found to be .00000599 for untempered steel. Hence, substituting the known values in formula 1, 14 × .00000599 × 80 = .0067088 ft., or .0067088 × 12 = .0805056 in. Ans.
33. Expansion of Liquids. — As a rule, liquids shrink, or contract, when they freeze, and most solids expand when melted. Water is a marked exception to the general rule. If water is cooled from its boiling point, it continually contracts until it reaches 39.1° F., the temperature of maximum density, when it begins to expand, until it freezes at 32° F. On the other hand, if water at 32° F. is heated, it contracts until it reaches 39.1° F., when it commences to expand. Therefore, the density of water is greatest where this change occurs. The importance of this exception is seen in the fact that ice forms on the surface of water, since it is lighter than the warmer body of water lying at varying depths below it. Were it not for this fact, all the large bodies of water would freeze solid, and would so affect the climate of the earth that it would be uninhabitable. The coefficient of expansion of water is a very changeable quantity, varying with the temperature. In being heated from 32° to 212° F., the volume of alcohol becomes 1.11, that of mercury 1.0182, that of sea-water 1.05, and that of pure water 1.0444 times as great as the original volume.
34. Expansion of Gases. — Suppose that a cylinder a,
Fig. 6,
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is closed at its upper end by a piston b having an
area of 200 square inches and weighing 1,060 pounds. The pressure on the air due to the piston only is therefore 1,060 ÷ 200 = 5.3 pounds per square inch. If the pressure of the atmosphere is 14.7 pounds to the square inch, there is a total pressure of 14.7 + 5.3 = 20 pounds per square inch acting at the bottom surface of the piston. The contained air will, therefore, be under an absolute pressure of 20 pounds per square inch; suppose that at 32° F. it has a volume of exactly 1 cubic foot. If the temperature of the air in the cylinder is raised 1°, it will be found that the piston has moved upwards a certain amount, while the
