# Volumetric Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Volumetric thermal expansion coefficient, abbreviated as $$\alpha_v$$ (Greek symbol alpha), also called coefficient of volumetric thermal expansion, is the ratio of the change in size of a material to its change in temperature.

## Volumetric thermal expansion coefficient Formulas

 $$\large{ \alpha_v = \frac { 1 }{ V } \; \frac {\Delta V } {\Delta T} }$$ $$\large{ \alpha_v = \frac{ v_f \;-\; v_i }{ v_i \; \left( T_f \;-\; T_i \right) } }$$ $$\large{ \alpha_v = 3 \; \overrightarrow{\alpha_l} }$$

### Where:

 Units English Metric $$\large{ \alpha_v }$$  (Greek symbol alpha) = volumetric thermal expansion coefficient $$\large{ \frac{in^3}{in^3\;F} }$$ $$\large{ \frac{mm^3}{mm^3\;C} }$$ $$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$ $$\large{ \frac{mm}{mm\;C} }$$ $$\large{ \Delta T }$$ = temperature change $$\large{F}$$ $$\large{C}$$ $$\large{ T_f }$$ = final temperature $$\large{F}$$ $$\large{C}$$ $$\large{ T_i }$$ = initial temperature $$\large{F}$$ $$\large{C}$$ $$\large{ v_f }$$ = final velocity $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$ $$\large{ v_i }$$ = initial velocity $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$ $$\large{ V }$$ = volume of object $$\large{in^3}$$ $$\large{mm^3}$$ $$\large{ \Delta V }$$ = volume change $$\large{in^3}$$ $$\large{mm^3}$$ $$\large{ V_f }$$ = final volume $$\large{in^3}$$ $$\large{mm^3}$$ $$\large{ V_i }$$ = initial volume $$\large{in^3}$$ $$\large{mm^3}$$