Thermal Physics

Linear Expansivity

Most substances expand when the temperature increases. One important exception is water between 0°C and 4°C.

The expansion is due to the increased amplitude of vibration of the particles.

Consider a metal rod of original length _o.
 

D is the increase in length due to a temperature change, DT. Experiments show that D is directly proportional to DT.

Now consider a rod of original length 2_o (made of the same metal). Along the length of this rod there will be twice as many "layers" of atoms all increasing their amplitudes of vibration as the temperature increases. We would therefore expect this rod to expand by 2D, for the same increase in temperature.

The constant is written as a and is called the linear expansivity of the metal.

Rearranging this result gives

= o(1 + aDT)

where is the length when the temperature has changed by DT.

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