# What is the change in length of an object when it undergoes a temperature change related to?

May 23, 2014

In general, the length of an object increases as the temperature increases.

#### Explanation:

Change in length is related to original length, the type of material and the amount of temperature change.

The formula for linear expansion is

$\Delta L = \alpha {L}_{o} \Delta T$
where
$\Delta L$ is the change in length of the object, in meters
$\alpha$ is the coefficient for linear expansion of the material in question, in $^ o {C}^{-} 1$
${L}_{o}$ is the original length of the object, in meters
${\Delta}_{T}$ is the change in temperature, in Kelvin (or degrees Celsius)

The coefficient for linear expansion for the material can be referenced from a chart in your textbook or on the Internet.

For example: The longest steel arch bridge in the US is 517 m long. If this bridge undergoes a temperature change from $- {25.0}^{o} C$ in the winter to ${45.0}^{o} C$ in the summer, how much will it expand?

(Let us use only the coefficient of linear expansion for steel, to simplify this question.)

$\Delta L = \alpha {L}_{o} \Delta T$
$\Delta L = \left(24 x {10}^{-} 6\right) \left(517\right) \left(70\right)$
$\Delta L = 0.86586 m$

That means that, overall, the bridge actually increases in length a total of 86.6 cm from winter to summer. This is why it will have expansion joints built into it.