## Tuesday, 12 January 2016

### Linear Expansivity

Definition
Linear expansivity is the increase of 1m of material in size for a 1℃ rise in temperature.

When designing bridges, railway tracks and copper piping etc. engineers have to allow for linear expansivity.

Linear expansivity is the amount by which a material increases in size due to an increase in temperature. It's measured in meters per degree Celsius. It's symbol is the greek symbol for alpha, α.

To calculate the linear expansion of something, you need to know the following:

• The length of the bridge
• The range of temperatures it will experience
• The linear expansivity of the material that's going to be used
The linear expansivity of materials is found through experimenting.
Steel's linear expansivity is 0.000 012m per ℃, so 1m will become 1.000 012m if the temperature increases by 1℃.

Equation

expansion = linear expansivity ⨉ original length ⨉ temperature rise

Example question and working

Question: How long will a 100m long steel  bridge become if the temperature increases by 60℃? Note that the linear expansivity of steel is 0.000 012m.

Answer: The bridge would expand by 0.000 012m ⨉ 100m if the temperature rose by 1℃. So if the temperature rises by 60℃, then the bridge would expand by
0.000 012m ⨉ 100m ⨉ 60℃ = 0.072m or 7.2cm

Change in length

Delta (the greek letter) often means the change in a quantity or the difference. So the change in temperature in the above question is 60℃ and the change in length is 7.2cm.
You need to remember the following symbols:

Delta:
Change in length:
Change in temperature: