Linear Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Linear thermal expansion coefficient, abbreviated as $$\alpha_l$$  (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

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

Where:

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

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

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

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

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

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

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

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

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

Solve For:

 $$\large{ l_f - l_i = \alpha_l \; l_i \; \left( T_f - T_i \right) }$$ $$\large{ l_f = \alpha_l \; l_i \; \left( T_f - T_i \right) + l_i }$$ $$\large{ l_i = \frac{ l_f }{ \alpha_l \; \left( T_f - T_i \right) \;+\; 1 } }$$ $$\large{ T_f - T_i = \frac{ l_f \;-\; l_i }{ \alpha_l \; l_i } }$$ $$\large{ T_f = \frac{ l_f \;-\; l_i }{ \alpha_l \; l_i } + T_i }$$ $$\large{ T_i = T_f -\; \frac{ l_f \;-\; l_i }{ \alpha_l \; l_i } }$$