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Linear Thermal Expansion

Linear temperature expansion - online calculator

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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.

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

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)


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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.

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