# 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 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)

Note! - linear expansion coefficients for most materials varies with temperature.

For wider temperature ranges - calculate for smaller spans and integrate the results.

### Online Thermal Linear Expansion Calculator

L0 - initial length (m, inches)

α - linear expansion coefficient (m/moC, in/inoF)

t0 - initial temperature (oC, oF)

t1 - final temperature (oC, oF)

### 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 length of the beam at minimum temperature -30oC can be calculated as

dl = (6 m) + (6 m) (0.000023 m/moC) ((-30 oC) - (20 oC))

=  5.993 (m)

The longest length of the beam at maximum temperature 50oC can be calculated as

dl = (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.

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