Linear Thermal Expansion of Solids Formula |
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\( \Delta L \;=\; \overrightarrow{\alpha_l } \cdot L_i \cdot \Delta T \) (Linear Thermal Expansion of Solids) \( \overrightarrow{\alpha_l } \;=\; \dfrac{ \Delta L }{ L_i \cdot \Delta T }\) \( L_i \;=\; \dfrac{ \Delta L }{ \overrightarrow{\alpha_l } \cdot \Delta T }\) \( \Delta T \;=\; \dfrac{ \Delta L }{ \overrightarrow{\alpha_l } \cdot L_i }\) |
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| Symbol | English | Metric |
| \( \Delta L \) = Change in Length | \( in \) | \( mm \) |
| \( \overrightarrow{\alpha_l} \) (Greek symbol alpha) = Linear Thermal Expansion Coefficient | \(in \;/\; in\;F\) | \(mm \;/\; mm\;C\) |
| \( L_i \) = Initial Length of the Object | \( in \) | \( mm \) |
| \( \Delta T \) = Change in Temperature | \(^\circ F \) | \(^\circ C \) |
Thermal expansion of solids refers to the change in dimensions (length, area, or volume) of a solid material in response to a change in temperature. When a solid is heated, its constituent particles gain kinetic energy and vibrate more vigorously, resulting in an increase in average separation between particles. This increase in particle spacing leads to the expansion of the solid material.
The extent of expansion depends on the material's coefficient of linear expansion, which quantifies the change in length per unit length per degree change in temperature. The linear expansion coefficient varies for different materials and is typically positive, indicating that most solids expand when heated. The linear expansion coefficient can be used to calculate the change in dimensions for other geometrical shapes, such as the change in area or volume.
Area Thermal Expansion of Solids Formula |
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\( \Delta A \;=\; 2 \cdot \overrightarrow{\alpha_l} \cdot A_i \cdot \Delta T \) (Area Thermal Expansion of Solid) \( \overrightarrow{\alpha_l} \;=\; \dfrac{ \Delta A }{ 2 \cdot A_i \cdot \Delta T }\) \( A_i \;=\; \dfrac{ \Delta A }{ 2 \cdot \overrightarrow{\alpha_l} \cdot \Delta T }\) \( \Delta T \;=\; \dfrac{ \Delta A }{ 2 \cdot \overrightarrow{\alpha_l} \cdot A_i }\) |
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| Symbol | English | Metric |
| \( \Delta A \) = Change in Area | \( in^2 \) | \( mm^2 \) |
| \( \overrightarrow{\alpha_l} \) (Greek symbol alpha) = Linear Thermal Expansion Coefficient | \(in \;/\; in\;F\) | \(mm \;/\; mm\;C\) |
| \( A_i \) = Initial Area of the Object | \( in^2 \) | \(mm^2 \) |
| \( \Delta T \) = Change in Temperature | \(^\circ F \) | \(^\circ C \) |
It's important to note that not all materials expand uniformly in all directions. Anisotropic materials have different expansion coefficients in different directions, leading to non-uniform expansion or contraction. Thermal expansion is a critical consideration in various applications, including construction, engineering, and manufacturing. Understanding the thermal expansion behavior of materials is crucial to design structures, components, and systems that can accommodate the dimensional changes associated with temperature variations and prevent unwanted stresses or deformations.
Volumetric Thermal Expansion of Solids Formula |
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\( \Delta V \;=\; 3 \cdot \overrightarrow{\alpha_l} \cdot V_i \cdot \Delta T \) (Volumetric Thermal Expansion of Solid) \( \overrightarrow{\alpha_l} \;=\; \dfrac{ \Delta V }{ 3 \cdot V_i \cdot \Delta T }\) \( V_i \;=\; \dfrac{ \Delta V }{ 3 \cdot \overrightarrow{\alpha_l} \cdot \Delta T }\) \( \Delta T \;=\; \dfrac{ \Delta V }{ 3 \cdot \overrightarrow{\alpha_l} \cdot V_i }\) |
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| Symbol | English | Metric |
| \( \Delta V \) = Change in Volume | \( in^3 \) | \( mm^3 \) |
| \( \overrightarrow{\alpha_l} \) (Greek symbol alpha) = Linear Thermal Expansion Coefficient | \(in \;/\; in\;F\) | \(mm \;/\; mm\;C\) |
| \( V_i \) = Initial Volume of the Object | \(in^3 \) | \( mm^3 \) |
| \( \Delta T \) = Change in Temperature | \(^\circ F \) | \(^\circ C \) |