A steel section of the Alaskan pipeline had a length of 68.2 m and a temperature of 21.0^{\circ}C...

Question:

A steel section of the Alaskan pipeline had a length of 68.2 m and a temperature of {eq}21.0^{\circ}C {/eq} when it was installed. What is its change in length when the temperature drops to a frigid {eq}-45.7^{\circ}C {/eq}?

Thermal Contraction:


A phenomenon in which an object undergoes fractional changes in size, shape, area, or volume, due to a change in the temperature is called a thermal expansion (or contraction). These changes, which are particularly evident for solids and metals, are quantitatively determined using the material's initial length, change in temperature, and a coefficient that dictates the fractional change in size of the material. Temperature changes in a unidimensional material is referred as a linear thermal expansion, with the change in length, {eq}\Delta L {/eq}, obtained through the formula:

$$\Delta L = \alpha L_0 \Delta T $$

where:

  • {eq}L_0 = \rm initial\ length\ of\ material {/eq}
  • {eq}\alpha = \rm coefficient\ of\ linear\ expansion\ of\ specific\ material {/eq}
  • {eq}\Delta T = {\rm change\ in\ temperature} = T_f - T_i {/eq}

Answer and Explanation: 1

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The change in length of the steel section of the Alaskan pipeline is due to the phenomenon of linear expansion or compression. An equation used to...

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Thermal Expansion: Definition, Equation & Examples

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Chapter 17 / Lesson 3
102K

In this lesson, you will learn what thermal expansion is and discover an equation for calculating how much different materials expand. You'll look at a number of examples of thermal expansion. A short quiz will follow.


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