Specific Latent Heat

1. Definitions (Must Know)

Specific latent heat, l (J kg⁻¹), is the energy required per unit mass to change the state of a substance without changing its temperature: l = Q/mqquador Q = ml

• lf: specific latent heat of fusion, for solid–liquid changes.
• lᵥ: specific latent heat of vaporisation, for liquid–gas changes.

2. Key Ideas (What Earns Marks)

• During a phase change of a pure substance at fixed pressure, energy changes microscopic potential energy while the temperature remains constant.
• Melting and vaporisation require energy transfer to the substance; freezing and condensation transfer energy from it.
• Use Q = ml only for the phase-change stage.
• Use Q = mcΔ T before or after the phase change when temperature changes.
• In a multi-stage process, calculate each energy term separately and then add them.

3. Detailed Explanations

A. Why temperature stays constant

Temperature is proportional to mean microscopic kinetic energy. During melting or boiling, the transferred energy changes the arrangement and separation of particles, increasing microscopic potential energy rather than mean kinetic energy. The temperature therefore stays constant until the phase change is complete.

B. Energy balance with ice or steam

For ice initially below 0circC that becomes water above 0circC, write separate terms: Q = m cᵢcₑ(0-Tᵢ) + mlf + m cwₐₜₑᵣ(Tf-0)

Do not combine these into one mcΔ T expression because the state and relevant property change.

4. Common Mistakes

• Saying energy is used to increase kinetic energy during a constant-temperature phase change.
• Using grams with l in J kg⁻¹.
• Omitting the warming or cooling that occurs before and after the phase change.
• Assuming every plateau on a measured curve is perfectly horizontal despite heat loss or changing power.

5. Exam Tips

• Sketch the sequence of states and label the temperature at each boundary.
• Write one energy term per stage.
• State whether each part gains or loses energy before forming the balance.
• Check units: kgtimesJ kg⁻¹ = J.

6. Worked Examples

Example 1: Melting ice at its melting pointCore

Find the energy needed to melt 35 g of ice at 0circC if lf = 3.34 × 10⁵ J kg⁻¹.

Show Answer

Q = mlf = (0.035)(3.34 × 10⁵) = 1.17 × 10⁴ J

Example 2: Warm ice, melt it, then warm the waterCore

0.050 kg of ice at -10circC becomes water at 20circC. Use cᵢcₑ = 2.1 × 10³ J kg⁻¹ K⁻¹, lf = 3.34 × 10⁵ J kg⁻¹ and cwₐₜₑᵣ = 4.2 × 10³ J kg⁻¹ K⁻¹.

Show Answer

Q = m cᵢcₑ(10) + mlf + m cwₐₜₑᵣ(20); = (0.050)(2100)(10) + (0.050)(3.34 × 10⁵) + (0.050)(4200)(20); = 2.20 × 10⁴ J

7. Mind Stretchers

Mind stretcher 1: Test for incomplete meltingExtension

5.0 kJ is supplied to 0.020 kg of ice at 0circC. Does all the ice melt? Use lf = 3.34 × 10⁵ J kg⁻¹.

Show Answer

Melting all the ice requires mlf = (0.020)(3.34 × 10⁵) = 6.68 kJ Only 5.0 kJ is available, so some ice remains and the equilibrium mixture stays at 0circC in the ideal model.

8. Practice, Quiz and Next Step

Close your notes and use Specific Latent Heat in the supplied context below. This requires a constructed explanation or working, not recognition of an option.

Fresh context: An unfamiliar data set or physical system requires you to apply Specific Latent Heat while stating the model, regime and assumptions.

1. Retrieve: define specific latent heat in your own words, including units, sign or conditions where relevant.
2. Represent: Choose and label an appropriate diagram, graph, table or symbolic model; derive or justify the relationship used.
3. Apply: Reach a conclusion, then evaluate it using units, uncertainty, a limiting case and one practical or modelling limitation.

Check the response before looking back

• The model, regime, coordinates and assumptions are explicit.
• The derivation or multi-step reasoning is visible rather than implied.
• The conclusion is tested against units, data quality and a limiting case.
• A practical control, uncertainty or model limitation is evaluated where applicable.

If one check fails, name that exact gap, revisit the matching explanation or worked example, and redo the task with different values or a different situation. Then use theA-Level Physics course hub orpractice browser for an independent re-test.