This is what I read on Chemwiki:

Rudolf Clausius was a German physicist, and he developed the Clausius statement, which says "Heat generally cannot flow spontaneously from a material at a lower temperature to a material at a higher temperature." However, there is one exception to this statement and that is sometimes a hot material will take heat from the cold material, making the hot material warmer and the cold material colder.

Chemwiki does not provide a reference for the exception about heat transfer from cold material to hot material. How is this possible? What is an example of this happening?

  • 2
    $\begingroup$ Hmm, good question. I suppose the exception is when there is some work done on the system. $\endgroup$ – M.A.R. Mar 30 '15 at 10:25
  • $\begingroup$ Fridge or example :) $\endgroup$ – Mithoron Mar 30 '15 at 15:10
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    $\begingroup$ I admit that was confused about that sentence too and agree it didn't make much sense. I have erased it from the ChemWiki. We accept all suggestions to improve the site graciously and appreciatively. $\endgroup$ – user20687 Sep 7 '15 at 5:53

The statement is wrong and/or poorly formulated. Heat cannot spontaneously flow from cold areas to hot areas, there are no exceptions known. It contradicts Clausius' statement of the second law and hence also the more general observation/statement that the entropy of an isolated system is increasing.

Of course you can drain heat from cold regions and transport it to hotter regions, but this should always go paired with some other (larger) increase in entropy somewhere else, e.g. by doing work like in a Linde refrigeration. An other example is that some salts have a very high entropy of solvation and can cool water to ~ -15 °C in a lab at room temperature. These salts can be/are used in practical chemistry for cooling a reaction mixture.

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