Physics: Principles and Problems
9th Edition
ISBN: 9780078458132
Table of contents
Textbook solutions
All Solutions
Page 363: Section Review
Exercise 45
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You should fit the door tightly in the frame as aluminum tends to shrink when it’s cool as opposed to concrete. It’s better to have a tightly fit door from the start.
Exercise 46
Solution 1
Solution 2
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Candle wax is considered a solid as it has a definite shape and volume. However, it is also a viscous liquid because the small particles that make up the candle don’t actually form a fixed crystalline pattern.
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Candle wax could be considered a solid because it doesn’t need a container in order to have a defined shape and volume. It can also be considered a viscous fluid because its internal structure is amorphic and reminiscent of liquids.
Exercise 47
Solution 1
Solution 2
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No. The piece will melt before its length be doubled.
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**Given information:**
Thermal expansion coefficient for copper: $alpha=16times 10^{-6}mathrm{frac{1}{ ^oC}}$
Change in length: $Delta L=L$
We need to determine is this situation possible.
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Equation that governs the change in length of a solid due to the thermal expansion is given by:
$$
Delta L=alpha LDelta T
$$
We will try to prove that this situation is not possible by calculating the change in temperature and then to conclude that at such high temperature copper is not even a solid. Firstly we solve the last equation for the change in temperature and then plug in the given information to get
$$begin{align*}
Delta T&=frac{Delta L}{alpha L}\
&=frac{L}{alpha L}\
&=frac{1}{alpha}\
&=frac{1}{16times 10^{-6}}\
&=62500 mathrm{ ^oC}
end{align*}$$
Whatever the starting temperature is, final temperature is so high that copper at this temperature would be vaporized so the situation is not possible.
$$
Delta L=alpha LDelta T
$$
We will try to prove that this situation is not possible by calculating the change in temperature and then to conclude that at such high temperature copper is not even a solid. Firstly we solve the last equation for the change in temperature and then plug in the given information to get
$$begin{align*}
Delta T&=frac{Delta L}{alpha L}\
&=frac{L}{alpha L}\
&=frac{1}{alpha}\
&=frac{1}{16times 10^{-6}}\
&=62500 mathrm{ ^oC}
end{align*}$$
Whatever the starting temperature is, final temperature is so high that copper at this temperature would be vaporized so the situation is not possible.
Exercise 48
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At the Table 13-2 we see that the coefficient of volume expansion of liquids is 10 or 100 times greater than the metals.
Exercise 49
Solution 1
Solution 2
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The particles in a solid are much closer together and more tightly bound. They will vibrate in a fixed position which allows the solid to be bent, but can also resist bending.
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The particles in a liquid are farther apart and are less tightly bound. Their particles can freely flow pass one another; hence, liquid cannot bend. They take the shape of the container they are in.
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In a solid there generally exists a periodic array of atoms, i.e., atoms are forming a lattice. In this arrangement there exist strong attractive forces between atoms and because of the periodicity all forces between constituents are the same and hence the solid is very good at resisting the deformations, but if forces of great magnitude are applied the atoms in the solid will change their arrangement but still be in fixed positions because of the small thermal energy.
In liquids thermal energy is higher so the movement of atoms is greater than in the case of solids. This results in weaker bonds between atoms that are not the same between all constituents and hence they are much easier to break and because of greater thermal energy atoms will less likely stay in the same or similar position after the bond breaks.
Exercise 50
Solution 1
Solution 2
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The gap will become much wider as all of the measurements will increase when it’s heated.
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When heat is applied to a metal it generally expands in all directions. One might think that the gap will become narrower because we often think only of length expansion. But upon closer inspection we can see that the ring will also expand in other directions which will make the gap wider and not narrower.
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