Materials expand when heated due to increased kinetic energy of atoms. The coefficient of linear expansion relates length difference to temperature change. Liquids expand with a coefficient of cuboidal expansion, while gases increase in pressure. Tables of values are available in engineering manuals. Thermal expansion must be considered in designing long items and parts with tight tolerances.
Many materials, particularly metals, physically expand when heated, due to increases in the kinetic energy of atoms. This expansion moves outward in all three dimensions, though not necessarily to the same extent. The coefficient of linear expansion is the value that relates the difference in length of an object to the difference in temperature of the object when the two length measurements were made. A larger value means that the material expands more during a set temperature rise than a material with a lower coefficient.
Strictly speaking, the coefficient of linear expansion is also a function of temperature, but for most materials it can be considered a constant in the range of 32° to 212°C (0° to 100°F). Liquids also expand, and the three-dimensional equivalent, the coefficient of cuboidal expansion at a given temperature, is used in calculations of volume changes. Gases expand to fill any container they are placed into. Since their volume is fixed, gases increase in pressure with increasing temperature.
Tables of these values \u200b\u200bare available in engineering manuals. Values are given in units of 10,000a’ or 10-6 m/m K or 10-6in/in °F. The a’ symbol is used in the American standard measurement system. Evaluating an example will help clarify these units.
This value is expressed in units of length. The coefficient of linear expansion for brass wire is listed at 18.7 x 10-6 m/m K and 10.4 x 10-6 in/in °F. The calculation for the length expansion of a 10-foot-long (3.048 m) brass wire at 70°F (21.1°C) and heated to 80°F (26.6°C) is:
10 feet is 120 inches. The brass wire will expand 10.4 x 10-6 inches per inch of initial length per degree Fahrenheit of temperature rise. 120 + (10.4 x 10-6) x 120 x 10 = 120.0125 inches.
In metric units, the calculation is 3.048m + (18.7 x 10-6) x 3.048 x 10×5/9 = 3.048316m, which equals 120.0124 inches. The 5/9 in the equation converts one degree Fahrenheit to one degree Celsius.
This difference in length may seem trivial, but when designing items such as power cables hundreds of miles or kilometers long that will experience temperature differences of 150° or more, however, thermal expansion must be taken into consideration. Even parts with very tight tolerances, such as in optical devices, must be protected from temperature changes or accommodate for uneven expansion of parts made from different materials.
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