Why does ice melt? Why does water boil? Or freeze? This must have something to do with heat (thermal energy).
First, think about all those phase changes and all that… Okay, good… moving on…
Indeed, there is something going on with heat!
Let's think about melting…
There is a certain amount of energy that holds the molecules of a solid in place. If you want to melt the solid, you have to add energy (heat). Doing this will free the molecules.
How much heat? Well…
First off, the amount of heat needed to break the bonds has a name.
Heat of Fusion: the heat absorbed by a unit mass of a given solid at its melting point that completely converts the solid to a liquid at the same temperature: equal to the heat of solidification. (dictionary.com)
(It is not uncommon to just say "heat of fusion" regardless of whether it is melting or freezing)
Now, what does that mean? So, let's go with grams for discussion… for any gram of a thing, there is a certain amount of heat needed to break all the bonds and make it into a liquid. Pretty easy, really.
Each substance has different requirements. Google will provide lists!
So, if you understand the concept of Heat of Fusion, then the idea fits directly with boiling (vaporization and condensation).
Heat of Vaporization: the heat absorbed by a unit of mass of a given liquid at its boiling point that completely converts the liquid to a gas at the same temperature.
(There is a corresponding "heat of condensation" as well that some people might use.)
So… for any given mass of something, there are certain values for the amount of heat needed to cause a phase change.
Think about that ice… it heats up gradually until it is all at 0°C. Then, as heat goes into the ice, the temperature does not change. Instead, the molecules become free. Once all of the ice has become water, it starts warming up again.
The same is true at the boiling point.
Well… There must be math, right?
Of course, there is math!
Where m is the mass of the substance and… you're going to love this variable… where ∆Hf is heat of fusion, the heat of the phase change, Q, is found as
Q = m • ∆Hf
So… super easy. Multiply two numbers.
Same for boiling and condensing. The only difference is that "f" is a "v".
Q = m • ∆Hv
So, mass times some number you look up. How easy can that be?
The heat of fusion for brass is 168 J/g. How much heat energy is needed to completely melt 250 grams of brass?
Q = m • ∆Hf
Q = 250 • 168
Q = 42,000 J
There has to be some way to make this harder!
Actually, for this in particular, there isn't. However… Of course there's a however! …phase change and temperature change can both be tracked in the same interaction. So, the heat gain, for instance, could be raising the temperature of the ice to the melting point, then melting it, then raising the temperature of the water…
So, it can be more complex. Not really harder, but definitely longer.