inch. Table I gives the coefficients of expansion for a number of solids. The coefficient of cubic expansion of a solid is not often used. It is approximately three times the coefficient of linear expansion. It should be noted that the coefficients of expansion, both cubic and linear, although sufficiently exact and uniform for all ordinary purposes, are not absolutely constant.
32. The amount of expansion of metals, due to heating, may be calculated approximately by means of the following formulas:
in which
L = length of any body;
l = amount of expansion or contraction due to
heating or cooling the body;
A = area of any section of body;
a = increase or decrease of area of same section after heating or cooling the body;
V = volume of body;
v = increase or decrease in volume due to heating or cooling the body;
= coefficient of linear expansion, taken from
Table I;
= coefficient of surface expansion, taken from
Table I;
— coefficient of cubic expansion, taken from
Table I;
t = difference, in degrees, of temperature between
original temperature and temperature of body after it has been heated or cooled.
Example. — How much will a bar of untempered steel, 14 feet long, expand if its temperature is raised 80°?
Solution. — Since only one dimension is given, that of length, linear expansion only can be considered. From Table I, the coefficient of linear expansion per unit of length for a rise in temperature of 1° is
