Temperature

This guide covers Topic 14, Temperature, in full — subtopics 14.1 Thermal equilibrium, 14.2 Temperature scales and 14.3 Specific heat capacity and specific latent heat — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is A Level content and begins the thermal physics strand of the course.

Before studying this

This resource assumes energy conservation from Work, Energy and Power.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — A Level, Topic 14

14.1 Thermal equilibrium — understanding that thermal energy is transferred from a region of higher temperature to a region of lower temperature; understanding that regions of equal temperature are in thermal equilibrium.

14.2 Temperature scales — understanding that a physical property that varies with temperature can be used for the measurement of temperature, and identifying such properties; understanding that the thermodynamic (Kelvin) scale is the absolute scale, and that absolute zero is the temperature at which all substances have a minimum internal energy; converting between Kelvin and Celsius temperatures, T/K = θ/°C + 273.15.

14.3 Specific heat capacity and specific latent heat — defining and using specific heat capacity; defining and using specific latent heat, and distinguishing between specific latent heat of fusion and specific latent heat of vaporisation.

Thermal equilibrium

Thermal (internal) energy naturally flows from a region at higher temperature to a region at lower temperature. Two objects are said to be in thermal equilibrium when there is no net flow of thermal energy between them — this happens when, and only when, they are at the same temperature.

Temperature scales

Any physical property that changes measurably and consistently with temperature — for example the resistance of a metal wire, the e.m.f. of a thermocouple, the pressure of a gas at constant volume, or the density of a liquid — can be used as the basis of a thermometer.

The thermodynamic (Kelvin) scale is the absolute scale of temperature: it does not depend on the properties of any particular substance. Absolute zero (0 K) is the temperature at which a substance has the minimum possible internal energy. Kelvin and Celsius temperatures are related by:

T / K = θ / °C + 273.15

A change of 1 K is equal to a change of 1 °C — only the zero points of the two scales differ.

What temperature measures at the molecular level

Temperature is a measure of the mean kinetic energy of the molecules of a substance, not the total thermal energy it contains. A large volume of lukewarm water can hold far more total thermal energy than a small volume of boiling water, even though the boiling water is at a much higher temperature — because thermal energy depends on both temperature and the total number of molecules present, while temperature depends only on their mean kinetic energy.

Absolute zero and the triple point of water are the two fixed points that define the thermodynamic scale in practice. Absolute zero (0 K) needs no reference substance, since it is the temperature at which a substance reaches its minimum possible internal energy. The triple point of water, 273.16 K, is used as the second fixed point rather than the ordinary melting point of ice, because the triple point occurs at one unique combination of temperature and pressure at which ice, water and water vapour coexist in equilibrium, making it perfectly reproducible; the melting point, by contrast, varies with pressure and so cannot fix a scale precisely.

Types of thermometer

Different physical properties are used as the basis of practical thermometers, each with different strengths:

Thermometer	Property measured	Strengths	Limitations
Liquid-in-glass	Expansion of a liquid	Cheap, direct reading, portable	Limited range, slow response, low sensitivity
Thermocouple	E.m.f. generated at a junction of two metals	Wide range, fast response, small thermal capacity, can be read remotely	Non-linear, needs calibration
Resistance thermometer (platinum)	Resistance of a metal wire	Very accurate, wide range	Slow response, large thermal capacity
Thermistor	Resistance of a semiconductor	Very sensitive, fast response	Narrow range, highly non-linear
Constant-volume gas thermometer	Pressure of a gas at constant volume	Very wide range, most accurate, closest to the thermodynamic scale	Bulky, slow response, not portable

The choice of thermometer depends on what the measurement requires: a thermocouple is preferred for a rapidly changing temperature, because its small thermal capacity means it absorbs very little energy from the system and so barely disturbs what it is measuring; a platinum resistance thermometer is preferred where high accuracy matters more than speed; and a thermistor is preferred where high sensitivity over a narrow range of temperatures is needed.

Specific heat capacity

Specific heat capacity c of a substance is the energy required to raise the temperature of unit mass of the substance by one degree (kelvin or Celsius, since the two scales have the same size interval), without a change of state:

Q = mcΔθ

Worked example. 500 g of water (c = 4200 J kg⁻¹ K⁻¹) is heated from 20 °C to 80 °C. Energy required:

Q = mcΔθ = 0.500 × 4200 × (80 − 20) = 126,000 J = 126 kJ

Specific latent heat

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

Q = mL

Latent heat of fusion refers to melting/freezing; latent heat of vaporisation refers to boiling/condensing. On a cooling curve (temperature against time as a substance cools), the temperature falls steadily while the substance remains in a single state, but stays constant during a change of state, since the energy transferred is latent heat rather than energy that changes the temperature.

Common mistakes

• Applying Q = mcΔθ across a change of state — heat capacity equations and latent heat equations apply to different regions of a heating/cooling curve and must not be combined into one calculation without splitting the process into stages.
• Forgetting that a temperature change of 1 K equals a temperature change of 1 °C — only the fixed points differ, not the interval size.
• Assuming a substance’s temperature keeps rising while it is changing state — it remains constant until the change of state is complete.
• Confusing specific heat capacity (J kg⁻¹ K⁻¹) with specific latent heat (J kg⁻¹) — check units and whether a state change is involved.

Quick revision checklist

• Thermal equilibrium: no net energy flow when temperatures are equal
• T/K = θ/°C + 273.15, and why the Kelvin scale is absolute
• Q = mcΔθ for specific heat capacity
• Q = mL for specific latent heat, and the flat regions of a cooling curve

Related resources

• Gravitational Fields — the previous A Level topic
• Ideal Gases — the next A Level topic
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.