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Thermal physics is the study of heat, temperature and the microscopic motion of atoms and molecules that underlies both. It is one of the most successful branches of physics, and it bridges everyday observations — ice melting, water boiling, a cup of tea cooling on your desk — with the atomic theory of matter. Module 5.1 (Thermal physics) of the OCR A-Level Physics A specification (H556) asks you to master the ideas of temperature, internal energy, specific heat capacity, latent heat, the ideal gas laws and the kinetic theory of gases. In this first lesson we lay the foundations: what we actually mean by temperature, and the idea of thermal equilibrium that makes temperature a well-defined physical quantity at all.
Temperature is one of those concepts that feels perfectly familiar until you are asked to define it. Everyone knows that a hot object has a higher temperature than a cold object, and everyone knows that a thermometer measures temperature. But what is temperature, as a physical quantity?
At A-Level we adopt the following operational definition:
Temperature is a measure of the average random kinetic energy of the particles in a substance.
In a gas, where the molecules are in free flight, this kinetic energy is almost entirely translational — the molecules move bodily through space. In a solid, where atoms vibrate about fixed lattice positions, it is vibrational. In a liquid, it is a mixture. In every case, however, a higher temperature means that the particles are moving more energetically on average.
This is a statistical definition. You cannot assign a temperature to a single molecule; temperature is a property of a large collection of particles whose motions, when averaged, give a well-defined mean. A single air molecule whizzing through a vacuum does not have a temperature. A balloon full of them does.
Imagine placing a hot cup of tea on a cold kitchen worktop. Over time, the tea cools, the worktop warms slightly, and eventually both settle to a common temperature close to that of the surrounding room. At this point, no further net transfer of thermal energy takes place between the tea, the worktop and the air. We say that the system has reached thermal equilibrium.
Thermal equilibrium: Two objects are in thermal equilibrium when there is no net transfer of thermal energy between them. This occurs when, and only when, they are at the same temperature.
Notice the words "no net transfer". Energy may still be exchanged at the microscopic level — individual molecules of tea collide with the cup, individual air molecules collide with the worktop — but the energy flowing one way exactly balances the energy flowing the other. On the macroscopic scale, nothing appears to change.
Thermal equilibrium obeys a beautifully simple rule known as the zeroth law of thermodynamics:
If body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C, then body A is in thermal equilibrium with body C.
This sounds trivial, but it is the logical foundation of thermometry. It guarantees that "being at the same temperature" is a transitive relation, which means we can label every body with a single number — its temperature — and use that number to predict whether heat will flow if two bodies are brought into contact.
Without the zeroth law, the very idea of a thermometer would not work. When you place a thermometer under your tongue, you rely on the thermometer and your tongue reaching thermal equilibrium. If you then place the same thermometer in a bowl of soup and it reads the same temperature, you know — by the zeroth law — that the soup and your tongue are also in thermal equilibrium: a reassuring result, because it means the soup is at body temperature.
When two bodies at different temperatures are placed in thermal contact, thermal energy always flows from the hotter body to the cooler body. It does not flow the other way on its own. You can, with effort, push heat "uphill" from cold to hot, but only by doing work on the system (that is how a refrigerator works); left to itself, heat flows downhill in temperature.
This one-way direction of heat flow is a consequence of the second law of thermodynamics, which you will meet in more depth at university. At A-Level, simply remember:
Heat flows from high temperature to low temperature — never spontaneously the other way.
graph LR
A[Hot body<br/>T_H] -- net Q --> B[Cold body<br/>T_C]
B -- smaller Q --> A
A -. thermal contact .-> B
Both bodies radiate, conduct and convect energy to the other, but the net flow is always from hot to cold until the two temperatures are equal.
Although they are not examined in detail in Module 5.1, it is worth remembering the three ways thermal energy can move from one place to another. You will meet them again in applied contexts throughout the course.
graph TD
HT[Heat transfer] --> CD[Conduction<br/>through direct<br/>particle contact]
HT --> CV[Convection<br/>bulk motion of<br/>a fluid]
HT --> RD[Radiation<br/>electromagnetic<br/>waves]
CD --> S1[Solids especially<br/>metals]
CV --> S2[Liquids and gases]
RD --> S3[Requires no medium —<br/>works in a vacuum]
Two temperature scales are important for A-Level work.
The Celsius scale is based on two historical fixed points: the freezing point of pure water at atmospheric pressure (0 °C) and its boiling point at atmospheric pressure (100 °C). It is convenient for everyday life — the weather forecast is in Celsius, and you bake a cake at 180 °C — but it is not a fundamental scale. Its zero is an arbitrary choice (the freezing point of water), and negative Celsius temperatures are perfectly physical.
The Kelvin scale (also called the absolute scale) is the SI unit of temperature. It is defined so that its zero — called absolute zero — corresponds to the lowest possible temperature: the temperature at which, classically, all molecular motion would cease. The size of one kelvin is chosen to be exactly the same as the size of one Celsius degree, so temperature differences in K and °C are numerically identical.
Key fact: Absolute zero is
0K, which corresponds to-273.15°C. For A-Level calculations we often use-273°C.
The relationship between the two scales is:
T(K) = θ(°C) + 273.15
where T is the temperature in kelvin and θ (theta) is the same temperature in Celsius. The OCR data sheet writes this in the slightly simpler form T/K = θ/°C + 273.
| Situation | Celsius (°C) | Kelvin (K) |
|---|---|---|
| Absolute zero | -273.15 | 0 |
| Dry ice sublimation | -78.5 | 194.65 |
| Water freezes | 0 | 273.15 |
| Body temperature | 37.0 | 310.15 |
| Room temperature | 20.0 | 293.15 |
| Water boils | 100.0 | 373.15 |
| Iron melts | 1538 | 1811.15 |
Notice how the difference between two temperatures has the same numerical value in both scales. The difference between boiling and freezing water is 100 °C = 100 K, not 100 °C = 373 K — K and °C have the same size of unit.
Exam Tip: OCR examiners always expect you to use kelvin in gas law and kinetic theory calculations.
pV = nRTandpV = NkTboth requireTin kelvin. Using Celsius will give you nonsense — a negative answer forpV, for example, ifθhappens to be below zero. Train yourself to convert immediately on reading the question.
The Kelvin scale is sometimes called the absolute scale because its zero is not arbitrary but is the theoretical limit of the lowest possible temperature. In the classical picture, at absolute zero every molecule would be completely stationary: the average kinetic energy would be zero, and since it cannot be negative (kinetic energy is non-negative by definition), nothing colder is possible.
Modern quantum theory modifies this picture slightly. Even at 0 K, a small zero-point energy remains due to the uncertainty principle — molecules cannot be completely stationary in both position and momentum. But the zero-point energy is not thermal, and the macroscopic conclusion stands: 0 K is the lowest temperature a system can approach. In practice, laboratories have cooled atoms to within a few billionths of a kelvin, but never reached absolute zero.
A lump of metal has a temperature of θ = 85 °C. Express this in kelvin.
T = θ + 273.15
T = 85 + 273.15
T = 358.15 K
For most A-Level calculations, we would round and quote this as 358 K (three significant figures).
Liquid nitrogen boils at 77 K. What is this temperature in Celsius?
θ = T - 273.15
θ = 77 - 273.15
θ = -196.15 °C
This is very cold indeed — cold enough to flash-freeze a banana and shatter it like glass.
A copper block is heated from 20 °C to 95 °C. What is the temperature change in kelvin?
Δθ = 95 - 20 = 75 °C
ΔT = 75 K
The temperature difference is 75 K, numerically identical to 75 °C, because one kelvin and one Celsius degree are the same size. This is why the specific heat capacity equation E = mcΔθ, which involves only a difference, can be used interchangeably with Δθ in K or °C — even though absolute temperatures must be in kelvin.
A cup of tea at 80 °C is left on a desk in a room at 20 °C. Over time, the tea cools until it reaches 20 °C and then stops cooling. At every instant, heat flows from the (hotter) tea to the (cooler) air — via conduction through the cup, convection in the air around the cup, and infrared radiation. The rate of heat loss is approximately proportional to the temperature difference (Newton's law of cooling, which you may have met at GCSE). As the tea cools, the difference narrows, and the rate of cooling slows. Eventually, equilibrium is reached.
If you pour 1 kg of water at 80 °C into 1 kg of water at 20 °C, the final temperature of the mixture (assuming no heat loss to the surroundings) is the average, 50 °C. At this point the two bodies of water are in thermal equilibrium: no further heat flow, same temperature throughout. In Lesson 3 you will see exactly how to calculate this using specific heat capacity.
A mercury-in-glass thermometer is used to measure the temperature of 10 cm³ of a hot liquid. Once placed in the liquid, the thermometer warms up while the liquid cools slightly. Equilibrium is reached when both are at the same temperature. But this common equilibrium temperature is slightly lower than the liquid was to begin with, because the thermometer has absorbed some heat from it. This is one reason why thermometers are designed to have a very small thermal capacity — you want them to reach thermal equilibrium with the measured body without significantly changing its temperature.
We have given an operational definition of temperature (what a thermometer measures) and a statistical definition (average random kinetic energy). The link between them is deep: you are seeing the bridge between macroscopic physics (thermometers, hot and cold bodies) and microscopic physics (molecules bouncing around). The two pictures are perfectly consistent, as we shall see in detail when we derive
(1/2) m <c²> = (3/2) k T
in Lesson 10. For now, the crucial point is that temperature is not the same thing as the total energy of a body. A bathtub of water at 30 °C contains more internal energy than a teacup of water at 90 °C, because although the tea particles are moving faster on average, there are vastly more particles in the bath. Temperature measures the average energy per particle, not the total energy.
pV = nRT is a hard rule: T must be in kelvin. Using T = 25 instead of T = 298 gives an answer 12 times too small.T(K) = θ(°C) - 273. The sign is wrong. Kelvin is always bigger by 273 (for positive Celsius temperatures). Check: water freezes at 0 °C = 273 K, not at 0 °C = -273 K.0 K is the temperature at which the system is in its quantum ground state and has the lowest possible internal energy.A is in equilibrium with B and B is in equilibrium with C, then A is in equilibrium with C. This is what makes temperature a consistent physical quantity.0 K at absolute zero. The conversion is T(K) = θ(°C) + 273.15.In the next lesson we will connect temperature to internal energy — the total random kinetic and potential energy of the particles — and see how changes in internal energy underlie all of thermal physics.