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:

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

Tags: Equations for Thermal Equations for Coefficient Equations for Expansion