Thermal Expansion
Thermal expansion describes the phenomenon wherein substances increase in size as their temperature rises, affecting their length, area, and volume depending on their state. The primary types of thermal expansion are:
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Linear Expansion: The proportional increase in length for solids. It is quantified using the coefficient of linear expansion (αl), expressed as:
$$ \frac{\Delta l}{l} = \alpha_l \Delta T $$
where Δl is the change in length, l is the original length, and ΔT is the change in temperature. For example, copper expands about five times more than glass when subjected to the same temperature change due to its higher coefficient of linear expansion.
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Area Expansion: This describes the increase in surface area of solids, related to linear expansion, and is given by:
$$ \alpha_A = 2 \alpha_l $$
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Volume Expansion: This applies to both liquids and gases; it defines how their volume changes with temperature, utilizing the coefficient of volume expansion (αv):
$$ \frac{\Delta V}{V} = \alpha_V \Delta T $$
The relationship between αv and αl is represented as:
$$ \alpha_V = 3 \alpha_l $$
Thermal stress can occur when thermal expansion is constrained, leading to potential structural failures in systems like railway tracks or bridges during temperature fluctuations.
Another unique property is that water expands upon freezing and has its maximum density at 4°C, a critical factor for aquatic life in frozen lakes.
In gases, the expansion coefficient (αv) can be derived from the ideal gas law relation, indicating significant differences with solids and liquids.
Overall, thermal expansion is vital in engineering, architecture, and environmental science, emphasizing the importance of understanding this fundamental physical property.