Heating and cooling curves show how the temperature of a substance changes as heat is added or removed. They matter because they connect energy, temperature, and phase changes in one simple graph. A typical heating curve rises during warming within one phase, then becomes flat during melting or boiling.
A cooling curve has the same ideas in reverse as a substance releases energy and changes from gas to liquid to solid.
During a sloped part of the curve, added or removed heat changes the average kinetic energy of the particles, so the temperature changes. During a flat plateau, the energy changes the particle arrangement and intermolecular forces instead of changing temperature. The heat needed for a phase change is calculated with q = mΔHfus or q = mΔHvap, while heating within one phase uses q = mcΔT.
Reading the curve carefully helps identify the phase, the phase change, and which equation to use.
Key Facts
- Temperature changes only on sloped segments of a heating or cooling curve.
- Temperature stays constant during a phase change because energy changes potential energy, not average kinetic energy.
- Heating within one phase uses q = mcΔT.
- Melting or freezing uses q = mΔHfus.
- Boiling or condensing uses q = mΔHvap.
- For the same substance, ΔHvap is usually greater than ΔHfus because separating particles into a gas requires more energy.
Vocabulary
- Heating curve
- A graph showing how the temperature of a substance changes as heat is added.
- Cooling curve
- A graph showing how the temperature of a substance changes as heat is removed.
- Heat of fusion
- The energy required to melt a unit mass or mole of a substance at its melting point.
- Heat of vaporization
- The energy required to vaporize a unit mass or mole of a substance at its boiling point.
- Plateau
- A flat part of a heating or cooling curve where temperature stays constant during a phase change.
Common Mistakes to Avoid
- Using q = mcΔT during a plateau is wrong because ΔT = 0 during a phase change, so latent heat equations must be used instead.
- Thinking the substance stops absorbing heat on a flat segment is wrong because heat is still being used to overcome or form intermolecular attractions.
- Confusing melting point with boiling point is wrong because the lower plateau is usually melting or freezing and the higher plateau is usually boiling or condensing.
- Ignoring the direction of the curve is wrong because heating adds energy while cooling removes energy, even if the phase-change temperatures are the same.
Practice Questions
- 1 A 50.0 g sample of ice at 0°C melts completely. If the heat of fusion of water is 334 J/g, how much heat is absorbed?
- 2 A 25.0 g sample of liquid water warms from 20.0°C to 80.0°C. If c = 4.18 J/g°C, how much heat is absorbed?
- 3 On a heating curve, a substance reaches a flat segment at 100°C while heat continues to be added. Explain what is happening to the particles and why the temperature does not rise.