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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 = 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 .

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

Work, heat and energy systems.

## Related Documents

### Bimetallic Strips

Heat and bending of bimetallic strips.

### Circular Ring - Temperature Expansion

Calculate ring (or pipe) diameter expansion or contraction when temperature changes.

### Copper, Ductile Iron, Carbon Steel, Stainless Steel and Aluminum Piping Materials - Temperature Expansion

Thermal expansion of typical piping materials.

### Metals - Temperature Expansion Coefficients

Thermal expansion coefficients metals.

### Pipes and Tubes - Temperature Expansion

Pipes expands when heated and contracts when cooled and the expansion can be expressed with the expansion equation.

### 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.

### Piping Materials - Temperature Heat Expansion and Cooling Contraction

Expansion and contraction when cast iron, carbon and carbon molybdenum steel, wrought iron, copper, brass and aluminum pipes are heated or cooled.

### PVC, CPVC, Carbon Steel, Stainless Steel and Fiberglass Pipes - Thermal Expansion Diagrams

Thermal expansion of PVC, CPVC, Carbon and Stainless Steel and Fiberglass pipes.

### Restricted Thermal Expansion - Force and Stress

Stress and force when thermal expansion a pipe, beam or similar is restricted.

### Shrink-Fits Assembly

Assembly temperatures for shrink-fits.

### Solids - Volume Temperature Expansion Coefficients

Cubical expansion coefficients for solids.

### Steam Pipes - Thermal Expansion

Thermal expansion of steam pipes heated from room temperature to operation temperature (mm pr. 100 m pipe).

### Steel Pipes - Temperature Expansion

Calculate temperature expansion with carbon steel pipes.

### Steel Pipes - Thermal Expansion Loops

Calculating and sizing steel pipe thermal expansion loops.

### Thermal Expansion - Linear Expansion Coefficients

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

### Thermal Expansion - Superficial i.e. Area

Superficial i.e area temperature expansion - online calculator.

### Thermal Expansion of Steam Pipes - (inches)

Expansion of steam pipes heated from room temperature to operation temperature.

### Volumetric (Cubic) Thermal Expansion

Volumetric temperature expansion calculator.

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