# 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*. If a beam's length is

^{o}C*6 m*when assembled at

*20*- the shortest final length of the beam at minimum temperature

^{o}C*-30*can be calculated as

^{o}C* 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 and expansion coefficients. Expansion pipes and tubes made of stainless steel, carbon steel, copper, plastics and more.

### • Thermodynamics

Work, heat and energy systems.

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