Thermal Behavior of Matter and Heat Engines - Department of ...

pipelines typically include loops that allow for expansion and contraction when the
temperature changes.
11.12 Area expansion
Since the length of an object changes with temperature, it follows that its area changes
as well. The initial area of the square is A = L 2 . If the temperature of the square is
changed by ∆T, and the length of each side of the square by ∆L,
2
2 2 2
2 2 2
A'
= ( L + ∆L)
= ( L + α L∆T
) = ( L + 2αL
∆T
+ α L ∆T
) .
2 2
Neglect the higher order term, e.g. α L ∆T
2
2
, since α ∆T
2
relatively small, we have
2 2
A'
= L + 2αL
∆T
= A + 2αA∆T
That is
∆A
≈ 2 αA∆T
.
Though the calculation works out from square, it is applicable to area of any shape.
Example
A washer has hole in the middle. As the washer is heated, does the hole (a) expand,
(b) shrink, or (c) stay the same?
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