# Linear Thermal Expansion Coefficient

on . Posted in Thermodynamics

Linear thermal expansion coefficient, abbreviated as $$\overrightarrow{\alpha_l}$$  (Greek symbol alpha), also called coefficient of linear thermal expansion, is a material property that quantifies how a material's length or dimension changes in response to a change in temperature.  It describes the fractional change in length per unit change in temperature.

Different materials have different linear thermal expansion coefficients, and this property is important in various engineering and construction applications, such as designing structures and systems that need to withstand temperature changes without excessive deformation or stress.  It's worth noting that materials expand when heated and contract when cooled, so the sign of the linear thermal expansion coefficient (positive or negative) indicates the direction of the change (expansion or contraction) with temperature change.

## Linear thermal expansion coefficient Formula

$$\large{ \overrightarrow{\alpha_l} = \frac{ \Delta l }{ l_i \; \Delta T } }$$     (Linear Thermal Expansion Coefficient)

$$\large{ \Delta l = \overrightarrow{\alpha_l} \; l_i \; \Delta T }$$

$$\large{ l_i = \frac{ \Delta l }{ \overrightarrow{\alpha_l} \; \Delta T } }$$

$$\large{ \Delta T = \frac{ \Delta l }{ \overrightarrow{\alpha_l} \; l_i } }$$

### Solve for αl

 length change, Δl initial length, li temperature change, ΔT

### Solve for Δl

 linear thermal expansion coefficient, αl initial length, li temperature change, ΔT

### Solve for li

 length change, Δl linear thermal expansion coefficient, αl temperature change, ΔT

### Solve for ΔT

 length change, Δl linear thermal expansion coefficient, αl initial length, li

Symbol English Metric
$$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$  $$\large{ \frac{mm}{mm\;C} }$$
$$\large{ \Delta l }$$ = length change of the material due to the temperature change $$\large{ft}$$ $$\large{m}$$
$$\large{ l_i }$$ = initial length of the material at a reference temperature $$\large{ft}$$ $$\large{m}$$
$$\large{ \Delta T }$$ = temperature change $$\large{F}$$ $$\large{C}$$ 