Question

A long steel I-beam used in bridge construction has a length of 15.0 m. The beam may be exposed to temperatures as low as −23°C in the winter and as high as 32°C in the summer. What is the difference in length of the beam between these two temperature extremes? (Give the absolute value of the difference. Enter your answer in mm.)

Answer 1

To solve this problem it is necessary to apply the concepts of thermal expansion. Thermal expansion can be expressed in longitudinal terms such as

`\Delta L = L_0 \alpha \Delta T`

Where,

`\alpha =` Thermal Expanssion Coefficient

`L_0 =` Initial Length

`\Delta T =` Change in Temperature

Our values are given as

`\alpha = 11*10^(-6)/\°C \rightarrow` from Steel

`L_0 = 15m`

`T_1 = -23\°C`

`T_2 = 32\°C`

Replacing we have that,

`\Delta L = L_0 \alpha \Delta T`

`\Delta L = (17)(11*10^(-6))(32-(-21))`

`\Delta L = 0.009911m`

`\Delta L = 9.911mm`

Therefore the difference in length of the beam between these two temperature extremes is 9.911mm