Ch 3 · 2.2.1 Thermal Expansion of Solids, Liquids and Gases · O Level Physics 5054
Topic 3 of 9 in Thermal Physics — O Level Physics 5054 — 59 lessons.
Introduction
Railway tracks have small gaps between rails. Power lines sag more in summer. A tight metal jar lid loosens under hot water. All three come from one idea: most things expand (get bigger) when they are heated and contract (get smaller) when they cool. (Syllabus section 2.2.1.)
Key ideas — Why things expand: the particle explanation
When a substance is heated, its particles gain kinetic energy and move faster.
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. When the music is slow, everyone stays close together, just swaying slightly in their spots. This is like a solid: the people (particles) are packed tight and only vibrate around a fixed spot. As the music gets faster and more energetic, people start moving around more wildly, bumping into each other and pushing their neighbors further away to make room for their bigger movements. This is thermal expansion.
📖 Definitions
🔍 Worked example — Easy
A solid block of metal is heated. Using the particle model, explain why its volume increases.
🔍 Worked example — Standard
Convert a temperature of 35 ^circC to Kelvin.
🔍 Worked example — Exam-style
A liquid-in-glass thermometer is used. Explain why the liquid level rises when the bulb is placed in hot water, considering the relative expansion of solids and liquids.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Explain, in terms of particles, why the mercury level rises when the bulb is placed in hot water. [2] (b) State the relative order of magnitude of expansion for solids, liquids, and gases. [1] [3 marks]
Key ideas — Which expands most?
For the same temperature rise:
🧑🏫 Teacher's explanation
Imagine a crowded room of people. In a solid, everyone is standing shoulder-to-shoulder, holding hands tightly; even if they start dancing more vigorously (increasing temperature), they can't move very far from their neighbors. In a liquid, people are still close but are just brushing past each other; they have more room to move around when the music gets faster. In a gas, people are sprinting across a massive hall with huge gaps between them; even a small increase in speed sends them flying much further apart.
📖 Definitions
🔍 Worked example — Easy
A substance is heated from 20 ^circC to 70 ^circC. Convert the final temperature to Kelvin.
🔍 Worked example — Standard
Rank the following substances in order of increasing expansion for the same temperature rise: Iron (solid), Water (liquid), Helium (gas).
🔍 Worked example — Exam-style
A liquid-in-glass thermometer uses the expansion of mercury to measure temperature. If the mercury expands by 0.5 mm when heated, why does the mercury level rise in the narrow capillary tube?
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Explain, in terms of the motion and arrangement of particles, why the mercury level rises when the thermometer is placed in hot water. [2] (b) State the relative order of magnitude of expansion for solids, liquids, and gases. [1] [3 marks]
Key ideas — Consequences and applications
🧑🏫 Teacher's explanation
Imagine a crowd of people in a room. If everyone is standing still, they take up a certain amount of space. If everyone starts dancing wildly and moving their arms around, they will need more space to avoid bumping into each other. This is exactly what happens when you heat a substance. The particles gain kinetic energy and move more vigorously, pushing their neighbors further away. This increase in the average distance between particles is what we call thermal expansion.\n\nCrucially, not all substances expand by the same amount. Because the forces holding particles together differ, gases expand much more than liquids, and liquids expand much more than solids. Think of it as a hierarchy: gases are the most 'roomy' when excited, while solids are the most 'stubborn'.
📖 Definitions
🔍 Worked example — Easy
A temperature of 45 ^circC is measured. Convert this temperature to Kelvin.
🔍 Worked example — Standard
A metal bridge gap is 5.0 mm wide at 10 ^circC. If the temperature rises to 40 ^circC, calculate the new temperature in Kelvin.
🔍 Worked example — Exam-style
A student observes that a liquid in a thermometer expands significantly when placed in boiling water. Rank the expansion magnitude of a gas, a liquid, and a solid from largest to smallest.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — The liquid-in-glass thermometer
A thin glass tube with a bulb of liquid (mercury or coloured alcohol) at the bottom.
🧑🏫 Teacher's explanation
Imagine a crowd of people in a room. When it is cold, everyone stands close together, barely moving. As the room gets warmer, people start dancing and moving around more vigorously. Because they are moving more, they need more space, so they push outward, making the crowd spread across a larger area. This is exactly what happens to particles in a liquid when heated.
📖 Definitions
🔍 Worked example — Easy
A thermometer reads 25 ^circC. Convert this temperature to Kelvin.
🔍 Worked example — Standard
The temperature of a liquid is 350 K. Calculate the temperature in degrees Celsius.
🔍 Worked example — Exam-style
A liquid-in-glass thermometer is used to measure a substance. The liquid expands by 0.5 mm for every 1 ^circC rise. If the liquid level rises by 12.0 mm when the temperature increases, what is the change in temperature?
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — The kelvin scale
The kelvin scale starts at absolute zero (lesson 2.1.2). One kelvin is the same size as one degree Celsius, so only the starting point is different:
🧑🏫 Teacher's explanation
Imagine you are measuring the height of people. If you use a ruler starting from the floor, you get a standard measurement. But what if you measured height starting from a table? The 'size' of an inch remains the same, but the numbers change because your starting point changed. The Celsius scale is like measuring from a table (the freezing point of water), while the Kelvin scale is like measuring from the floor (absolute zero).\n\nIn physics, temperature is a measure of the average kinetic energy of particles. At 'absolute zero', particles have essentially stopped moving entirely. Because you cannot have less than zero motion, you cannot have a temperature lower than 0 K. This is why the Kelvin scale is called an 'absolute' scale. Because the 'step size' of one degree Celsius is exactly the same as one Kelvin, we don't say 'degrees Kelvin'; we just say 'Kelvin'.
📖 Definitions
🔍 Worked example — Easy
Convert a temperature of 25 ^circC to Kelvin.
🔍 Worked example — Standard
A liquid is cooled to 10 K. What is its temperature in degrees Celsius?
🔍 Worked example — Exam-style
The temperature of a gas increases from 300 K to 350 K. Calculate the temperature increase in degrees Celsius.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Worked example
Example 1. Convert 37 °C (body temperature) to kelvin.
🔍 Worked example — Easy
A chemist measures a liquid at 45 ^circC. Convert this temperature to Kelvin.
🔍 Worked example — Standard
The boiling point of oxygen is 90 K. Convert this temperature to degrees Celsius.
🔍 Worked example — Exam-style
A railway track is made of steel. Explain, in terms of particles, why the tracks must have small gaps between them to prevent buckling on a hot day.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) The particles gain kinetic energy and vibrate more strongly about their positions, so on average they move further apart; the rod expands. (2) In winter they contract; without slack they would be pulled tight and could snap. (3) The liquid in the bulb expands when heated, more than the glass does; it rises up the narrow tube, and the length of the column is read on a scale. (4) (a) 298 K; (b) 127 °C.