Specific Heat Capacity and Latent Heat

Specific heat capacity $c$ is the energy needed per unit mass per unit temperature rise: $Q=mc\Delta\theta$ . Water's $c$ is about $4200$ J kg⁻¹ K⁻¹. Specific latent heat $L$ is the energy needed per unit mass to change state at constant temperature: $Q=mL$ . Vaporisation needs much more energy than melting because molecules must be completely separated and push back the atmosphere.

Cambridge 9702 Paper 4Edexcel YPH11 WPH15AQA 7408 Paper 2≈ 35 minRevision 5 · updated 2026-10-27

Section 1 of 14

Learning objectives

Define specific heat capacity and use $Q=mc\Delta\theta$ .
Describe an electrical method to measure $c$ and its errors.
Define specific latent heat of fusion and vaporisation; use $Q=mL$ .
Explain why $L_v$ is much greater than $L_f$ .

Pause and think

Steam at $100$ °C gives a much worse burn than the same mass of boiling water at $100$ °C. Why?

Section 2 of 14

Core idea

Start hereIce in a drink

An ice cube keeps a drink cold far longer than the same mass of 0 °C water. Melting the ice soaks up a large amount of energy without any temperature change. That's latent heat.

The big idea

$E=mc\Delta\theta$ (temperature change); $E=mL$ (state change, constant temperature).

1. The heating curve

Heating curve: steady heater, 0.5 kg ice from −20 °C

The boiling plateau is much longer than melting: separating particles completely needs far more energy than loosening them.

E=mc\Delta\theta\qquad E=mL

$c$: specific heat capacity (J kg⁻¹ K⁻¹).
$L$: specific latent heat (J kg⁻¹).

Worked exampleIce from −20 °C to water at 0 °C

0.5 kg; $c_{\text{ice}}=2100$ , $L_f=3.34\times10^5$ .

Goal: Total energy.
Strategy: Warm, then melt.

$0.5\times2100\times20=21000\text{ J}$
Warm the ice to 0 °C.
$0.5\times3.34\times10^5=167000\text{ J}$
Melt at 0 °C.
$188000\text{ J}$
Add.

Answer

1.88\times10^5

✓ CheckMelting dominates ✓.

2. Measuring c

Worked exampleElectrical method

1.0 kg aluminium; heater 12 V, 4.0 A, 300 s; rise 15.6 K.

Goal: $c$ .
Strategy: $VIt=mc\Delta\theta$ .

$E=12\times4.0\times300=14400\text{ J}$
Electrical energy.
$c=\frac{14400}{1.0\times15.6}=923$
J kg $^{-1}$ K $^{-1}$ .

Answer

923

J kg

^{-1}

^{-1}

✓ CheckHeat losses make this an overestimate: insulate ✓.

Key takeawayWhy $L_v>L_f$ Melting loosens bonds; boiling separates molecules completely and pushes back the atmosphere.

Pause and think

Boil off 0.2 kg at 100 °C ( $L_v=2.26\times10^6$ )?

Summary

$mc\Delta\theta$ on slopes; $mL$ on plateaus.

Specific latent heat: Energy per kg to change state.

HistoryBlack's hidden heat. In the

1760

s Joseph Black noticed that melting ice absorbs heat without getting warmer, calling it "latent" (hidden) heat. His student James Watt used the idea to make steam engines far more efficient by condensing steam in a separate chamber.

Fun factWhy coastal cities are mild. Water's specific heat capacity is about five times that of rock and sand. Oceans warm and cool slowly, so seaside cities like Karachi have much smaller temperature swings between summer and winter than inland cities like Jacobabad.

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