Skip to content

Thermal expansion

Heat and matter · level 4, lesson 5 of 6

A question to start

Bridges have small gaps in them, and railway tracks used to have gaps between the rails. Why leave gaps on purpose?

The idea

Most things expand (grow a little) when they warm up, and contract when they cool. The particles jiggle more and push each other slightly further apart.

For a rod or beam of length \(L\), the change in length is

\[\Delta L = \alpha L\,\Delta T,\]

where \(\alpha\) (alpha) is the material's expansion coefficient.

Material \(\alpha\), per °C
Aluminium \(23\times10^{-6}\)
Steel \(12\times10^{-6}\)
Concrete about \(12\times10^{-6}\)
Glass (window) about \(9\times10^{-6}\)

Mars swings far between day and night, so its structures stretch and shrink far more each sol:

A 10 m aluminium beam outdoors Mars Earth
Day to night swing 58 °C (Viking 1 site) suppose 15 °C
Change in length 13 mm 3.5 mm
gap to grow intobridge deck

Worked examples

1. The Mars beam. \(\Delta L = 23\times10^{-6} \times 10 \times 58 = 0.013\) m, or 13 mm.

2. A steel railway rail. 25 m long, warming by 30 °C: \(12\times10^{-6} \times 25 \times 30 = 0.009\) m, 9 mm.

3. Over a year. Every sol on Mars, the beam grows and shrinks 13 mm. Joints that flex this much, hundreds of times a year, must be designed not to wear out or crack.

Try it

  1. Why do most materials expand when warmed?
  2. Find the change in length of a 2 m steel bar warmed by 100 °C.
  3. Why are concrete roads laid in slabs with small gaps between them?
  4. A Mars greenhouse frame is aluminium with glass panels. Why might that cause trouble each night?
Answers
  1. Their particles jiggle more and push slightly further apart.
  2. \(12\times10^{-6} \times 2 \times 100 = 0.0024\) m, 2.4 mm.
  3. So the slabs can expand on hot days without pushing into each other and cracking.
  4. Aluminium shrinks more than glass when it cools, so the frame squeezes the glass. Seals must allow for it.

Common mistake

"Everything shrinks when it freezes." Water is odd: it expands by about 9% when it turns to ice. That is why frozen pipes burst.

Where it leads