A Level Physics: Temperature — Revision Notes

Condensed for the final weeks. For the full explanation, use the Temperature study guide.

What temperature actually measures

Temperature is a measure of the mean translational kinetic energy of the molecules — not the total energy, and not the amount of heat.

mean translational KE per molecule = (3/2) k T

This is why a cup of boiling water and a bath of warm water can hold very different amounts of thermal energy despite the cup being hotter. Temperature and thermal energy are different quantities, and conflating them is the most common conceptual error in the topic.

Thermal equilibrium

Two bodies are in thermal equilibrium when there is no net flow of thermal energy between them — which happens when they are at the same temperature.

Thermal energy flows from higher to lower temperature, not from higher to lower internal energy. A large cold object may hold far more internal energy than a small hot one, yet energy still flows from the hot object to the cold one.

Thermal equilibrium is what makes thermometry possible: a thermometer reads its own temperature, which equals the temperature of the body once equilibrium is established.

The thermodynamic scale

The thermodynamic (absolute) scale is defined independently of any material property. That independence is its whole advantage.

T / K = theta / C + 273.15

Two fixed points:

• Absolute zero, 0 K — the temperature at which substances have minimum internal (kinetic) energy — zero, per mean translational KE = (3/2)kT.
• Triple point of water, 273.16 K — the unique temperature and pressure at which ice, water and water vapour coexist in equilibrium.

The triple point is used rather than the melting point because it occurs at one unique pressure, so it is perfectly reproducible; a melting point varies with pressure.

A temperature interval is the same size in K and °C, so a change of 20 °C is a change of 20 K. Only absolute temperatures need converting — which is why ΔT can be left in °C in q = mcΔT, but T must be in kelvin in pV = nRT.

Empirical scales and thermometers

An empirical scale depends on a physical property that varies with temperature, calibrated between two fixed points. Different thermometric properties do not vary in the same way between the fixed points, so two empirical thermometers can agree at the fixed points and disagree everywhere between them. The thermodynamic scale has no such problem.

Thermometer	Property	Strengths	Limitations
Liquid-in-glass	Expansion of liquid	Cheap, direct reading, portable	Limited range, slow, low sensitivity, fragile
Thermocouple	E.m.f. from two junctions	Wide range, fast, small thermal capacity, remote reading	Non-linear, needs calibration
Resistance (platinum)	Resistance of a wire	Very accurate, wide range	Slow response, large thermal capacity
Thermistor	Resistance of a semiconductor	Very sensitive, fast	Narrow range, highly non-linear

Choosing a thermometer: small thermal capacity for rapidly changing temperatures (a thermocouple, because it absorbs little energy and so barely disturbs the system it measures); high accuracy where speed does not matter (platinum resistance); high sensitivity over a narrow range (thermistor).

Specific heat capacity and specific latent heat

Specific heat capacity c is the energy required to raise the temperature of unit mass of a substance by one degree, without a change of state:

Q = mcΔθ

Worked example: 500 g of water (c = 4200 J kg⁻¹ K⁻¹) heated from 20 °C to 80 °C requires Q = 0.500 × 4200 × 60 = 126,000 J.

Specific latent heat L is the energy required to change the state of unit mass of a substance without a change of temperature:

Q = mL

Fusion refers to melting/freezing; vaporisation refers to boiling/condensing. On a cooling curve (temperature against time), temperature falls steadily while the substance stays in one state, but is constant during a change of state, since the energy transferred is latent heat rather than energy that raises or lowers temperature.

Exam traps

• Saying molecules retain some residual motion at absolute zero — per mean translational KE = (3/2)kT, kinetic energy is exactly zero at 0 K.
• Converting an interval from °C to K by adding 273.
• Using °C in pV = nRT.
• Saying thermal energy flows from higher internal energy to lower.
• Treating temperature and thermal energy as the same quantity.
• Giving the melting point rather than the triple point as a fixed point.
• Forgetting that Q = mcΔθ only applies while the substance stays in one state — once melting or boiling starts, use Q = mL instead, since the temperature is no longer changing.
• Assuming a larger mass always needs more energy for the same temperature change — c varies hugely between substances, so a large mass of a low-c material can need less energy than a small mass of water.

Self-test

1. What does temperature measure?
2. Define thermal equilibrium and state the direction of energy flow.
3. Why is the triple point used as a fixed point rather than the melting point?
4. Is a change of 15 °C equal to a change of 15 K?
5. Why is a thermocouple preferred for rapidly changing temperatures?
6. Distinguish specific latent heat from specific heat capacity.
7. Why does temperature stay constant while a solid melts, even though energy is still being supplied?

Answers: 1. The mean translational kinetic energy of the molecules — not the total thermal energy. 2. No net flow of thermal energy between two bodies, which occurs when they are at the same temperature; energy flows from higher to lower temperature, regardless of internal energy. 3. The triple point occurs at one unique temperature and pressure, so it is perfectly reproducible, whereas a melting point varies with pressure. 4. Yes — intervals are identical on the two scales; only absolute temperatures differ, by 273.15. 5. It has a small thermal capacity, so it responds quickly and absorbs very little energy from the system being measured. 6. Specific latent heat is the energy needed to change state without a change of temperature, while specific heat capacity is the energy needed to change temperature without a change of state. 7. During melting the temperature stays constant because the energy supplied is latent heat, going into breaking intermolecular bonds rather than increasing mean translational kinetic energy.