Thermal Expansion
Thermal Expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature, through heat transfer.
The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed: volumetric, area, and linear. This is used depending on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, or over some area.
Over small temperature ranges, the linear nature of thermal expansion leads to expansion relationships for length, area, and volume in terms of the linear expansion coefficient.
Linear Expansion The relationship governing the linear expansion of a long thin rod can be reasoned out as follows:
General volumetric thermal expansion coefficient In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by
The subscript p indicates that the pressure is held constant during the expansion, and the subscript "V" stresses that it is the volumetric (not linear) expansion that enters this general definition. In the case of a gas, the fact that the pressure is held constant is important, because the volume of a gas will vary appreciably with pressure as well as temperature. For a gas of low density this can be seen from the ideal gas law.
Area expansion
The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, we may write:
where is some area of interest on the object, and is the rate of change of that area per unit change in temperature.
The change in the area can be estimated as:
This equation works well as long as the area expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature, through heat transfer.
The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed: volumetric, area, and linear. This is used depending on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, or over some area.
Over small temperature ranges, the linear nature of thermal expansion leads to expansion relationships for length, area, and volume in terms of the linear expansion coefficient.
Linear Expansion The relationship governing the linear expansion of a long thin rod can be reasoned out as follows:
General volumetric thermal expansion coefficient In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by
The subscript p indicates that the pressure is held constant during the expansion, and the subscript "V" stresses that it is the volumetric (not linear) expansion that enters this general definition. In the case of a gas, the fact that the pressure is held constant is important, because the volume of a gas will vary appreciably with pressure as well as temperature. For a gas of low density this can be seen from the ideal gas law.
Area expansion
The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, we may write:
where is some area of interest on the object, and is the rate of change of that area per unit change in temperature.
The change in the area can be estimated as:
This equation works well as long as the area expansion