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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.
 

DELTA01 is the increase in length due to a temperature change, DELTA01T. Experiments show that DELTA02 is directly proportional to DELTA02T.

Now consider a rod of original length 2o (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 2DELTA01, for the same increase in temperature.

Experiments confirm this hypothesis.

We can therefore write

(a constant)×DT

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

The linear expansivity of a substance, a, is the fractional change in length of a sample of the substance per degree C change in temperature.

Rearranging this result gives

= o(1 + aDT)

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

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