Page:International Library of Technology, Volume 93.djvu/42

is heated, it expands so much that it will no longer pass through the ring.

31. Coefficient of Expansion. — Suppose that the temperature of the metal rod shown in Fig. 4 was 32° F. before heating, and that its length was 10 feet; and that after the temperature had been raised 1°, or to 33°, the bar was 10 feet + ¹⁄₁₂₀₀ inch long. The linear expansion will then be ( 10 feet + ¹⁄₁₂₀₀ inch) — 10 feet = ¹⁄₁₂₀₀ inch, and the ratio

TABLE 1 COEFFICIENTS OF EXPANSION OF SOLIDS Name of Substance Linear Expansion $C_{1}$ Surface Expansion $C_{2}$ Cubic Expansion $C_{3}$ Aluminum (cast) Cast iron Steel (untempered) Steel (tempered) Copper Brass (cast) Silver Wrought iron Lead Zinc Tin Porcelain .00001234 .00000617 .00000599 .00000702 .00000955 .00001037 .00001060 .00000686 .00001571 .00001634 .00001230 .00000200 .00002468 .00001234 .00001198 .00001404 .00001910 .00002074 .00002120 .00001372 .00003142 .00003268 .00002460 .00000400 .00003702 .00001850 .00001798 .00002106 .00002864 .00003112 .00003180 .00002058 .00004713 .00004903 .00003690 .00000600

between this expansion and the original length of the bar will be ${\frac {1}{1200}}:10\times 12,or{\frac {1}{1200\times 120}}:1,or.000006944:1$ For every increase of temperature of 1°, this rod will elongate .000006944 of its length. This number .000006944, which equals the expansion of the rod for 1° rise of temperature divided by the original length, is called the coefficient of linear expansion. Had the temperature of the rod been increased 100° instead of 1°, the amount of elongation would have been $.000006944\times 100=.0006944$ of its length, or