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

1 Answer

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


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#
#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.