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The cooling of the interior of a refrigerator does not violate the laws of thermodynamics because work has to be input to the system in order to run the compressor that helps pump the heat out of the refrigerator. The typical refrigeration cycle runs like this:

  1. The refrigeration fluid is compressed by the compressor. Energy must be supplied to the compressor to make this happen. As the fluid is compressed, it gets hotter because the compression is nearly adiabatic.
  2. The hot compressed fluid is warmer than the surroundings so it can be cooled down by passing it through coils where it gives off heat to the surroundings.
  3. The cooled, compressed fluid is passed through a valve where it expands nearly adiabatically and at least partially vaporizes. As it does so, the temperature drops significantly to a point below the temperature of the interior of the refrigerator.
  4. The lower pressure fluid (gas and possibly some liquid) is passed through coils in the interior walls of the refrigerator where it absorbs heat from the somewhat warmer interior.

Note that in each instance where there is heat transfer, the heat moves from the warmer to the colder part of the system - in keeping with the second law. Overall the heat taken out of the fridge and the heat given off by the compressor creates a greater increase in entropy of the surroundings than the decrease in entropy of the interior of the fridge - again in keeping with the second law. Overall the energy input to the compressor exactly balances the heat released by the compressor and given off by the coils minus the energy removed from the interior of the fridge - thus complying with the first law.

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