Specific heat capacity and specific latent heat

These two quantities tell you how much energy is needed to change the temperature of a substance, or to change its state.

Specific heat capacity (c)

The energy required to raise 1 kg of a substance by 1 degree C (or 1 K).

Equation: Q = m c (delta theta)

Units: c is in J/kg/degree C (or J/kg/K).

Worked example: heat 0.50 kg of water (c = 4200 J/kg/degree C) from 20 to 80 degrees C.

• delta theta = 60 degrees C.
• Q = 0.50 x 4200 x 60 = 126 000 J = 126 kJ.

Water has a high specific heat capacity (4200) so it takes a lot of energy to warm — useful in central heating systems and as a coolant.

Specific latent heat (L)

The energy required to change the state of 1 kg of a substance with no temperature change.

Equation: Q = m L

• Specific latent heat of fusion (L_f): solid <-> liquid (melting / freezing).
• Specific latent heat of vaporisation (L_v): liquid <-> gas (boiling / condensing).

Units: L is in J/kg.

For water: L_f ~ 334 000 J/kg, L_v ~ 2 260 000 J/kg. Vaporisation is far higher because all intermolecular bonds must be broken.

Heating curve

When a solid is heated steadily, the temperature rises until the melting point. The line then flattens (energy goes into breaking bonds, not raising T) until all has melted. Temperature rises again to the boiling point, then flattens again until all has boiled.

WJEC exam tip

A common mistake is using m in grams. Specific heat capacity values for WJEC are quoted in J/kg/degree C, so mass MUST be in kilograms. Always convert before substituting.