The melting point and the freezing point of a substance are the same thing.
The solidification process is what we also call freezing. When we say that water freezes at 32 degrees Fahrenheit (0 degrees Celsius), we could just as well say that that’s the melting point of ice. The reason they are the same is that the slithering molecules of a liquid must be slowed down to a certain definite energy in order for them to fall into their permanent, rigid places in a solid crystal; on the other hand, they must be heated up to that same amount of energy in order to break free from those rigid positions and begin to flow as a liquid.
A calorie is not a Calorie. A calorie is an amount of energy. While energy can exist in a variety of interchangeable forms, the most familiar form to most people is heat. So a calorie is generally regarded as an amount of heat.
But precisely how much heat? Ask a chemist and you’ll get one answer, but ask a dietitian or nutritionist and you’ll get another. And they’re not even close; one “calorie” is a thousand times bigger than the other. It’s as if one person’s kilometer were another person’s meter; in order to interpret a highway sign, you’d have to know who wrote it.
There’s no indication that the chemists and nutritionists will ever agree; they’re both too set in their ways. So the world is stuck with two sizes of calories.
The chemist’s calorie, which we might call a gram calorie, is the amount of heat it takes to raise the temperature of one gram of water (about 20 drops) by one degree Celsius. But that’s a pretty small amount of energy, so the nutritionist uses the food calorie: the amount of heat it takes to raise the temperature of a thousand grams of water by one degree Celsius. Thus, one food calorie is equal to a thousand gram calories.
To avoid confusion, I’ll use calorie with a lower-case c for the gram calorie and Calorie with a capital C for the food calorie. So when you see it written both ways, they’re not typos. Anyway, you can pretty much tell which one is meant by its context.
Thus, a certain definite amount of heat is involved in the melting-freezing transition of any substance between its solid and liquid forms. For pure water, that amount of heat happens to be eighty calories per gram. If you want to melt a gram of ice, you’ve got to put eighty calories of heat into it; if you want to freeze a gram of liquid water, you’ve got to take eighty calories of heat out of it.
Just to be contrary, chemists do not call that amount of heat the “heat of melting” or the “heat of freezing.” They call it the “heat of fusion.”
To make things even worse, whenever a substance happens to be a liquid at room temperature and we have to cool it to make it a solid, people call the transition temperature a freezing point, whereas if the substance is a solid at room temperature and we have to heat it to convert it to a liquid, people call that very same transition temperature a melting point.
Go fight City Hall.