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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.

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