# 1.3 Thermal expansion  (Page 5/10)

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## Summary

• Thermal expansion is the increase of the size (length, area, or volume) of a body due to a change in temperature, usually a rise. Thermal contraction is the decrease in size due to a change in temperature, usually a fall in temperature.
• Thermal stress is created when thermal expansion or contraction is constrained.

## Conceptual questions

Pouring cold water into hot glass or ceramic cookware can easily break it. What causes the breaking? Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less susceptible.

The cold water cools part of the inner surface, making it contract, while the rest remains expanded. The strain is too great for the strength of the material. Pyrex contracts less, so it experiences less strain.

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.

Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.

In principle, the lid expands more than the jar because metals have higher coefficients of expansion than glass. That should make unscrewing the lid easier. (In practice, getting the lid and jar wet may make gripping them more difficult.)

When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down slightly before going up. Explain why.

Calculate the length of a 1-meter rod of a material with thermal expansion coefficient $\alpha$ when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter? Should it be? How can you account for the result you got?

After being heated, the length is ( $1+300\alpha$ ) ( $1\phantom{\rule{0.2em}{0ex}}\text{m}$ ). After being cooled, the length is $\left(1-300\phantom{\rule{0.2em}{0ex}}\alpha \right)\left(1+300\phantom{\rule{0.2em}{0ex}}\alpha \right)\left(1\phantom{\rule{0.2em}{0ex}}\text{m}\right)$ . That answer is not 1 m, but it should be. The explanation is that even if $\alpha$ is exactly constant, the relation $\text{Δ}L=\alpha L\text{Δ}T$ is strictly true only in the limit of small $\text{Δ}T$ . Since $\alpha$ values are small, the discrepancy is unimportant in practice.

Noting the large stresses that can be caused by thermal expansion, an amateur weapon inventor decides to use it to make a new kind of gun. He plans to jam a bullet against an aluminum rod inside a closed invar tube. When he heats the tube, the rod will expand more than the tube and a very strong force will build up. Then, by a method yet to be determined, he will open the tube in a split second and let the force of the rod launch the bullet at very high speed. What is he overlooking?

## Problems

The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is $35.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C.}$ What will its height be on a day when the temperature falls to $-10.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

Using [link] to find the coefficient of thermal expansion of marble:
$L={L}_{0}+\text{Δ}L={L}_{0}\left(1+\alpha \text{Δ}T\right)=170\phantom{\rule{0.2em}{0ex}}\text{m}\left[1+\left(2.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\text{/}\text{°}\text{C}\right)\left(-45.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right)\right]=169.98\phantom{\rule{0.2em}{0ex}}\text{m}$ .
(Answer rounded to five significant figures to show the slight difference in height.)

Newton's second laws is call with
Really
Arzoodan
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show mathematically that an electron has the greater speed than the proton when they attract each other
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charge at rest
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set of character...
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oky
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good
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A dipole moment it's a mechanical electrical effect used in nature
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Cyclone