# Thermal Expansion

Written by Jerry Ratzlaff on . Posted in Thermodynamics

## Thermal Expansion

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.

Area thermal expansion - Expands twice as much as lengths do.

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

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.

### Thermal Expansion Gases Formula

$$\large{ pV = n R T }$$ = ideal gas law

### Thermal Expansion Liquids Formula

$$\large{ \Delta V = \beta V_o \Delta T }$$ = volumetric or cubical expansion

### Thermal Expansion Solids Formulas

$$\large{ \Delta l = \alpha l_o \Delta T }$$ = linear expansion

$$\large{ \Delta A = 2 \alpha A_o \Delta T }$$ = aerial or superficial expansion

$$\large{ \Delta V = 3 \alpha V_o \Delta T }$$ = volumetric or cubical expansion

### Formula Definations

$$\large{ \Delta A }$$ = area differential

$$\large{ \Delta l }$$ = length differential

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

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

$$\large{ A_o }$$ = origional area of object

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

$$\large{ l_o }$$ = initial length of object

$$\large{ n }$$ = number of moles of gas

$$\large{ p }$$ = pressure

$$\large{ R }$$ = specific gas constant (gas constant)

$$\large{ T }$$ = temperature

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

$$\large{ V }$$ = volume

$$\large{ V_o }$$ = origional volume of object