# Thermal Expansion

Written by Jerry Ratzlaff. Posted in Thermodynamics

The increase in length, area or volume due to the increase (in some cased decrease) in temperature.  The stored energy in the molecular bonds between atoms changes when the heat transfer occurs.  The length of the molecular bond increases as the stored energy increases.

Linear Thermal Expansion - can only be measured in the solid state. The expansion is proportional to temperature change.

Area Thermal Expansion - Expands twice as much as lengths do.

Volumetric Thermal Expansion - can be measured for all substances (liquid or solid) of condensed matter.  Expands three times as much as lengths do.

Some substances such as water can increase or decrease depending on the temperature.

## LINEAR FORMULA

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

Where:

$$\Delta l$$ = length differential

$$\alpha$$ = linear thermal expansion coefficient

$$l_i$$ = initial length

$$\Delta T$$ = temperature differential

## AREA FORMULA

$$\Delta A = \gamma A_i \Delta T$$

$$\Delta A = 2 \alpha A_i \Delta T$$

Where:

$$\Delta A$$ = area differential

$$\gamma$$ = area thermal expansion coefficient

$$A_i$$ = initial area

$$\Delta T$$ = temperature differential

## VOLUMETRIC FORMULA

$$\Delta V = 3 \alpha V_i \Delta T$$

$$\Delta V = \beta V_i \Delta T$$

Where:

$$\Delta V$$ = volume differential

$$\beta$$ = volume thermal expansion coefficient

$$V_i$$ = initial volume

$$\Delta T$$ = temperature differential