Chapter 6 of 8

All 8 chapters
  1. 1The particle model, readunderstood
  2. 2Evidence for particles, readunderstood
  3. 3Changes of state, readunderstood
  4. 4Diffusion and temperature, readunderstood
  5. 5Gas pressure, readunderstood
  6. 6Expanding and shrinking, readunderstood
  7. 7Dissolving and solutions, readunderstood
  8. 8Density, readunderstood

S3.5.6 Chapter 6

Expanding and shrinking

Why do railway lines have small gaps between them?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Explain why things expand when heated, using particles
  • Explain why bridges and railway lines have small gaps

Some railway lines have small gaps between the rails. Many bridges have gaps in their road. Why leave a gap in something that should be joined?

Most solids, liquids and gases get bigger when they are heated. They expand. When they cool, they get smaller. They contract.

Draw it first

Draw two rails, cold and hot

  1. Two pictures of the same two rails, side by side. Each rail is a block of circles in two rows, fixed to a thick post at the outer end. In the picture labelled cold, the circles touch, and there is a wide gap between the rails. In the picture labelled hot, the circles are the same in number but a little further apart, each rail is longer, and the gap is smaller. Labels: gap, cold, gap, hot. The picture is drawn much bigger than real life.gapcold

    1 Draw two rails end to end, fixed at the outer ends. Make each rail two rows of touching circles. Leave a gap between them.

  2. Two pictures of the same two rails, side by side. Each rail is a block of circles in two rows, fixed to a thick post at the outer end. In the picture labelled cold, the circles touch, and there is a wide gap between the rails. In the picture labelled hot, the circles are the same in number but a little further apart, each rail is longer, and the gap is smaller. Labels: gap, cold, gap, hot. The picture is drawn much bigger than real life.gapcoldgaphot

    2 Draw them again, hot. Use the same number of circles, but set them a little further apart. Each rail is longer, so the gap is smaller.

The picture is drawn much bigger than real life, so that you can see it. In a real hot rail the particles are still almost touching. They vibrate harder and sit a tiny bit further apart.

Heat gives the particles energy. In a solid, each particle vibrates harder. It shakes a little further from its place and pushes on its neighbours. So the average space between particles grows, and the whole rail gets longer.

The particles do not get bigger. The same particles are just a little further apart. Cool the rail and they come back together.

Liquids expand too. Gases expand much more than solids, because their particles are free to fly further apart.

Two liquid thermometers side by side with a scale in degrees Celsius from 0 to 100. In the one labelled cold water, the dark liquid stands at 10 °C. In the one labelled hot water, the dark liquid stands higher, at 70 °C. Labels: cold water, hot water, 0, 20, 40, 60, 80, 100, °C.020406080100°Ccold water020406080100°Chot water
The liquid in a thermometer expands as it warms, so it climbs the tube.
A long hatched bar for a steel rail, with a line above it marked 10 m. At its right end a small dark piece shows how much it grows, labelled grows 6 mm. The label not to scale says the growth is drawn far too big. Labels: 10 m, grows 6 mm, not to scale.10 mgrows 6 mmnot to scale
The growth is small. It is drawn much too big, so that you can see it.

The change is small. A steel rail 10 m long grows about 6 mm when it warms by 50 °C. That is about the width of a pencil.

A longer rail has more particles in a row, so it grows more. Double the length and the growth doubles.

Long cables between poles expand too. In the heat a cable is longer, so it hangs lower.

Two pairs of poles with a cable between each pair. On the cold day the cable sags a little. On the hot day the same cable is longer and sags more. Labels: cold day, hot day. The sag is drawn bigger than in real life.cold dayhot day
A longer cable between two fixed poles must hang lower. The sag is drawn bigger than in real life.

Engineers leave gaps so that hot rails do not push on each other and bend. The gaps in a bridge do the same job. Some modern lines have no gaps. Their rails are welded and held firmly in place.

See it three ways

With things

A metal lid is stuck on a jar. Hot water poured over the lid makes it a little bigger, and it comes loose.

As a picture

A bar chart of how much a steel rail grows when it warms by 50 degrees, in millimetres. The bars for 10 m, 20 m and 30 m reach 6, 12 and 18. Labels: 10 m, 20 m, 30 m, growth in mm.0510152010 m20 m30 mgrowth in mm

In words

A longer rail has more particles in a row. Each pair moves a little further apart, so the rail grows by more.

In symbols

10 m grows 6 mm. 20 m grows 12 mm. 30 m grows 18 mm.

Try it

Warm the air in a bottle

You need: a plastic bottle, a balloon, two bowls, cold water, hot water from a grown up.

Be safe: A grown up must pour the hot water. Use hot, not boiling, water, because it can soften the bottle. Use a plastic bottle, never glass.

  1. Stretch the balloon over the neck of the empty bottle. The bottle holds air.
  2. Stand the bottle in a bowl of cold water. Wait a minute. Look at the balloon.
  3. Move the bottle into a bowl of hot, not boiling, water that a grown up pours. Wait a minute. Look at the balloon.

What you will see: In the hot water, the balloon stands up and swells a little. The air in the bottle got warmer and expanded. Put the bottle back in cold water and the balloon goes limp again.

If you cannot try it, this is what happens.
Two plastic bottles, each standing in a bowl of water, with a balloon over its neck. In the bowl labelled cold water, the balloon is limp. In the bowl labelled hot water, the balloon stands up and is a little bigger. Labels: cold water, hot water.cold waterhot water

A wrong idea many people have

Things expand because their particles get bigger.

Why it feels right: The object gets bigger, so it seems each part of it must have grown.

The test that breaks it: If growing particles made things expand, a solid would grow most, because its particles touch. In fact the air in the bottle grows far more than a steel rail does. So it is the space between the particles that grows.

What is true: The particles stay the same size. They move or vibrate more, so the average space between them grows. A gas has much more empty space to gain, so it expands far more.

Key words

expand
get bigger when heated, because the particles move further apart.
contract
get smaller when cooled, because the particles move closer together.

Back to your guess

The answer is C: Rails get longer when they are hot, so they need room to grow.

Heat makes the particles vibrate harder and sit further apart, so the rail gets longer. The gap gives it room to grow.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Why do railway lines have small gaps between them?

    Tap your answer.

    1. Yes, that is right. Heat makes the particles vibrate harder and sit further apart. The rails expand and need room.

    2. Not this one. Rain is not the reason. The gaps are for the rails to grow into when they are hot. Go to S3.5.6. Try another.

    3. Not this one. Heat makes things expand, not shrink. The gaps give the rails room to grow. Go to S3.5.6. Try another.

    See the answer

    The rails grow longer when hot, and the gaps give them room.

    Heat makes the particles vibrate harder and sit further apart. The rails expand and need room.

    • If you chose B: Rain is not the reason. The gaps are for the rails to grow into when they are hot. Go to S3.5.6.
    • If you chose C: Heat makes things expand, not shrink. The gaps give the rails room to grow. Go to S3.5.6.

  2. A metal lid is stuck on a glass jar. A grown up pours hot water over the lid. Why does the lid come loose?

    Tap your answer.

    1. Not this one. Heat makes a lid expand, not contract. Cooling makes it contract. Go to S3.5.6. Try another.

    2. Not this one. Metal does not dissolve in water. The lid only gets a little bigger. Go to S3.5.6. Try another.

    3. Yes, that is right. The metal warms first. Its particles move further apart, so the lid is a little wider.

    See the answer

    The hot lid expands, so it fits more loosely.

    The metal warms first. Its particles move further apart, so the lid is a little wider.

    • If you chose A: Heat makes a lid expand, not contract. Cooling makes it contract. Go to S3.5.6.
    • If you chose B: Metal does not dissolve in water. The lid only gets a little bigger. Go to S3.5.6.

  3. A steel rail 10 m long grows 6 mm when it warms by 50 °C. How much does a rail 50 m long grow in the same warming?

    Tap your answer.

    1. Not this one. That is the growth of the 10 m rail. A longer rail has more particles in a row, so it grows more. Go to S3.5.6. Try another.

    2. Not this one. You multiplied by the length. The rail is 5 times as long, so it grows 5 times as much. Go to S3.5.6. Try another.

    3. Yes, that is right. The rail is 5 times as long, so it grows 5 times as much. 6 × 5 = 30.

    See the answer

    30 mm

    The rail is 5 times as long, so it grows 5 times as much. 6 × 5 = 30.

    • If you chose A: That is the growth of the 10 m rail. A longer rail has more particles in a row, so it grows more. Go to S3.5.6.
    • If you chose B: You multiplied by the length. The rail is 5 times as long, so it grows 5 times as much. Go to S3.5.6.

  4. Two steel rails, each 10 m long, meet at a gap. Their far ends are fixed. On a hot day each rail grows 6 mm toward the gap. How wide must the gap be, at the least, so that the rails do not touch?

    Tap your answer.

    1. Yes, that is right. Each rail grows 6 mm, and there are two rails. 6 + 6 = 12. The gap must be at least that wide.

    2. Not this one. You counted only one rail. There are two, and each one grows toward the gap. Go to S3.5.6. Try another.

    3. Not this one. The growth is in millimetres, not metres. The rails grow by a few millimetres only. Go to S3.5.6. Try another.

    See the answer

    12 mm

    Each rail grows 6 mm, and there are two rails. 6 + 6 = 12. The gap must be at least that wide.

    • If you chose B: You counted only one rail. There are two, and each one grows toward the gap. Go to S3.5.6.
    • If you chose C: The growth is in millimetres, not metres. The rails grow by a few millimetres only. Go to S3.5.6.

  5. Why do power cables hang lower on a hot day?

    Tap your answer.

    1. Not this one. The cables do not gain any matter. They expand, so they get longer. Go to S3.5.6. Try another.

    2. Yes, that is right. A longer cable between two fixed poles has to hang lower. Bridges have gaps for the same reason: they give the road room to grow.

    3. Not this one. The poles stay put. It is the cables that get longer when they are hot. Go to S3.5.6. Try another.

    See the answer

    The cables expand, so they are longer and sag more.

    A longer cable between two fixed poles has to hang lower. Bridges have gaps for the same reason: they give the road room to grow.

    • If you chose A: The cables do not gain any matter. They expand, so they get longer. Go to S3.5.6.
    • If you chose C: The poles stay put. It is the cables that get longer when they are hot. Go to S3.5.6.

  6. From an earlier chapter

    Sealed air in a box is heated. What happens to its pressure?

    Tap your answer.

    1. Not this one. The box is sealed, so the particles are no further apart. They move faster, so the pressure rises. Go to S3.5.5. Try another.

    2. Not this one. Faster particles hit harder and more often. The pressure changes. Go to S3.5.5. Try another.

    3. Yes, that is right. Heat gives the particles energy, so they move faster. Each hit is harder, and there are more hits.

    See the answer

    It goes up, because faster particles hit the walls harder and more often.

    Heat gives the particles energy, so they move faster. Each hit is harder, and there are more hits.

    • If you chose A: The box is sealed, so the particles are no further apart. They move faster, so the pressure rises. Go to S3.5.5.
    • If you chose B: Faster particles hit harder and more often. The pressure changes. Go to S3.5.5.

Keep it

Copy this into your exercise book.

Heating gives particles energy. They move further apart, so the material expands. The particles stay the same size. Cooling makes it contract. Gaps give rails room to grow.

Draw: Draw two rails with a wide gap and cold circles touching. Draw them hot, with circles further apart and a smaller gap.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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