# Volumetric Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Volumetric thermal expansion coefficient, abbreviated as $$\alpha_v$$ (Greek symbol alpha), also known as 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 FORMULA

$$\large{ \alpha_v = \frac { 1 }{ V } \; \frac {\Delta V } {\Delta T} }$$

$$\large{ \alpha_v = \frac{ v_f \;-\; v_i }{ v_i \; \left( T_f \;-\; T_i \right) } }$$

$$\large{ \alpha_v = 3 \; \alpha_i }$$

Where:

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

$$\large{ V }$$ = volume of the object

$$\large{ \Delta V }$$ = volume differential

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

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

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

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

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

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

Solve for:

$$\large{ v_f = a_v \; v_i \; \left( T_f \;- \; T_i \right) + v_i }$$

$$\large{ v_i = \frac{ v_f }{ a_v \; \left( T_f \;- \; T_i \right) \;+\; 1 } }$$

$$\large{ T_f = \frac{ v_f \;- \; v_i }{ a_v \; v_i } + T_i }$$

$$\large{ T_i = T_f - \frac{ v_f \;- \; v_i }{ a_v \; v_i } }$$