# 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 of pipes and tubes - stainless steel, carbon steel, copper, plastics and more.

### • Thermodynamics

Work, heat and energy systems.

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