Control Panel Cooling units Technical Information

This section describes the expansion and contraction of substances by temperature change.

(1) As the temperature changes, the size also changes...Major Problems in Quality Control and Quality Inspection

In manufacturing industries, "reproducibility"* is important in the various processes of research and development, manufacturing, and inspections. This is well known that products themselves and materials that compose manufacturing or testing machines expand and contract with temperature. This is one of the most significant factors that affect "reproducibility," and it may change the product quality or test results. In this chapter, we show you the data on the coefficient of thermal expansion of representative substances used as materials for products and manufacturing/inspection equipment. We also have prepared a simulation result under situation between general air conditioning, and precision air conditioning of what kind of difference will occur when the expansion and contraction of each substance are compared.

* Reproducibility
Reproducibility is a term of description for measurement accuracy, it describes the extent of variation in test results under different environmental conditions. On the other hand, repeatability describes the extent of variation in test results under the same environmental conditions.

(2) Coefficient of linear expansion and Coefficient of cubic expansion

Caution! ...objects "stretch," "widen," and "expand" when the temperature rises.
There are "coefficients of linear expansion" and "coefficients of cubic expansion" in the expansion coefficient with temperature change.

Coefficient of linear expansion

The linear expansion coefficient of a solid expresses the rate of length change by temperature per unit length. The object length indicates L, and the Celsius degree is T.

Coefficient of linear expansion α= 1/L・dT/dL *

* dT/dL is an indicator that is the length of solid change when temperature T changes to d change. It varies depending on the solid substance, but it is a constant value regardless of the temperature.

The linear expansion coefficient of a solid is almost constant, regardless of temperature, so the length L of the object at T °C will be,

Object length = L0(1+αT)

* L0 is the length of the object at 0 °C.

Coefficient of cubic expansion

The coefficient of cubic expansion of a solid is defined by using the volume V of the object. If the coefficient of cubic expansion β=1/V・dV/dT and the volume V, is described with the length L of the object

The Volume V = L3

Therefore,

Coefficient of cubic expansionβ = 1V・dV/dT
                 =1/L3・dV/dL・dL/dT
                 =3/L・dL/dT=3α

Using the coefficient of cubic expansion β in the same way as the coefficient of linear expansion α

The Volume V = V0(1+βT) = V0(1+3αT)

※V0 is the volume of the substance at 0 °C.

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