Linear Thermal Expansion
Online linear temperature expansion 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 = 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
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