Linear Thermal Expansion
Linear temperature expansion - online calculator
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 = L0 α (t1 - t0) (1)
where
dl = change in object length (m, inches)
L0 = initial length of object (m, inches)
α = linear expansion coefficient (m/moC, in/inoF)
t0 = initial temperature (oC, oF)
t1 = final temperature (oC, oF)
The final length of the object can be calculated as
L1 = L0 + dl
= L0 + L0 α (t1 - t0) (2)
where
L1 = 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/moC) (23 μm/moC)
- steel: 0.000012 (m/moC) (12 μm/moC)
- copper: 0.000017 (m/moC) (17 μm/moC)
- more coefficients ..
- more metals ..
Example - Expansion of an Aluminum Beam
An aluminum construction is designed for temperatures ranging -30oC to 50oC. If a beam's length is 6 m when assembled at 20oC - the shortest final length of the beam at minimum temperature -30oC can be calculated as
L1 = (6 m) + (6 m) (0.000023 m/moC) ((-30 oC) - (20 oC))
= 5.993 m
The longest final length of the beam at maximum temperature 50oC can be calculated as
L1 = (6 m) + (6 m) (0.000023 m/moC) ((50 oC) - (20 oC))
= 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.
