Specific latent heat

CIE A-Level Physics· Unit 20: Thermal Physics· 10 min read

1. Core Definition of Specific Latent Heat★☆☆☆☆⏱ 4 min

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When a substance changes phase (solid to liquid, liquid to gas), heat energy is absorbed or released, but temperature does not change. This is because energy is used to break or form intermolecular bonds, not to change the average kinetic energy of molecules (which determines temperature).

📘 Definition

Specific Latent Heat

$L$

The amount of heat energy required to change the phase of 1 kilogram of a substance at constant temperature.

Example:

Water has two common specific latent heat values: one for melting, one for boiling.

Q = mL

- Specific latent heat of fusion ( $L_{f}$ ): For solid ↔ liquid phase change. For water, $L_{f} = 3.34 \times 1 0^{5}$ J kg⁻¹.
- Specific latent heat of vaporization ( $L_{v}$ ): For liquid ↔ gas phase change. For water, $L_{v} = 2.26 \times 1 0^{6}$ J kg⁻¹.

📐 Worked Example

How much heat energy is required to melt 250 g of ice at 0°C? Specific latent heat of fusion of ice is $3.34 \times 1 0^{5}$ J kg⁻¹.

1
Convert mass from grams to kilograms:
2
$m = 250 \text{ g} = 0.25 \text{ kg}$
3
Substitute into the formula $Q = m L_{f}$ :
4
$Q = 0.25 \times 3.34 \times 10^5 = 8.35 \times 10^4 \text{ J}$
5
83500 J of heat is required to melt the ice.

2. Solving Calorimetry Problems★★★☆☆⏱ 6 min

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Most CIE calculation problems use the principle of energy conservation: for an insulated system, heat lost by a hot substance equals heat gained by the substance undergoing phase change. We combine $Q = m L$ for phase change with $Q = m c Δ T$ for temperature changes.

📐 Worked Example

A 50 g block of ice at 0°C is added to 200 g of water at 40°C in an insulated container. Find the final temperature of the mixture, assuming no heat loss. $c_{w a t er} = 4200$ J kg⁻¹ °C⁻¹, $L_{f, i ce} = 3.34 \times 1 0^{5}$ J kg⁻¹.

1
Convert all masses to kg: $m_{i ce} = 0.05$ kg, $m_{h o t w a t er} = 0.2$ kg
2
Heat gained by ice = heat to melt ice + heat to warm melted ice to final temperature $T$ :
3
$Q_{gained} = m_{ice}L_f + m_{ice}c(T - 0)$
4
Heat lost by hot water cooling from 40°C to $T$ :
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$Q_{lost} = m_{hot\text{ }water}c(40 - T)$
6
Equate heat lost and heat gained:
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$0.2 \times 4200 (40-T) = 0.05 \times 3.34 \times 10^5 + 0.05 \times 4200 T$
8
Expand and solve for $T$ :
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$33600 - 840T = 16700 + 210T \\ 16900 = 1050T \\ T \approx 16.1^\circ \text{C}$

3. Experimental Measurement for Practical Exams★★☆☆☆⏱ 5 min

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CIE practical exams frequently ask to describe experiments to measure specific latent heat. The standard method uses an electrical heater to supply a known amount of energy, then measures the mass of substance that changes phase.

For measuring the specific latent heat of vaporization of water, an immersed electrical heater supplies energy to boiling water. The energy supplied is $V I t$ , where $V$ = voltage, $I$ = current, $t$ = time. If $m$ is the mass of steam condensed, then assuming no heat loss: $V I t = m L_{v}$ , so $L_{v} = \frac{V I t}{m}$ .

📐 Worked Example

A 50 W heater is run for 10 minutes to boil water. 13 g of water is converted to steam. Calculate $L_{v}$ from this data.

1
Calculate total energy supplied by the heater:
2
$E = Pt = 50 \times (10 \times 60) = 30000 \text{ J}$
3
Convert mass of steam to kg:
4
$m = 13 \text{ g} = 0.013 \text{ kg}$
5
Rearrange $E = m L$ to solve for $L_{v}$ :
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$L_v = \frac{E}{m} = \frac{30000}{0.013} \approx 2.3 \times 10^6 \text{ J kg}^{-1}$

4. Common Pitfalls

Wrong move:

Using mass in grams instead of kilograms

Why:

Specific latent heat is defined per kilogram, so using grams will give an energy result 1000 times too small

Correct move:

Always convert mass to kilograms before substituting into $Q = m L$ by dividing grams by 1000

Wrong move:

Adding a temperature change term for the phase change itself

Why:

Temperature is constant during phase change, so no temperature change occurs for the phase transition

Correct move:

Only use $Q = m L$ for the phase change, add $Q = m c Δ T$ separately for any temperature change before or after the phase change

Wrong move:

Mixing up $L_{f}$ and $L_{v}$ values for water

Why:

More intermolecular bonds are broken when turning liquid to gas than solid to liquid, so $L_{v}$ is much larger than $L_{f}$

Correct move:

Remember $L_{f} \approx 3.3 \times 1 0^{5}$ J kg⁻¹ and $L_{v} \approx 2.3 \times 1 0^{6}$ J kg⁻¹, a full order of magnitude difference

Wrong move:

Claiming experimental heat loss leads to a lower calculated $L$

Why:

Heat lost means less mass changes phase for the energy input, so the calculated value is higher than the true value

Correct move:

For electrical heating experiments, unaccounted heat loss always gives a higher calculated value of specific latent heat

5. Quick Reference Cheatsheet

Quantity	Symbol	Formula/Rule	Value for water
Specific latent heat	$L$	$Q = m L$ , units J kg⁻¹
Latent heat of fusion	$L_{f}$	Solid ↔ liquid phase change	$3.34 \times 1 0^{5}$ J kg⁻¹
Latent heat of vaporization	$L_{v}$	Liquid ↔ gas phase change	$2.26 \times 1 0^{6}$ J kg⁻¹
Calorimetry principle		Heat lost = Heat gained (insulated system)
Electrical experiment		Energy supplied = $V I t = m L$

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 11
MCQ: Mass of ice melted by steam
2022 · 22
Calculate latent heat of vaporization
2021 · 13
MCQ: Temperature during melting

Going deeper

simulationPhET Phase Change SimulationVisualize constant temperature during phase change

What's Next

Specific latent heat is a foundational thermal physics concept that underpins advanced topics including entropy, heat engines, and thermal energy transfer in engineering systems. It is regularly combined with specific heat capacity in mixed calculation questions across Papers 1, 2 and 3 of CIE 9702. Mastering this sub-topic prepares you for more complex calorimetry problems and practical assessment questions. Next, you can explore related thermal physics concepts or deepen your practical skills for A-Level exams.