Two identical refrigerators are plugged in for the ?rst time. Refrigerator A is

Question

Two identical refrigerators are plugged in for the ?rst time. Refrigerator A is empty

(except for air) and refrigerator B is ?lled with jugs of water. The compressors of both refrigerators immediately turn on and begin cooling the interior of the refrigerators. After

two hours the compressor of A turns off while the compressor of refrigerator B continues

to run. The next day, the compressor of refrigerator A can be heard turning on and off

every few minutes, while the compressor of refrigerator B turns off and on every few

hours (and stays on longer). Explain these observations.

Explanation / Answer

It has to do with the relative heat capacities for oxygen versus water. Heat capacity is the amount of heat required to change the temperature of a given amount of a substance in a given amount of time. The heat capacity for oxygen is 21 J/(mol*K), while it is 74.5 J/(mol*K) for liquid water at constant volume (refigerator size stays the same). Heat capacity is calculated by (C=Delta Q/ Delta T) where delta Q is the change in thermal energy. As you can see, a substance with a larger heat capacity requires more thermal energy to cause a change in its temperature. That explains why the fridge containing water would need to be on longer, initially, to change the temperature of the water. This also explains why the fridge containing the water would not need to be on as much the next day. Initially it took longer to cool the water than the air, but the water is now at the cooling temperature. Because it has a higher heat capacity, it is better able to resist a change in temperature. The air, however, has a lower heat capacity. So it's temperature can be changed more easily; it can be cooled more easily and it can be heated more easily. As soon as the compressor turns off, the air will increase in temperature faster than the water. This explains why the next day, the compressor of the fridge containing the air turns on and off more frequently, as it is less able to resist a change in temperature, while the compressor of the fridge containing water turns on and off less frequently, as it is more able to resist a change in temperature.

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