# 13.2 Thermal expansion of solids and liquids  (Page 5/10)

 Page 5 / 10

Another example of thermal stress is found in the mouth. Dental fillings can expand differently from tooth enamel. It can give pain when eating ice cream or having a hot drink. Cracks might occur in the filling. Metal fillings (gold, silver, etc.) are being replaced by composite fillings (porcelain), which have smaller coefficients of expansion, and are closer to those of teeth.

Two blocks, A and B, are made of the same material. Block A has dimensions $l×w×h=L×2L×L$ and Block B has dimensions $2L×2L×2L$ . If the temperature changes, what is (a) the change in the volume of the two blocks, (b) the change in the cross-sectional area $l×w$ , and (c) the change in the height $h$ of the two blocks?

(a) The change in volume is proportional to the original volume. Block A has a volume of $L×2L×L={2L}^{3}\text{.}$ . Block B has a volume of $2L×2L×2L={8L}^{3},$ which is 4 times that of Block A. Thus the change in volume of Block B should be 4 times the change in volume of Block A.

(b) The change in area is proportional to the area. The cross-sectional area of Block A is $L×2L={2L}^{2},$ while that of Block B is $2L×2L={4L}^{2}\text{.}$ Because cross-sectional area of Block B is twice that of Block A, the change in the cross-sectional area of Block B is twice that of Block A.

(c) The change in height is proportional to the original height. Because the original height of Block B is twice that of A, the change in the height of Block B is twice that of Block A.

## Section summary

• Thermal expansion is the increase, or decrease, of the size (length, area, or volume) of a body due to a change in temperature.
• Thermal expansion is large for gases, and relatively small, but not negligible, for liquids and solids.
• Linear thermal expansion is
$\text{Δ}L=\mathrm{\alpha L}\text{Δ}T,$
where $\text{Δ}L$ is the change in length $L$ , $\text{Δ}T$ is the change in temperature, and $\alpha$ is the coefficient of linear expansion, which varies slightly with temperature.
• The change in area due to thermal expansion is
$\text{Δ}A=2\mathrm{\alpha A}\text{Δ}T,$
where $\text{Δ}A$ is the change in area.
• The change in volume due to thermal expansion is
$\text{Δ}V=\mathrm{\beta V}\text{Δ}T,$
where $\beta$ is the coefficient of volume expansion and $\beta \approx 3\alpha$ . Thermal stress is created when thermal expansion is constrained.

## Conceptual questions

Thermal stresses caused by uneven cooling can easily break glass cookware. Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less susceptible.

Water expands significantly when it freezes: a volume increase of about 9% occurs. As a result of this expansion and because of the formation and growth of crystals as water freezes, anywhere from 10% to 30% of biological cells are burst when animal or plant material is frozen. Discuss the implications of this cell damage for the prospect of preserving human bodies by freezing so that they can be thawed at some future date when it is hoped that all diseases are curable.

One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion? Explain your answer.

Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
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Igor
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e.g. heart Uses 2 W per beat.
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1.75cm
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A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
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What is the far point of a person whose eyes have a relaxed power of 50.5 D?
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In what ways does physics affect the society both positively or negatively