Define and apply specific heat capacity and specific latent heat to calculate energy transfers during temperature changes and changes of state

What this dot point is asking

SEAB wants you to define and apply specific heat capacity (energy to change temperature) and specific latent heat (energy to change state), and to handle problems that combine heating and phase change. The key conceptual point is that a change of state happens at constant temperature, because the energy goes into breaking molecular bonds rather than speeding molecules up.

The answer

Specific heat capacity

The specific heat capacity $c$ of a substance is the energy required to raise the temperature of $1\ \text{kg}$ of it by $1\ \text{K}$:

where $m$ is the mass, $c$ the specific heat capacity ($\text{J kg}^{-1}\text{K}^{-1}$) and $\Delta\theta$ the temperature change. Water has an unusually high specific heat capacity ($4200\ \text{J kg}^{-1}\text{K}^{-1}$), which is why it is an effective coolant and moderates climate.

Specific latent heat

The specific latent heat $L$ of a substance is the energy required to change the state of $1\ \text{kg}$ of it without any change in temperature:

• The specific latent heat of fusion applies to melting and freezing.
• The specific latent heat of vaporisation applies to boiling and condensing.

The latent heat of vaporisation is generally much larger than that of fusion, because separating molecules completely (liquid to gas) requires more energy than loosening them (solid to liquid).

Why temperature is constant during a change of state

During melting or boiling, the supplied energy goes into increasing the molecular potential energy by breaking or weakening intermolecular bonds, not into increasing molecular kinetic energy. Since temperature measures average molecular kinetic energy, the temperature stays constant until the change of state is complete.

Multi-stage problems

Heating a substance through a phase change requires adding the energies for each stage in turn: temperature change ($mc\Delta\theta$), then change of state ($mL$), then any further temperature change. A heating curve (temperature against energy supplied) shows sloping sections (temperature rising) separated by flat plateaus (state changing at constant temperature).

Examples in context

Example 1. Why sweating cools you. As sweat evaporates from your skin, it absorbs its latent heat of vaporisation from your body. Because that latent heat is large, even a small mass of evaporating sweat removes a significant amount of energy, cooling you efficiently. This is the same physics that makes steam burns more severe than hot-water burns.

Example 2. Climate moderation by the sea. Water's high specific heat capacity means coastal regions warm and cool more slowly than inland regions. The sea absorbs and releases large amounts of energy for modest temperature changes, smoothing out daily and seasonal extremes near the coast.

Try this

Q1. Define specific heat capacity and state its SI unit. [2 marks]

• Cue. Energy to raise the temperature of $1\ \text{kg}$ by $1\ \text{K}$; unit $\text{J kg}^{-1}\text{K}^{-1}$.

Q2. Find the energy to heat $0.40\ \text{kg}$ of aluminium ($c = 900\ \text{J kg}^{-1}\text{K}^{-1}$) from $25\ ^\circ\text{C}$ to $75\ ^\circ\text{C}$. [2 marks]

• Cue. $Q = mc\Delta\theta = 0.40 \times 900 \times 50 = 1.8 \times 10^4\ \text{J}$.

Q3. Explain, in terms of molecules, why the temperature of melting ice stays at $0\ ^\circ\text{C}$ while energy is supplied. [3 marks]

• Cue. The supplied energy increases molecular potential energy by breaking the bonds of the solid lattice, not the kinetic energy; since temperature measures average kinetic energy, it stays constant until melting is complete.