3.6.2.1ThermalCore

Thermal Energy Transfer

Why does the temperature of boiling water stay at exactly 100 °C while you keep heating it, right up until every last drop has turned to steam? The answer lies in what temperature actually measures at a microscopic level — and what "internal energy" means when a substance changes state rather than simply getting hotter.

40 min Video by Science Shorts 3.6.2 Thermal physics

Thermodynamics — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Describe internal energy as the sum of the random kinetic and potential energies of a substance’s particles
Explain what absolute zero represents in terms of particle motion
Use the specific heat capacity equation $Q = m c Δ θ$
Use the specific latent heat equation $Q = m L$ for melting/freezing and boiling/condensing
Explain why temperature stays constant during a change of state

Internal energy and absolute zero

The $internal energy$ of a substance is the sum of the random kinetic energies and potential energies of all its particles. Kinetic energy comes from the particles’ constant random motion (vibrating in a solid, or moving more freely in a liquid or gas); potential energy comes from the (electrostatic) bonds between particles, which can be stretched, broken or formed.

$Absolute zero$ (0 K, equal to $- 273.15°$ C) is the theoretical temperature at which particles have the minimum possible kinetic energy. Temperature on the Kelvin scale is directly related to the average random kinetic energy of a substance’s particles — a link explored fully in kinetic theory.

Tip — Kelvin and Celsius have the same size "degree" — only the zero point differs. To convert, just add (or subtract) 273: T(K) = θ(°C) + 273.

Specific heat capacity

The $specific heat capacity$ , $c$ , of a substance is the energy required to raise the temperature of 1 kg of it by 1 K (equivalently, 1 °C), measured in J kg⁻¹ K⁻¹. A substance with a high specific heat capacity (like water) needs a lot of energy to change its temperature much — which is exactly why water is used in central heating systems and why coastal regions have a milder climate than inland areas.

Q = m c Δ θ

Energy transferred to change temperature by Δθ.

1Temperature change:

Δ θ = 80 - 20 = 60

2Use

Q = m c Δ θ

Q = 0.50 \times 4200 \times 60

Answer

Q = 126000

J (126 kJ)

Specific latent heat

When a substance changes state — melting, freezing, boiling or condensing — energy is transferred, but the temperature does $not$ change during the process. All the energy goes into breaking (or forming) the bonds between particles, changing the substance’s $potential$ energy, rather than increasing (or decreasing) the particles’ kinetic energy. This is why the specific latent heat, rather than a simple temperature-rise calculation, applies during a change of state.

The $specific latent heat of fusion$ , $L_{f}$ , is the energy needed to change 1 kg of a substance between solid and liquid with no temperature change; the $specific latent heat of vaporisation$ , $L_{v}$ , is the corresponding energy for a change between liquid and gas. Vaporisation almost always needs far more energy than fusion for the same substance, because boiling must separate particles completely (breaking essentially all the intermolecular bonds), whereas melting only needs to loosen the rigid structure of a solid into a liquid.

Q = m L

Energy transferred during a change of state (no temperature change).

1Use

Q = m L

Q = 0.20 \times 2.26 \times 1 0^{6}

Answer

Q = 4.52 \times 1 0^{5}

J (452 kJ)

Tip — A multi-step heating problem (e.g. ice → water → steam) always alternates between mc∆θ (while temperature is changing) and mL (while state is changing, at constant temperature) — never mix the two into one calculation at once.

Equation recap

Q = m c Δ θ

Energy for a temperature change.

Q = m L

Energy for a change of state (constant temperature).

T (K) = θ (° C) + 273

Converting Celsius to Kelvin.

Common mistakes to avoid

Assuming temperature keeps rising while a substance is melting or boiling.

Temperature stays constant during any change of state — all the energy goes into changing potential energy (bonds), not kinetic energy.

Using the same latent heat value for melting and boiling of the same substance.

Specific latent heat of fusion and of vaporisation are different for the same substance — vaporisation is almost always much larger since it separates particles completely.

Trying to combine a temperature-change step and a state-change step into a single mcΔθ or mL calculation.

Handle each stage of a multi-step heating problem separately — Q = mcΔθ while temperature changes, Q = mL while state changes — then add the energies together.

Key takeaways

Internal energy is the sum of particles’ random kinetic and potential energies; absolute zero (0 K) is the minimum possible.
Specific heat capacity: Q = mcΔθ, the energy to change temperature.
Specific latent heat: Q = mL, the energy to change state at constant temperature.
Vaporisation needs more energy per kg than fusion, since boiling separates particles completely.

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Thermal Energy Transfer

40 min Video by Science Shorts 3.6.2 Thermal physics