# Linear Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Linear thermal expansion coefficient, abbreviated as $$\alpha$$, also known as 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 FORMULA

$$\large{ \alpha_l = \frac{ 1 }{ l } \; \frac{\Delta l }{\Delta T} }$$

$$\large{ \alpha_l = \frac{ l_f \;-\; l_i }{ l_i \; \left( T_f \;-\; T_i \right) } }$$

$$\large{ \alpha_l = \frac{ \alpha_v }{ 3 } }$$

Where:

$$\large{ \alpha_l }$$   (Greek symbol alpha) = linear thermal expansion coefficient

$$\large{ l }$$ = length of object

$$\large{ \Delta l }$$ = length differential

$$\large{ l_f }$$ = final length

$$\large{ l_i }$$ = initial length

$$\large{ \Delta T }$$ = temperature differential

$$\large{ T_f }$$ = final temperature

$$\large{ T_i }$$ = initial temperature

$$\large{ \alpha_v }$$  (Greek symbol alpha) = volumetric thermal expansion coefficient