# Heat Capacity and Melting Points

Q:
This is a different question all together. If water has the highest heat capacity and iron, a metal with a much lower heat capacity, why is it that water will boil at 100 degrees celsius while iron will boil at 2862 degrees celsius.
- paul (age 21)
SANTA ROSA
A:

It turns out that the higher heat capacity of water, compared to iron, is related to its lower melting point and lower boiling point. Here's some background on where the main heat capacities of ordinary materials comes from.

When atoms are just running around freely and separately in a gas, the heat capacity comes from the kinetic energy of the particles moving around. If the atoms pack together tightly into a crystal, the motions become very high-frequency vibrations. The energy of those vibrations comes in such big packets ("quanta", yes this part is from quantum mechanics) that at ordinary temperatures there's almost never enough energy in one mode to supply a quantum. The heat capacity drops because these modes are frozen out.

What happens in between, where the atoms are "touching" but not really rigidly packed in? (This could be either in a liquid or a squishy solid.) There the motional kinetic energy is still present, plus potential energy from the atoms squashing together or pulling apart, like little springs. The heat capacity per atom is higher than in either the gas or the rigid solid.

Liquid water is right in that sweet spot where you get lots of heat capacity from both the kinetic and potential parts of the energy. Solid iron has such inflexible bonds between the atoms that most of that heat capacity is frozen out at room temperature. So the lower heat capacity of iron is nature's way of telling you that it's so tightly bonded that you'll have to heat it up a lot to melt it, much less boil it. The very high heat capacity of water is a hint that its molecules aren't stuck together all that well, so you shouldn't be surprised that it boils at fairly low temperature.

I don't mean to imply that you can directly read melting or boiling points off of heat capacities, which depend on atomic masses and other factors as well. It's just that the general trend you'd expect is fit nicely by water and iron.

Mike W.

(published on 07/16/2015)

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