Energy of Phase Changes

Temperature measures the average kinetic energy of particles, how fast they are moving. When a substance is melting or boiling, the particles are rearranging their positions relative to each other, not speeding up. Every joule you add goes into stretching or breaking the intermolecular forces holding the particles in their current arrangement. That is why an ice cube sitting at 0 degrees C can take minutes to melt while its thermometer reading never budges. The energy is doing the work of separation, not the work of accelerating particles. Once every particle has finished the transition, added energy goes back into kinetic energy, and the temperature starts climbing again.

The amount of energy needed is just mass times a constant specific to the substance and the transition: q = m times heat of fusion for melting or freezing, and q = m times heat of vaporization for boiling or condensing. These constants are measured in joules per gram, so multiplying by the mass in grams gives total joules directly. Heat of vaporization is almost always much bigger than heat of fusion for the same substance, because melting only has to loosen a solid's rigid structure enough for particles to slide past each other while staying close together, but vaporization has to rip particles apart entirely, overcoming nearly all the remaining attraction to scatter them into a gas.

This sits right next to heating curves, where flat plateaus mark phase changes and sloped segments mark temperature change within one phase. It also connects forward to intermolecular forces: substances with stronger attractions, like hydrogen-bonded water, demand more energy per gram to vaporize than weakly attracting substances like nonpolar hydrocarbons of similar size.