all that apply.) V Energy that continuously leaks into the interior must be extracted. V Energy must also be extracted from the container in which the water is placed. O Energy from the environment must be extracted into the refrigerator. EXERCISE Compare the cost to make 44 kg of ice using two different refrigerators; one has a COP of 5.00 and the other has a COP of 6.00. Electricity costs $0.1 per kWh. Using the same assumptions given in the example, find the cost difference (in dollars) between the refrigerators to freeze the water. Calculate the cost for the refrigerator with a COP of 5, then calculate the cost for the refrigerator with a COP of 6, and finally take the difference.