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

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 `^oC ^-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^oC` in the winter to `45.0^oC` 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 = (24 x 10^-6) (517) (70)`
`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.