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# Coefficients of Expansion

Definition. - A coefficient of expansion by heat may be defined as the ratio of the change of a volume, area, or length per degree of temperature to the value of that volume, area, or length at zero centigrade.

In solids and liquids the expansion is so small that in practice we may generally use, instead of the value of the quantity at zero, its value at the lower of the two temperatures observed in the experiment.

For solid bodies we have the coefficients of linear, superficial, and cubical expansion depending on the alteration of length, breadth, or thickness (linear), of surface (superficial), and of volume (cubical) respectively.

Let α, β, γ be these three respectively, and suppose the body to be isotropic, i.e. to have similar properties in all directions round any given point; then it can be shown that β = 2α, γ = 3α(1)

For liquid bodies we have to deal only with the coefficient of cubical expansion.

Any measurement of expansion is attended with considerable difficulty.

A liquid requires to be contained in some vessel, and thus we have to consider the alteration in volume of the vessel as well as that of the liquid itself. In the case of a solid, any cause which changes the temperature of the body to be measured probably changes that of the measuring apparatus and causes it to expand also. Our measurements will therefore give the expansion of one substance relatively to another. Thus, we should find, mercury and most liquids expand considerably as compared with glass, while the metals expand greatly in comparison with wood or stone.

Methods, it is true, have been devised for determining the absolute expansion either of a liquid or a solid, but tl ese are too complicated for an elementary course.

We shall explain how to determine (1) by means of reading microscopes, the coefficient of linear expansion of any solid which can be obtained in the form of a long rod, and (2), by means of the weight thermometer, the coefficient of expansion of a liquid and also that of cubical expansion of a solid.

In the case of a gas we may consider either the alteration of volume under constant pressure or the alteration of pressure at constant volume. We shall describe an experimental method of measuring the latter of these two.

 (1) Garnett, Heat, §77. Deschanel, Natural Philosophy, p. 265.

Last Update: 2011-03-27