# Thermal Expansion of Solids

Written by Jerry Ratzlaff on . Posted in Thermodynamics ## Mean depth formula

 $$\large{ \Delta l = \overrightarrow{\alpha_l} \; l_i \; \Delta T }$$ (linear expansion) $$\large{ \Delta A = 2\; \overrightarrow{\alpha_l} \; A_i \; \Delta T }$$ (aerial or superficial expansion) $$\large{ \Delta V = 3\; \overrightarrow{\alpha_l} \; V_i \; \Delta T }$$ (volumetric or cubical expansion)

### Where:

 Units English Metric $$\large{ \Delta l }$$ = length differential $$\large{ in }$$ $$\large{ mm }$$ $$\large{ \Delta A }$$ = area differential $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ \Delta V }$$ = volume differential $$\large{ in^3 }$$ $$\large{ mm^3 }$$ $$\large{ A_i }$$ = initial area of object $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ l_i }$$ = initial length $$\large{ in }$$ $$\large{ mm }$$ $$\large{ V_i }$$ = initial volume of object $$\large{ in^3 }$$ $$\large{ mm^3 }$$ $$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$ $$\large{ \frac{mm}{mm\;C} }$$ $$\large{ \Delta T }$$ = temperature differential $$\large{ F }$$ $$\large{ C }$$ 