Linear Thermal Expansion
When an object is heated or cooled, its length changes by an amount proportional to the original length and the change in temperature. The linear thermal expansion - the change in length - of an object can be expressed as
dl = L 0 α (t 1 - t 0 ) (1)
where
dl = change in object length (m, inches)
L 0 = initial length of object (m, inches)
α = linear expansion coefficient (m/m o C, in/in o F)
t 0 = initial temperature ( o C, o F)
t 1 = final temperature ( o C, o F)
The final length of the object can be calculated as
L 1 = L 0 + dl
= L 0 + L 0 α (t 1 - t 0 ) (2)
where
L 1 = final length of object (m, inches)
Note! - linear expansion coefficients for most materials varies with temperature .
Example - Expansion of Copper, Carbon and Stainless Steel Pipes
For wider temperature ranges - calculate for smaller spans and integrate the results.
Online Thermal Linear Expansion Calculator
Linear Temperature Coefficients - α - for some common metals
- aluminum : 0.000023 (m/m o C) (23 μm/m o C)
- steel: 0.000012 (m/m o C) (12 μm/m o C)
- copper: 0.000017 (m/m o C) (17 μm/m o C)
- more coefficients ..
- more metals ..
Example - Expansion of an Aluminum Beam
An aluminum construction is designed for temperatures ranging -30 o C to 50 o C . If a beam's length is 6 m when assembled at 20 o C - the shortest final length of the beam at minimum temperature -30 o C can be calculated as
L 1 = (6 m) + (6 m) (0.000023 m/m o C) ((-30 o C) - (20 o C))
= 5.993 m
The longest final length of the beam at maximum temperature 50 o C can be calculated as
L 1 = (6 m) + (6 m) (0.000023 m/m o C) ((50 o C) - (20 o C))
= 6.004 m
Superficial Expansion
The amount by which a unit area of a material increases when the temperature is raised by one degree is called the coefficient of superficial (area) expansion .
Cubic Expansion
The amount by which a unit volume of a material increases when the temperature is raised by one degree is called the coefficient of cubic expansion .
Related Topics
• Temperature Expansion
Thermal expansion of pipes and tubes - stainless steel, carbon steel, copper, plastics and more.
• Thermodynamics
Work, heat and energy systems.
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