# Linear Thermal Expansion Coefficient

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Linear thermal expansion coefficient is a porportional change in the origional length and change in temperature due to the heating or cooling of an object.

## formula

$$\alpha_l = \frac { \Delta l } { l_i \Delta T }$$

Where:

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

$$\Delta l$$ = initial length minus final length

$$l_i$$ = initial length

$$l_f$$ = final length

$$\Delta T$$ = initial temperature minus final temperature

$$T_i$$ = initial temperature

$$T_f$$ = final temperature

$$\alpha$$ (Greek symbol alpha) = thermal expansion coefficient

Solve for:

$$\Delta_l = \alpha l_i \Delta T$$

$$l_f = \alpha l_i \Delta T + l$$

$$l_i = \frac {l_f} {\alpha \Delta T +1 }$$

$$\Delta T = \frac {\Delta l}{\alpha l_i }$$

$$T_f = \frac {\Delta l} {\alpha l_i} +T_i$$

$$T_i = T_f \frac {\Delta l} {\alpha l_i}$$