Encyclopedian Dictionary: expansion

Pronunciation key

( ik-span′shən )

ex•pan•sion

[LL. expansio < L. expansus see EXPANSE].

An act or process of expanding or being expanded; enlargement; dilation.
State of a thing or part being expanded.
The degree, amount or extent something has expanded.
A development or full treatment, as of a topic.
In algebra, the process in written form of developing an equation which is expanded to a fuller form through a series of steps or sum of terms.
In mechanics, expanding in volume of steam within the cylinder of a steam engine after cutoff, or of gas that is in the cylinder of an internal-combustion engine following explosion.

Expansion

Chemistry and Physics. Expansion is the increase in length or volume of a material body without addition of weight or material as a consequence of an increase in its temperature or pressure so that it occupies a greater space, while the weight remains constant. The majority of solids, liquids and gases expand when heated, and the amount of such expansion can be measured by the expansion coefficient of each substance, that is, a number which represents the change in length per unit length (or change in volume per unit volume) for each degree of increase in temperature. An expansion coefficient is a unique to each substance; for instance, platinum is .0000089 and copper is .000014. Expansion may also be the result of removal or application of a mechanical force in which case it is then called compressibility.

Expansion is the result when a constant mass undergoes an increase in its volume. Heat is the most common cause for expansion. The majority of solids and liquids will expand when subjected to heat and contract when cooled. Gases tend to expand when heat levels rise at a constant pressure. If a gas is heated in a container that is expansion-resistant, the overall pressure increases as well. Heat creates expansion because it increases the vibrations of sub-molecular particles and increased vibrations force atoms and molecules farther apart and therefore the body as a whole increases in size. Different materials expand by variegated amounts when temperature is increased by one degree. For instance, aluminum expands twice as much as iron with the same increase in temperature.

Expansion of solids must be considered in the design of engineering structures and product manufacturing. For instance, steel rails are separated with a narrow gap which allow expansion during higher temperatures. Such expansion gaps are provided in concrete roads and sidewalks in the prevention of cracking and heaving. Another example is that some kitchen utilities such as a pot that is made of two different metals expand at approximately the same rate. If it were not designed in such a manner the pots or pan may bend when heated.

It is possible to quantitively measure the rate of expansion if the coefficient of expansion is known. If 1_O is the length of a metal rod at 0ºC and α is the coefficient of linear expansion at a temperature t the final length of the metal rod l_t is given for the expression l_t = 100 (1 + .0000110 x 75) or 100.082 cm. This solution only takes into consideration the linear expansion of the metal rod. For a more accurate explanation of expansion the increase in volume would have to also be taken in consideration.

This may also be utilized to calculate expansion of volume. V_t = V_O (1 + 3 αt), with V_O for volume at 0ºC and V_t its volume tºC when the coefficient of linear expansion is α.

Two example of how such calculations of expansion are used in the manufacturing of products are to avoid or perhaps utilize nonuniform expansion results. For instance, the fact that coefficient of expansion in glass is nearly that of platinum, it is possible to seal platinum wires inside glass bulbs for electric light bulbs. Another example is bimetallic thermometer strips. When a strip of iron is applied to a strip of zinc so that at a certain temperature both strips are straight, an increase in temperature will lead to the zinc bending more than the iron due to its higher coefficient of expansion.

Due to the simultaneous increase in size of the containers which hold liquids, reducing the expansion, the expansion of liquids are complicated. Thus, to determine the real expansion of liquids the container must first be taken into account. This fact is important in the construction of thermometers and barometers which are regularly used in precise measurements. The expansion of liquids upon increased temperature, cause it to rise. The same principal is utilized with some home heating systems. On a larger scale, nonuniform heating and expansion of water gives rise to increased strength in ocean currents.

Gases have far more expansion rates than do liquids or solids, and vary little. The coefficient of expansion for air is .00367, that comes to about 20 times greater than mercury, 70 times greater than brass and approximately the same as any other gas. The volume of gas varies inversely as the pressure, the coefficient of expansion can be determined by either keeping the pressure at a constant rate and taking measurements of the increase in volume, apparent by a rise in temperature or by maintaining constant volume and determining the increase in pressure. Hot air heating systems and internal combustion system technology rely heavily on the knowledge of how expansion of gases is affected with an increase in temperature. Variable weather over the planet is largely due to convection of air in the atmosphere in combination with the earth's rotation.

Water in cooling ceases to contract when it reaches 39.2°F and in lowering temperature, it expands again until frozen when expansion reaches about 1/11th of its original volume. Water, when at its greatest density which is at 39.2°F presents a curious phenomenon of expanding whether heat or cold are applied. Expansion occurs with all substances although gases expand more than liquids and liquids more often than solids. Winds are created by air expanding under the sun's heat, the phenomena of oceanic currents have the same cause.

Also see Heat. Convection.

Mathematics. Used in this manner, expansion is the process of expressing a quantity as a sum or continuous product of its individual terms. The process of factoring consists of expressing a sum as a product. Therefore the sum abt + abW is written as the product of ab (t + W) by factoring. The opposite of factoring is called expansion, or, the writing of a product as a sum. Therefore, by expansion, the product ab (t + W) is expressed as the sum abt + abW. The process of writing term by term any power of a binomal expression without actually performing the steps of multiplication applies the binomial theorem. Other methods exist which serve a similar purpose, for instance, Maclaurin's and Taylor's methods of expanding a function in terms of a sum of ascending powers of the variable, and Fourier's method of expanding a function in a trigonometric series.