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# 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 = 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.

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

### Online Thermal Linear Expansion Calculator

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)

#### 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.

## Related Topics

### • Temperature Expansion

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

### • Thermodynamics

Work, heat and energy systems.

## Related Documents

### Piping Materials - Temperature Expansion Coefficients

Temperature expansion coefficients for materials used in pipes and tubes like aluminum, carbon steel, cast iron, PVC, HDPE and more.

### Steel Pipes - Temperature Expansion

Calculate temperature expansion with carbon steel pipes.

### Thermal Expansion - Linear Expansion Coefficients

Linear temperature expansion coefficients for common materials like aluminum, copper, glass, iron and many more.

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