Thermal Expansion - Maple Programming Help

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Thermal Expansion


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


 Lfinal=Linitial ⅇaTfinalTinitial.


For small changes in temperature, you can use a linear approximation instead:


 LfinalLinitial=a Linitial TfinalTinitial.


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.


Linitial : m

Lfinal :  m

 Tinitial : C

  Tfinal :  C

a : ×106 K-1

Note that for typical materials at 20°C the linear expansion coefficient ranges from 1×106 K1 (diamond) to 250×106 K1 (ethanol).


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