Q: A steel railroad track is laid down with small gaps between each segment. On a very hot day, the temperature increases by $$35\ ^\circ\mathrm{C}. If $$each segment is $$12\ \mathrm{m}$$ long at $$0\ ^\circ\mathrm{C}$$ and the coefficient of linear expansion for steel is $$1.2 \times 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the increase in length of each segment?

$$\Delta L = \alpha L_0$ \Delta T = 1.2 \times 10$$^{-5}$$ \times 12 \times 35 = 0.00504\ \mathrm{m}$$

Q: A cube of aluminum with side $$L_0 = 0.10$$\ \mathrm{m}$$ is heated from 20$$\ ^\circ\mathrm{C}$$ to 120$$\ ^\circ\mathrm{C}$$. If $$\alpha_{\mathrm{Al}} = 2.4 \times $$10^{-5}$$\ \mathrm{K}^{-1}$$, what is the approximate increase in volume?

$$\Delta V = 3\alpha V_0$ \Delta T = 3 \times 2.4 \times 10$$^{-5}$$ \times (0.10)^3$ \times 100 = 7.2 \times 10$$^{-5}$$\ \mathrm{m}^3$$

Question 1

A steel railroad track is laid down with small gaps between each segment. On a very hot day, the temperature increases by $$35\ ^\circ\mathrm{C}. If $$each segment is $$12\ \mathrm{m}$$ long at $$0\ ^\circ\mathrm{C}$$ and the coefficient of linear expansion for steel is $$1.2 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the increase in length of each segment?

Accepted Answer

$$\Delta L = \alpha L_0$ \Delta T = 1.2 	imes 10$$^{-5}$$ 	imes 12 	imes 35 = 0.00504\ \mathrm{m}$$

Question 2

Which of the following best explains why a bimetallic strip bends when heated?

Accepted Answer

The two metals have different coefficients of linear expansion, causing one to expand more than the other.

Question 3

A glass vessel with a volume of $$200\ \mathrm{cm}^3 is $$filled with mercury. Both the glass and mercury are heated by $$30\ ^\circ\mathrm{C}. If$$ $$\beta_{\mathrm{Hg}} = 0.18 	imes 10$$^{-3}$$\ \mathrm{K}^{-1}$$ and $$\beta_{\mathrm{glass}} = 0.20 	imes 10$$^{-4}$$\ \mathrm{K}^{-1}$$, what is the volume of mercury that overflows?

Accepted Answer

$$\Delta V_{\mathrm{overflow}} = (\beta_{\mathrm{Hg}} - \beta_{\mathrm{glass}}) V \Delta T = (0.18 	imes 10$$^{-3}$$ - 0.20 	imes 10$$^{-4}$$) 	imes 200 	imes 30 = 0.88\ \mathrm{cm}^3$$

Question 4

Which of the following statements about the thermal expansion of water is correct?

Accepted Answer

Between $$0\ ^\circ\mathrm{C}$$ and $$4\ ^\circ\mathrm{C}$$, water decreases in volume as temperature increases.

Question 5

A metal plate with a circular hole is uniformly heated. What happens to the diameter of the hole?

Accepted Answer

The diameter of the hole increases.

Question 6

Which equation correctly relates the coefficient of volume expansion $$\beta to $$the coefficient of linear expansion $$\alpha$$ for an isotropic solid?

Accepted Answer

$$\beta = 3\alpha$$

Question 7

A thermometer uses mercury as the working liquid. Which property of mercury is most important for its use in thermometers?

Accepted Answer

Mercury's volume changes significantly with temperature.

Question 8

Why are expansion gaps left between segments of railroad tracks?

Accepted Answer

To prevent the tracks from buckling due to thermal expansion on hot days.

Question 9

Which material would you expect to expand the least for a given temperature increase, based on the coefficients of linear expansion provided?

Accepted Answer

Quartz (fused)

Question 10

A cube of aluminum with side $$L_0 = 0.10$$\ \mathrm{m}$$ is heated from 20$$\ ^\circ\mathrm{C}$$ to 120$$\ ^\circ\mathrm{C}$$. If $$\alpha_{\mathrm{Al}} = 2.4 	imes $$10^{-5}$$\ \mathrm{K}^{-1}$$, what is the approximate increase in volume?

Accepted Answer

$$\Delta V = 3\alpha V_0$ \Delta T = 3 	imes 2.4 	imes 10$$^{-5}$$ 	imes (0.10)^3$ 	imes 100 = 7.2 	imes 10$$^{-5}$$\ \mathrm{m}^3$$

Question 11

Which of the following is a real-world application that relies on the principle of thermal expansion?

Accepted Answer

Anti-scald valves in plumbing systems.

Question 12

Why do lakes and rivers freeze from the top down rather than from the bottom up?

Accepted Answer

Water is most dense at $$4\ ^\circ\mathrm{C}$$, so colder water stays on top and freezes first.

Question 13

If a rod is made twice as long, how does its change in length due to a given temperature change compare to the original rod?

Accepted Answer

It doubles.

Question 14

Which of the following best describes the molecular basis for thermal expansion in solids?

Accepted Answer

As temperature increases, atoms vibrate more and the average distance between them increases.

Question 15

A brass rod and a glass rod of equal length are both heated by $$50\ ^\circ\mathrm{C}. If$$ $$\alpha_{\mathrm{brass}} = 2.0 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$ and $$\alpha_{\mathrm{glass}} = 0.8 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$, which rod expands more and by what factor?

Accepted Answer

The brass rod expands 2.5 times more than the glass rod.

Thermal Expansion: Linear and Volume Expansion in Materials

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