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Melting point = Freezing Point

Why is the melting point of a substance is the same as its freezing point?

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    $\begingroup$ Related: chemistry.stackexchange.com/questions/53348/… $\endgroup$ – airhuff May 14 '17 at 6:41
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    $\begingroup$ We have a block of 10 g of ice at -5°C. Its melting temperature is ~0°C. If we let it warm up slowly, when it reaches 0°C some ice will melt, forming some (liquid) water. Thermodynamics shows that the temperature must stays constant as long as there are both solid and liquid. So at a given time you could have 5 g ice and 5 g water, necessarily at 0°C. Now you put this in the freezer (say at -5°C). What happens? The ice stops melting, and instead some water starts freezing and turning back into ice. But you still have both solid and liquid, so you must still be at 0°C. $\endgroup$ – user6376297 May 14 '17 at 7:32
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Consider a system that contains only a single substance. At the temperature where the solid and liquid phase of the substance are in thermodynamic equilibrium you cannot tell if the system initially consisted only of solid or only of liquid or of a mixture of both.

Thermodynamic equilibrium means that the substance has the same temperature all over the system.

If a small amount of heat is added to the system, some of the substance melts. So the temperature is the melting point of the substance.

If a small amount of heat is removed from the system, some of the substance freezes. So the temperature is the freezing point of the substance.

This shows that melting point and freezing point are the same.

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