According to typical sources on thermodynamics, the warmer a liquid is, the longer it will take to freeze it.

For example, I recently was reading a book on refrigeration and this book specifically said that the hotter the refrigerant is, the longer it will take to condense it, so the refrigeration system has to take that into account when it is designed.

The basic theory is that there are two quantities heat of cooling and then latent heat of melting. So, the refrigeration system must remove both to freeze the liquid. Since the refrigeration system generally has a fixed rate of heat removal, the hotter the gas is, the longer it takes condense it.

However, it is well known that hot water freezes faster than cool water. If two cups containing water are placed in a freezer, one being hot, the other cool, then the hot one will freeze first and this can be proved by anyone. So, how is the anomaly explained theoretically?

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    $\begingroup$ Scientifically, if all things are equal, having the hot water freeze faster is impossible. So all things aren't equal. Specifically for example the hot cup melts the frost in the freezer and makes better thermal contact. Another factor is that the hot water can evaporate a substantial amount of liquid. So the phenomena isn't well known, it just has been well hyped without proper experimentation. $\endgroup$ – MaxW Nov 17 '18 at 15:44

The comment by MaxW is insightful: the phenomenon is not well-known, just well-hyped.

Well, let's assume that the phenomenon is real, that is, can be observed, at least under certain circumstances. If you believe in the phenomenon, even if is is only observable sometimes, if you do enough experiments, you will observe the phenomenon. A good explanation for the inconsistency is that there are factors involved which are energetically much smaller than the energy of freezing, and we don't know how to account for them.

Now, in practice, such a variation in outcomes might cause a process upset: something clogs, or doesn't clog when it is supposed to. In such cases, an overriding effect will be installed (like a stirrer or bubbler) to shake things up so things fall where they are expected.

But there is lots of fun possible designing ever more sensitive experiments to find out why it happens (and why, in the end, the 2nd Law is true). The second law of thermodynamics says that heat flows naturally from an object at a higher temperature to an object at a lower temperature, and heat doesn’t flow in the opposite direction of its own accord. The glitch in the usefulness of the Law here is that thermodynamics does not specify kinetics (the rate of heat flow).

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    $\begingroup$ This does not even pretend to answer the question. $\endgroup$ – Shaka Boom Nov 18 '18 at 1:12

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