4.2.2 Calculating Specific Latent Heat

4.2.2 Calculating Specific Latent Heat: Use Eh = ml to find the energy for melting or boiling, and combine it with Eh = cmΔT for multi-stage problems.

The energy for a change of state depends only on the mass and the latent heat.

Relationship

Eh = ml, where Eh is the heat energy in joules, m is mass in kilograms and l is specific latent heat in J/kg.

Rearranged

l = Eh ÷ m finds the specific latent heat, and m = Eh ÷ l finds the mass changed.

No temperature term

There is no ΔT in this equation because the temperature does not change.

Choosing the value

Use the fusion value for melting and freezing and the vaporisation value for boiling and condensing.

Process	Latent heat used	Value for water (J/kg)
Melting ice	Fusion	3.34 × 10⁵
Boiling water	Vaporisation	22.6 × 10⁵

Calculations are straightforward once the correct stage is identified.

Examples

Melting ice

For 0.50 kg of ice at 0 °C: Eh = 0.50 × 3.34 × 10⁵ = 1.67 × 10⁵ J.

Boiling water

For 0.20 kg of water at 100 °C: Eh = 0.20 × 22.6 × 10⁵ = 4.52 × 10⁵ J.

Finding l

A 60 W heater running for 5.0 minutes supplies 18 000 J; if this melts 0.054 kg, l is about 3.3 × 10⁵ J/kg.

Heat losses

In experiments, some energy is lost, so the measured value of l is usually larger than the true value.

Break the process into separate heating and state-change steps.

Identify each stage, for example melting at 0 °C and then warming the liquid.

Use Eh = ml for each change of state, with the correct latent heat value.

Use Eh = cmΔT for each stage where the temperature changes.

Add the energies from all stages to find the total.

State the final answer with its unit and a sensible number of significant figures.

Question: Calculate the energy needed to change 0.20 kg of ice at 0 °C into water at 30 °C. (l fusion = 3.34 × 10⁵ J/kg, c water = 4180 J/kg °C.)

Melting: Eh = ml = 0.20 × 3.34 × 10⁵ = 66 800 J.
Warming the water: Eh = cmΔT = 4180 × 0.20 × 30 = 25 080 J.
Total = 66 800 + 25 080 = 91 880 J.

Answer: About 9.2 × 10⁴ J is needed.

4.2.2 – Key Points for the Exam

Eh = ml: Heat energy equals mass multiplied by specific latent heat.
Latent heat of fusion: Energy to melt or freeze a substance without a temperature change.
Latent heat of vaporisation: Energy to boil or condense a substance without a temperature change.
Multi-stage: A process with more than one stage, each needing its own calculation.

Common Mistakes

Using Eh = cmΔT while a substance is melting or boiling.
Choosing the vaporisation value when the question describes melting.
Forgetting to add the energy for warming the liquid in a multi-stage question.
Leaving the mass in grams.