Heat capacity, specific heat capacity (E = mcΔT), specific latent heat of fusion and vaporisation (E = mL), heating and cooling curves, and the distinction between evaporation and boiling.
Different materials need different amounts of heat to reach the same temperature rise. This is described by two related quantities.
Heat capacity () of an object is the energy required to raise its temperature by 1 K (or 1 °C):
Unit: J K⁻¹.
Specific heat capacity () of a substance is the energy required to raise the temperature of 1 kg of that substance by 1 K (or 1 °C):
The working formula is:
where is heat energy in joules (J), is mass in kilograms (kg), and is the temperature change in kelvin or degrees Celsius.
Unit of : J kg⁻¹ K⁻¹.
The two quantities are related by: .
| Substance | / J kg⁻¹ K⁻¹ |
|---|---|
| Water | 4 200 |
| Aluminium | 900 |
| Copper | 400 |
| Iron | 500 |
| Air | 1 000 |
Water has the highest specific heat capacity of common liquids. A large mass of water (ocean, lake) can absorb or release enormous amounts of thermal energy with a small temperature change, this moderates coastal climates.
A 300 g liquid sample is heated by an electric heater rated at 105 W. Temperature readings are taken every 60 s. The temperature rises from 25.3 °C to 56.8 °C over 360 s.
Gradient of temperature-time graph:
Specific heat capacity (using ):
Comparing with the table of liquids (cooking oil: 1700, paraffin: 2100, milk: 3900), the liquid is most likely milk.
When a substance changes state (melts, freezes, boils, or condenses), it absorbs or releases heat energy without any change in temperature. This hidden energy is the latent heat ("latent" means "hidden").
Specific latent heat () is the energy absorbed or released when 1 kg of a substance changes state without a change in temperature:
where is in joules, is mass in kilograms, and is the specific latent heat in J kg⁻¹.
Two specific latent heats exist for each substance:
For water: J kg⁻¹, J kg⁻¹.
The latent heat of vaporisation of water is about 7 times its latent heat of fusion, it takes far more energy to convert water to steam than to melt ice.
When a pure substance is heated at a constant rate, a temperature-time graph shows flat regions during each phase change.
The slope of each rising section equals (rate of temperature rise at constant heating power). The flat sections have slope zero because the energy input goes into breaking intermolecular bonds rather than increasing kinetic energy.
Both processes convert liquid to vapour, but they differ in several ways:
| Property | Evaporation | Boiling |
|---|---|---|
| Location | Surface of the liquid only | Throughout the bulk of the liquid |
| Temperature | Occurs at all temperatures | Occurs at the boiling point only |
| Rate | Slow; depends on surface area, air movement, humidity | Rapid; requires continuous heat input |
| Temperature of remaining liquid | Falls (faster molecules escape) | Stays at the boiling point |
| Bubbles | No bubbles form | Bubbles of vapour form inside the liquid |
Evaporation cools the liquid because the fastest-moving molecules escape from the surface, lowering the average kinetic energy of those remaining. This is why sweating cools the body.
An immersion heater rated at 150 W boils water for 5 minutes. The mass of water decreases from 0.28 kg to 0.26 kg.
Energy supplied by heater:
Mass of water vaporised:
Specific latent heat of vaporisation:
This is close to the accepted value of J kg⁻¹ for water.
In latent heat calculations, identify the mass that actually changes state, it is often the mass difference between the start and end of an experiment, not the total mass present.
On a heating curve, the flat region at 0 °C is melting (latent heat of fusion). The flat region at 100 °C is boiling (latent heat of vaporisation). Rising sections represent temperature change governed by specific heat capacity.