# Linear Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Linear thermal expansion coefficient, abbreviated as $$\overrightarrow{\alpha_l}$$  (Greek symbol alpha), also called coefficient of linear thermal expansion, is the ratio of the change in size of a material to its change in temperature.

## Linear thermal expansion coefficient Formulas

 $$\large{ \overrightarrow{\alpha_l} = \frac{ 1 }{ l } \; \frac{\Delta l }{\Delta T} }$$ $$\large{ \overrightarrow{\alpha_l} = \frac{ l_f \;-\; l_i }{ l_i \; \left( T_f \;-\; T_i \right) } }$$ $$\large{ \overrightarrow{\alpha_l} = \frac{ \alpha_v }{ 3 } }$$

### Where:

 Units English Metric $$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$ $$\large{ \frac{mm}{mm\;C} }$$ $$\large{ \alpha_v }$$  (Greek symbol alpha) = volumetric thermal expansion coefficient $$\large{ \frac{in^3}{in^3\;F} }$$ $$\large{ \frac{mm^3}{mm^3\;C} }$$ $$\large{ l }$$ = length of object $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta l }$$ = length change $$\large{ft}$$ $$\large{m}$$ $$\large{ l_i }$$ = initial length $$\large{ft}$$ $$\large{m}$$ $$\large{ l_f }$$ = final length $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta T }$$ = temperature change $$\large{F}$$ $$\large{C}$$ $$\large{ T_f }$$ = final temperature $$\large{F}$$ $$\large{C}$$ $$\large{ T_i }$$ = initial temperature $$\large{F}$$ $$\large{C}$$ 