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  4. Temperature and heat
  5. Thermal expansion

1.3 Thermal expansion  (Page 2/10)

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Thermal expansion coefficients
Material Coefficient of Linear Expansion α ( 1 / ° C ) Coefficient of Volume Expansion β ( 1 / ° C )
Solids
Aluminum 25 × 10 −6 75 × 10 −6
Brass 19 × 10 −6 56 × 10 −6
Copper 17 × 10 −6 51 × 10 −6
Gold 14 × 10 −6 42 × 10 −6
Iron or steel 12 × 10 −6 35 × 10 −6
Invar (nickel-iron alloy) 0.9 × 10 −6 2.7 × 10 −6
Lead 29 × 10 −6 87 × 10 −6
Silver 18 × 10 −6 54 × 10 −6
Glass (ordinary) 9 × 10 −6 27 × 10 −6
Glass (Pyrex®) 3 × 10 −6 9 × 10 −6
Quartz 0.4 × 10 −6 1 × 10 −6
Concrete, brick ~ 12 × 10 −6 ~ 36 × 10 −6
Marble (average) 2.5 × 10 −6 7.5 × 10 −6
Liquids
Ether 1650 × 10 −6
Ethyl alcohol 1100 × 10 −6
Gasoline 950 × 10 −6
Glycerin 500 × 10 −6
Mercury 180 × 10 −6
Water 210 × 10 −6
Gases
Air and most other gases at atmospheric pressure 3400 × 10 −6

Thermal expansion is exploited in the bimetallic strip ( [link] ). This device can be used as a thermometer if the curving strip is attached to a pointer on a scale. It can also be used to automatically close or open a switch at a certain temperature, as in older or analog thermostats.

Figure a shows two vertical strips attached to each other. It is labeled T0. Figure b shows the same two strips bent towards the right. It is labeled T greater than T0.
The curvature of a bimetallic strip depends on temperature. (a) The strip is straight at the starting temperature, where its two components have the same length. (b) At a higher temperature, this strip bends to the right, because the metal on the left has expanded more than the metal on the right. At a lower temperature, the strip would bend to the left.

Calculating linear thermal expansion

The main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from – 15 ° C to 40 ° C . What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

Strategy

Use the equation for linear thermal expansion Δ L = α L Δ T to calculate the change in length, Δ L . Use the coefficient of linear expansion α for steel from [link] , and note that the change in temperature Δ T is 55 ° C .

Solution

Substitute all of the known values into the equation to solve for Δ L :

Δ L = α L Δ T = ( 12 × 10 −6 ° C ) ( 1275 m ) ( 55 ° C ) = 0.84 m .

Significance

Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.

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Thermal expansion in two and three dimensions

Unconstrained objects expand in all dimensions, as illustrated in [link] . That is, their areas and volumes, as well as their lengths, increase with temperature. Because the proportions stay the same, holes and container volumes also get larger with temperature. If you cut a hole in a metal plate, the remaining material will expand exactly as it would if the piece you removed were still in place. The piece would get bigger, so the hole must get bigger too.

Thermal expansion in two dimensions

For small temperature changes, the change in area Δ A is given by

Δ A = 2 α A Δ T

where Δ A is the change in area A , Δ T is the change in temperature, and α is the coefficient of linear expansion, which varies slightly with temperature.

Figure shows a circle inside a square. The circle is outlined by another, slightly bigger circle. The bigger circle is a dashed outline. Similarly, the square is outlined by a bigger, dashed square. Figure b is similar to figure a except that the inner circle is cut out of the square. Figure c is a cuboid surrounded by a bigger, dashed cuboid.
In general, objects expand in all directions as temperature increases. In these drawings, the original boundaries of the objects are shown with solid lines, and the expanded boundaries with dashed lines. (a) Area increases because both length and width increase. The area of a circular plug also increases. (b) If the plug is removed, the hole it leaves becomes larger with increasing temperature, just as if the expanding plug were still in place. (c) Volume also increases, because all three dimensions increase.
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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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