# Linear Thermal Expansion

## Linear temperature expansion - online calculator

When an object is heated or cooled, its length changes by an amount proportional to the original length and the change in temperature. The linear thermal expansion - the change in length - of an object can be expressed as

dl = L_{0}α (t_{1}- t_{0}) (1)

where

dl = change in object length (m, inches)

L_{0}= initial length of object (m, inches)

α = linear expansion coefficient (m/m^{o}C, in/in^{o}F)

t_{0}= initial temperature(C,^{o}^{o}F)

t_{1}= final temperature(C,^{o}^{o}F)

The final length of the object can be calculated as

*L _{1} = L_{0} + dl *

* = L _{0} + L_{0} α (t_{1} - t_{0}) (2)*

*where *

*L _{1} = final length of object (m, inches)*

**Note!** - linear expansion coefficients for most materials varies with temperature.

Example - Expansion of Copper, Carbon and Stainless Steel Pipes

For wider temperature ranges - calculate for smaller spans and integrate the results.

### Online Thermal Linear Expansion Calculator

L_{0}- initial length of object (m, inches)

α -linear expansion coefficient(m/m^{o}C, in/in^{o}F)

t_{0}- initial temperature (C,^{o}^{o}F)

t_{1}- final temperature (C,^{o}^{o}F)

#### Linear Temperature Coefficients - *α *-* for some common metals *

- aluminum :
*0.000023 (m/m*^{o}C) (23 μm/m^{o}C) - steel:
*0.000012 (m/m*^{o}C)*(12 μm/m*^{o}C) - copper:
*0.000017 (m/m*^{o}C)*(17 μm/m*^{o}C) - more coefficients ..
- more metals ..

### Example - Expansion of an Aluminum Beam

An aluminum construction is designed for temperatures ranging *-30 ^{o}C* to

*50*. If a beam's length is

^{o}C*6 m*when assembled at

*20*- the shortest final length of the beam at minimum temperature

^{o}C*-30*can be calculated as

^{o}C*L _{1} = (6 m) + (6 m) (0.000023 m/m^{o}C) ((-30 ^{o}C) - (20 ^{o}C))*

* = * 5.993 m

The longest final length of the beam at maximum temperature *50 ^{o}C* can be calculated as

*L _{1} *= (6 m) + (6 m) (0.000023

*m/m*

^{o}C) ((50*) - (20*^{o}C*)*^{o}C)* = * 6.004 m

### Superficial Expansion

The amount by which a unit area of a material increases when the temperature is raised by one degree is called *the coefficient of superficial (area) expansion*.

### Cubic Expansion

The amount by which a unit volume of a material increases when the temperature is raised by one degree is called *the coefficient of cubic expansion*.