When an object is heated, its particles expand and move faster, making the object itself bigger. Similarly, when an object is cooled, its particles move closer together and move more slowly, making the object smaller. The differential equation for this process is
ⅆ Lⅆ T= a L,
where L is the length of the object, T is its temperature, and a is the thermal expansion coefficient of the material. For a given initial length and initial and final temperatures, the final value of the length can be expressed as
For small changes in temperature, you can use a linear approximation instead:
Lfinal−Linitial=a ⋅Linitial ⋅Tfinal−Tinitial.
Using the controls below the plot windows, enter an initial length, thermal expansion coefficient, and initial and final temperatures to see how much the initial length will change under those conditions. The plots below will also illustrate the change in particle movement.
Note that for typical materials at 20°C the linear expansion coefficient ranges from 1×10−6 K−1 (diamond) to 250×10−6 K−1 (ethanol).
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