A2 Level · Topic 14.3
A-Level 9702 / Topic 14 / A2

Warming, and changing state.

Two relations carry almost every thermal calculation: one for warming a substance, one for changing its state. Knowing which to use, and adding stages separately, is the whole skill.

The key idea

To warm a substance without a state change needs Q = mcΔθ. To change its state at constant temperature needs Q = mL. Both c and L are defined per unit mass.

melting boiling T energy in
Fig. 1 — Sloped sections (c: temperature rises) and flat plateaus (L: state changes at constant T) on a heating curve
Section 01

The heating curve tells the story.

Supply energy at a steady rate and the temperature climbs on the sloping parts and holds steady on the flat parts. The slopes are governed by the specific heat capacity; the plateaus, where the state changes, are governed by the specific latent heat. The simulation traces the whole curve from solid to gas.

Section 02

c and L, defined.

The specific heat capacity c is the energy needed to raise the temperature of one kilogram by one kelvin, so Q = mcΔθ. The specific latent heat L is the energy needed to change the state of one kilogram at constant temperature, so Q = mL. Vaporisation needs far more energy than fusion, because the molecules must be separated completely rather than merely freed from the lattice.

Stage 1 · Learn

Check what the sim just showed you

Four quick checks on c, L and the heating curve. Each correct answer earns XP and lights this skill on your star map.

Quick check+10 XP

The specific heat capacity of a substance is the energy needed to:

Quick check+10 XP

During a change of state the temperature stays constant because the supplied energy:

Quick check+10 XP

2.0 kg of water, of specific heat capacity 4200 J kg⁻¹ K⁻¹, is warmed by 5.0 K. The energy needed Q = mcΔθ is:

Quick check+10 XP

Compared with the specific latent heat of fusion, the specific latent heat of vaporisation of a substance is usually:

Examiner trap

Use Q = mcΔθ only while the temperature is changing and Q = mL only at a change of state. In a multi-stage problem (warm, then melt, then warm again) work out each stage separately and add. Remember c and L are per kilogram, so multiply by the mass, and Δθ in K equals Δθ in °C.

Skill unlocked

Specific heat and latent heat

This skill is now lit on your star map. Keep the chain going.

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