Heating Curves

Add heat steadily to a sample and most of the time the temperature climbs. That climb is q = mc delta T: energy goes into faster molecular motion, and the slope of that rising segment is 1/(mc), so a phase with small specific heat rises steeply for the same heat input, while a phase with large specific heat rises more gradually. But at a melting or boiling point, the temperature stalls and sits on a flat shelf. The heat you're adding there isn't speeding molecules up, it's breaking the intermolecular forces holding the solid or liquid together. That energy is the latent heat, q = m x heat of fusion or m x heat of vaporization, and it buys a phase change at constant temperature, not a temperature increase.

A full heating curve for water strings five segments together: solid warming, melting shelf, liquid warming, boiling shelf, gas warming. To find total energy for some journey across that curve, you add every sloped segment and every flat segment in order, switching specific heat value each time you cross into a new phase. Skipping a segment, or using the wrong specific heat for the wrong phase, is the single easiest way to get this wrong.

This connects directly to calorimetry and bond enthalpies elsewhere in the unit: the same q = mc delta T and q = m x latent heat relationships describe heat flow in a calorimeter, and the shelves are a visual reminder that phase changes, like bond breaking, cost energy without changing kinetic energy or temperature.