States of Matter & Heating Curves

About this model

One sample, one energy budget. The sample is pure water at 1 atm in a sealed cylinder. The heater adds energy at a constant power with no losses, so the energy added is q = P × t, and the joule meter counts every joule. The model keeps track of the sample’s total energy (enthalpy) and works out its temperature and phase from it, segment by segment: ice, melting, liquid, boiling, steam.

Within one phase the temperature rises by q = mcΔT with constant specific heats: ice 2.09, liquid water 4.18 and steam 2.01 J/(g·°C). On the plateaus the temperature stays at 0 °C (melting) or 100 °C (boiling) while energy goes into the phase change: 334 J/g to melt (heat of fusion) and 2260 J/g to boil (heat of vaporisation). Values: OpenStax University Physics Vol. 2, §1.4–1.5 (rounded). Cooling (negative power) runs the same path backwards: condensing and freezing release the same energies.

What the model leaves out. Real heat capacities change a little with temperature; the container absorbs some heat and the surroundings take some away; boiling point depends on pressure (100 °C only at 1 atm); real water can supercool or superheat before it changes phase. None of these are in the model. The temperature range is −60 °C to 200 °C.

The particle view is a model too. It shows 96 water molecules. How many are solid, liquid or gas comes straight from the energy model’s melted and vaporised fractions, so each molecule that leaves the ice lattice stands for 1/96 of the heat of fusion. Their speed is set by temperature alone: the average kinetic energy of the particles is proportional to the absolute temperature in kelvin, so liquid and vapour at 100 °C move at the same average speed; vapour particles just travel farther before they hit something. On-screen speeds are slowed down enormously. The real rms speed of water-vapour molecules is v = √(3RT/M), about 719 m/s at 100 °C (OpenStax University Physics Vol. 2, §2.2); the speed meter shows that number for the gas only. The ice lattice is drawn flat (real ice is a 3-D hexagonal lattice), with a wider spacing than the liquid because ice is less dense.

The energy bars split the energy added into “speeding particles up (temperature)” and “pulling particles apart (phase change)”. This is the usual teaching split: in a real liquid some of the heat that raises the temperature also goes into stretching the attractions between molecules, which is one reason liquid water’s specific heat is about twice that of ice or steam.

The cylinder. A free piston with weights keeps the pressure at 1 atm. Vapour is an ideal gas: 1 g of steam takes about 1.7 L at 100 °C, roughly 1,700 times the volume of the liquid, so the piston is drawn on a squeezed scale (not to scale). Water vapour is an invisible gas; the bench shows it as a faint haze so you can see where it is. Ice: 0.917 g/mL, liquid: 1.00 g/mL (CRC Handbook).

OpenStax: specific heat · OpenStax: phase changes · OpenStax: temperature and rms speed

What am I looking at?

How the lab works. Pick Explore or one lab at the top. Each lab has five tabs: Pre-lab, Bench, Data & graph, Claim · Evidence · Reasoning, and Test. On the Bench, the coach lists your steps; they tick themselves as you work. Press What do I do now? when you are stuck.

① Bench. A sealed glass cylinder of water sits on a hot plate. The controller on the left sets the heater power in watts (below 0 W it cools). On the right: the thermometer (°C), the joule meter (energy added, J) and the stopwatch. The piston on top keeps the pressure at 1 atm and rises as vapour forms (not to scale). The round lens shows the particles; tap it to zoom in.

② Particles. The same sample, zoomed in to 96 water molecules. In ice they vibrate in a lattice joined by hydrogen bonds (dotted lines); in the liquid they slide past each other; in the gas they fly apart. The speed meter shows the average speed: it depends only on temperature. On a plateau, watch one molecule at a time break away: an orange ring for melting, a pink ring for boiling, a dashed blue ring when attractions form on cooling. The two energy bars show where the energy has gone.

Graph. Temperature against energy added (or time, in Advanced). Each phase has its own colour, marker and name; the flat plateaus are hatched and labelled.

Step moves 1 °C within a phase, or exactly one molecule on a plateau. Keys: Space heat / pause · → step · ← step back · R reset · Z / X zoom.