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Why is the melting and freezing point of a substance are always the same ? This was quoted in my textbook but they didn't give a reason for this being so.

Thank you.

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Melting-point depression is the phenomenon of reduction of the melting point of a material with reduction of its size. Presumbly different size of a material is still the same substance(?), then that's already falsifies the question... I guess one may show (by Lee-Yang phase transition theorem?) at the thernodynamics limit, $N \rightarrow \infty$, $V \rightarrow \infty$, $N/V \rightarrow \mathrm{constant}$, the phase transition point is a constant. Here $N$ and $V$ are the number of particles and volume. But I don't know how to do it :( –  user26143 Aug 17 '13 at 16:24

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Suppose you have a lump of ice, and you want to melt it to water completely, you will heat it.

As the temperature of the ice reaches $0^\circ \mathrm C$, temperature of the ice will stop rising, and all the heat will be used to convert the ice to water. While this is happening the ice and water will simultaneously exist in equilibrium(because all the ice cannot convert to water instantaneously). After a certain amount of heat is added, all the ice is converted to water.

Notice that this water is at $0^\circ \mathrm C$, because the temperature didn't rise during phase change. The same thing will happen in reverse when you cool down water.

The first process I described is melting, the same process in reverse is freezing. And as temperature doesn't change during melting and freezing, they both happen at the same temperature!

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Melting point depends on the size of the substance, wiki. Perhaps the explanation is not that simple... –  user26143 Aug 17 '13 at 17:24
There are other complicated cases too, where you cannot use this explanation. For instance, amorphous solids have no fixed melting point, they melt over a range of temperatures –  udiboy1209 Aug 17 '13 at 17:30

It's the same temperature because it's the only temperature at which the liquid phase and the solid phase may co-exist – which is a symmetric description of the temperature.

When we add heat to this mixture of "ice" and liquid, it will keep the temperature at the same point but the percentage of "ice" will be decreasing, and only when all the "ice" is gone, the temperature will stop rising. In the same way, if we remove heat from the mixture, the temperature will be constant for a while as more liquid turns into "ice", and only when the whole body is frozen, the temperature starts to drop.

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So , by liquid you mean water. And I understand the second para ,though I still don't understand the first.Please explain a little more. Thanks. –  Gaurang Tandon Aug 17 '13 at 15:36
The first paragraph just says that ice may swim in the water, and when it's so for extended periods of time, the temperature of everything in the mixture has to be equal to the melting point ie freezing point. –  Luboš Motl Aug 18 '13 at 5:57
Principle of Calorimetry ?? –  Gaurang Tandon Aug 18 '13 at 12:02

Dumb answer: Because they are the same thing, viewed from different sides. In one direction, it's melting. In the other direction, it's freezing.

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