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 \(\large{F}\) \(\large{C}\)

 

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Tags: Thermal Equations Coefficient Equations Expansion Equations