Phase transitions

In brief

Put a pot of ice water on a stove and watch a thermometer in it while the burner runs at a steady output. The temperature climbs toward zero degrees Celsius, then stops, and holds at zero for a long stretch even though the flame never wavers, until every last sliver of ice is gone, at which point the temperature resumes climbing. The heat did not stop flowing in. It stopped raising the temperature. Something else was being paid for during that flat stretch, and understanding what that something is, the reorganization of the water molecules from a rigid crystal into a mobile liquid, is the key to melting, freezing, boiling, and condensation alike. This entry builds that understanding from a simple energy count and shows how to read or construct the graph that makes it visible.

The full treatment

First look: the flat spots on a heating curve

Take a block of ice at minus twenty degrees Celsius and heat it steadily, plotting temperature against total heat added. The curve rises smoothly as the ice warms, following the ice's specific heat. At zero degrees it goes flat: heat keeps entering but the temperature does not move, until the last of the ice becomes liquid water, at which point the curve resumes climbing, now along the liquid's specific heat, all the way to one hundred degrees at standard pressure. There it goes flat again, this time for a much longer stretch, until every drop has become steam, after which the curve climbs a third time through the specific heat of steam. Two flat plateaus interrupt three sloped segments. The plateaus are the phase transitions, and the length of each plateau along the heat axis is exactly the latent heat of that transition.

Building the idea: two jobs for one flame

Heat added to a substance can do one of two things. It can speed up the molecules, which is what a thermometer detects as rising temperature. Or it can pull molecules apart against the forces holding them together, without changing how fast any individual molecule moves once the pulling is done. A solid's molecules sit in fixed positions, vibrating around a lattice point and held there by intermolecular attraction. Melting does not make those molecules move faster on average; it breaks the fixed arrangement so they can slide past one another as a liquid. All the extra energy goes into that structural change, into potential energy of configuration, not into kinetic energy, so the temperature does not rise while the melting is in progress. Boiling repeats the story at a larger scale: liquid molecules are still touching their neighbors, but vapor molecules are essentially free, so separating a liquid into gas costs far more energy per unit mass than melting a solid into a liquid, which is why the boiling plateau on a heating curve is so much longer than the melting plateau.

The formal model: latent heat and the phase diagram

Define the heat required for a phase change at constant temperature as Q equals m times L, where m is the mass undergoing the transition and L is the specific latent heat of that transition, measured in joules per kilogram, a different value for melting, called the latent heat of fusion, than for boiling, called the latent heat of vaporization. For water, the latent heat of vaporization is roughly seven times the latent heat of fusion, which is exactly why the boiling plateau above dwarfs the melting one. Reading a phase-change energy curve means matching each sloped segment to Q equals m times specific heat times the temperature change, and each flat segment to Q equals m times L, then adding every segment to get the total heat for a full journey from one state to another.

Why does a phase change happen at a fixed temperature at all, rather than gradually? At any temperature and pressure, a substance settles into whichever phase has the lowest available free energy, a quantity that combines the internal energy that favors an ordered, low energy phase with the entropy that favors a phase with more accessible microscopic arrangements. At low temperature the energy term wins, so molecules lock into the ordered solid. At high temperature the entropy term, multiplied by the now-large temperature, wins, favoring the far more numerous arrangements of a gas. At one specific temperature for a given pressure, the two phases have exactly equal free energy, neither more stable than the other, and both can coexist; that is the transition point, and it is why the thermometer refuses to move past it until every molecule has finished switching sides. This same competition explains why the transition temperature shifts with pressure: squeezing a substance changes how much room the more spread out phase actually has, which is why water boils at a lower temperature on a mountain, where atmospheric pressure is lower, and why a pressure cooker raises the boiling point by raising the pressure.

Superheating, supercooling, and the limits of the plateau picture

The flat plateau describes equilibrium, not speed. In practice, a very clean liquid can be cooled below its freezing point without freezing, or heated above its boiling point without boiling, because starting a new phase requires a nucleation site, a tiny seed crystal or bubble, and pure, undisturbed samples may lack one. Tap a supercooled bottle of water and it can freeze instantly as ice crystals suddenly nucleate throughout. This delay is a kinetic effect layered on top of the thermodynamic picture and does not overturn it: the free energy argument still says which phase is ultimately favored, it just does not promise how fast the substance gets there.

Lineage

The observation that heating a substance sometimes fails to raise its temperature was placed on a quantitative footing by the Scottish chemist Joseph Black in the 1750s and 1760s, who distinguished this "latent heat" from ordinary "sensible heat" using careful calorimetry, resolving a puzzle that had confused experimenters who assumed heat and temperature were the same thing. The French engineer Emile Clapeyron and later Rudolf Clausius, working from Carnot's ideas about engines, derived the relation between the slope of a substance's coexistence curve on a pressure-temperature diagram and its latent heat in the mid nineteenth century. Josiah Willard Gibbs, in the 1870s, supplied the general free energy framework that explains why one phase becomes favorable over another, work later extended into the statistical theory of continuous transitions by twentieth century physicists including Lars Onsager and Lev Landau.

The strongest case for it

The framework correctly predicts fixed, sharply reproducible transition temperatures at a given pressure, and those latent heats are measured with high precision and used constantly in engineering: refrigeration and air conditioning both work by forcing a fluid to evaporate, deliberately absorbing latent heat from whatever needs cooling, and steam engines and power plants both work by condensing steam, deliberately releasing it. The dependence of boiling point on pressure, predicted by the same theory, is exactly why altitude cooking instructions differ from sea level ones and why a pressure cooker shortens cooking time. The theory also correctly separates thermodynamic questions, which phase is ultimately stable, from kinetic ones, how fast the substance gets there, which lets it accommodate superheating and supercooling without contradiction.

The strongest case against it

The simple picture of a flat plateau and a single latent heat describes what is called a first order transition, and it does not cover every phase change nature offers. Continuous, or second order, transitions, such as a magnet losing its magnetism at its Curie temperature, involve no latent heat and no flat plateau at all; the properties change smoothly but with a sharp change in curvature, and near the transition the substance shows large, correlated fluctuations, a phenomenon called critical opalescence in fluids, that this simple energy-counting picture does not capture and that requires the more elaborate theory of critical phenomena. A common misconception is treating a melting or boiling point as a fixed constant of the substance; it is really a curve, one temperature for each pressure, and citing "the" boiling point without stating the pressure is incomplete. A second is assuming that a flat temperature reading during a phase change means heat has stopped flowing; it has not, it is simply being redirected entirely into rearranging molecular configuration.

Where it stands now

The thermodynamics of first order phase transitions is settled science, foundational to chemical engineering, materials science, meteorology, and everyday cooking and refrigeration. The physics of continuous transitions and critical phenomena remains an active and rich research area, connecting to magnetism, superconductivity, and even the early universe's cooling, but this is an extension of the theory into a different class of transition, not a challenge to the latent heat picture developed here for melting, freezing, boiling, and condensation.

Test yourself

You are given five hundred grams of ice starting at minus twenty degrees Celsius and asked to find the total heat required to turn it into steam at one hundred fifty degrees Celsius, at standard atmospheric pressure, given the specific heats of ice, water, and steam and the latent heats of fusion and vaporization for water. Sketch the heating curve you would expect, labeling which segments are sloped and which are flat, then compute the heat required for each segment and sum them. Explain, without doing any further arithmetic, why the boiling segment consumes far more heat than the melting segment even though both are flat, and state what single change to the surrounding pressure would shift the temperature of the boiling plateau without changing the melting plateau's temperature.