Heating and Cooling Curves Explained
A heating curve is a graph of temperature against time (or energy supplied) as a substance is heated at a constant rate, with sloping sections where one phase warms up and flat plateaus at the melting and boiling points where the substance changes state; a cooling curve is the reverse. In brief: on the sloping sections, the slope is inversely related to the specific heat capacity of the phase, and the plateau lengths are proportional to the latent heats. A pure substance has sharp plateaus, while a mixture or impure substance melts over a range.
The graphs are used to find melting and boiling points, to test purity and to study energy changes. This guide explains how to read a heating curve and a cooling curve, relates the shape to specific heat and latent heat, compares the sections in a table, works through a calculation of the times for each stage for 0.100 kg of water heated by a 500 W heater, and corrects common mistakes.
What does a heating curve show?
Imagine a block of ice at −10 °C heated by a heater of constant power. The temperature-time graph has five sections:
- A rising line: the solid warms. The slope is ΔT ÷ Δt = P ÷ (mcsolid).
- A flat line at the melting point: the solid melts and the temperature stays constant.
- A rising line, less steep (because c of liquid water is larger than that of ice): the liquid warms.
- A longer flat line at the boiling point: the liquid boils.
- A rising line, steeper than the liquid (the gas has a small specific heat capacity): the gas warms.
The length of the boiling plateau is greater than that of the melting plateau because Lv is larger than Lf.
What does a cooling curve show?
A cooling curve shows temperature against time when a substance loses energy, for instance when a liquid is cooled until it solidifies. It has a falling section for the liquid, a plateau at the freezing point (the same temperature as the melting point) while the latent heat is released, and a falling section for the solid. If a liquid is cooled very carefully, it can go below the freezing point (supercooling) and then rise suddenly to the freezing point when crystals start to form. In an impure substance or an alloy, the freezing takes place over a range of temperatures and the plateau is replaced by a gentle slope, so the shape of the curve can be used to check purity.
What happens to the particles?
On the sloping sections, the energy supplied increases the average kinetic energy of the particles (and the temperature). On the plateaus, the energy goes into the potential energy of the particles: bonds in the solid are broken during melting, and the remaining attractions are overcome during boiling. The kinetic energy and the temperature stay constant. During cooling, the opposite occurs.
Sections of the curve compared
| Section | Temperature | Energy goes to | Formula |
|---|---|---|---|
| Ice warming | Rising | Kinetic energy | mciceΔT |
| Melting | Constant at 0 °C | Potential energy | mLf |
| Water warming | Rising | Kinetic energy | mcwaterΔT |
| Boiling | Constant at 100 °C | Potential energy | mLv |
| Steam warming | Rising | Kinetic energy | mcsteamΔT |
Worked example: times for each section
A 500 W heater supplies energy at a constant rate to 0.100 kg of ice at −10 °C, with no losses. Time = energy ÷ power. Use the energies calculated for this mass: 2,100 J, 33,400 J, 41,800 J, 226,000 J and 2,010 J.
- Ice warming: t = 2,100 ÷ 500 = 4.2 s.
- Melting (plateau at 0 °C): t = 33,400 ÷ 500 = 66.8 s.
- Water warming from 0 °C to 100 °C: t = 41,800 ÷ 500 = 83.6 s. The slope is 100 K ÷ 83.6 s = 1.2 K/s.
- Boiling (plateau at 100 °C): t = 226,000 ÷ 500 = 452 s.
- Steam warming from 100 °C to 110 °C: t = 2,010 ÷ 500 = 4.0 s. The slope is 10 K ÷ 4.0 s = 2.5 K/s.
- Total time: 4.2 + 66.8 + 83.6 + 452 + 4.0 = 610.6 s, about 10 minutes.
The slope for the ice is 10 K ÷ 4.2 s = 2.4 K/s, for the water 1.2 K/s, and for the steam 2.5 K/s, which is consistent with the smaller c of ice and steam. The boiling plateau is 452 ÷ 66.8 = 6.8 times as long as the melting plateau, equal to the ratio of the latent heats, 2,260 ÷ 334 = 6.8.
How are curves used?
Chemists identify substances and check their purity by measuring melting points. Metallurgists use cooling curves to study alloys and to construct phase diagrams. In schools, the curve of stearic acid or wax cooling from liquid to solid is a standard experiment, and data loggers draw the graph.
Which mistakes are common?
Mistake 1: Reading the plateau as a time when no energy is supplied
The heater is still supplying energy; it is used for the change of state.
Mistake 2: Saying that the particles stop moving on the plateau
They keep moving with the same average kinetic energy. Their potential energy changes.
Mistake 3: Mixing up the steepness and specific heat capacity
A steeper line means a smaller specific heat capacity (a smaller mc).
Mistake 4: Drawing the cooling curve as the same as heating in time
The durations depend on the rate of heat loss, which usually falls as the object gets closer to the temperature of its surroundings.