Solved problems for the chapter:

Thermal Expansion of Solids, Liquids and Gases

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Thermal Expansion

1. Linear expansion

2. Cubic expansion

3. Forum

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Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:thermal_expansion_of_solids%2C_liquids_and_gases/3528/

Example 1.

Which of the following body temperatures do not change in the events described?

Pastry; after you put it in a hot oven and wait for it to bake.
Ball; when you give it to a friend.
Automotive engine; when you start it.
Air in a hot air balloon; as the balloon begins to rise from the ground.
The eraser; when you rub it against the table.
Cold water; after drinking it.
Juice; when you pour it from a bottle into a glass.

Example 2.

Calculate the expansion of a long aluminium wire if its temperature is increased by . The linear expansivity of aluminium is given as . This means that 1 m of aluminium wire extends by 0.023 mm when its temperature is increased by 1 K.

Why do we use iron bars to reinforce concrete and not lead or aluminum bars?

Reinforced Concrete

The temperature of a 6 m long steel bar is increased by . How much does it expand? The linear expansivity of steel is .

A rod of an unknown material is 4.00 m long at and 4.01 m at . What is the linear expansivity of the material from which the rod is made?

Why are there small gaps between the concrete slabs on the road? Why are the gaps flooded with asphalt?

Concrete roads and asphalt cracks .

At a temperature of 5 °C, we have 4.97 litres of oil in a 5.00-litre container. When the ambient temperature is slowly increased to 85 °C, the volume of the container increases by 0.02 litre, and 2 % of oil is spilled over the edge of the containe. What is the cubic expansivity of the container and oil?

An aluminium wire is used to form a rectangle of side length and width at 20 °C. The rectangle is then heated to 70 °C. Calculate the ratio of the:

diagonals
perimeters
areas

of the rectangle at the initial temperature (20 °C ) to that at the final temperature (70 °C), correct to 4 decimal places.

The linear expansivity of aluminium is .

What is the total linear expansion of a 40 km long railway line if the temperature increases by 40 K?

(The linear expansivity of the railway line is )

10.

A spherical iron ball has a radius of and density at . It is then placed in a furnace at . If the mass of the ball remains the same, what is the density of the ball at ? The linear expansivity of iron is .

11.

At 20 °C, the diameter of a plug is 8.753 cm and the inner diameter of a ring is 8.743 cm. At what temperature would the plug go into the ring in the following cases?

the plug is brass and inserted into an iron ring.
the plug is made of iron and the ring is made of brass.

Th linear expansivity of iron is and that of brass is .

12.

From a flask containing air, a thin tube leads into a container of water.

The flask is heated with a burner. What happens to the contents of the flask?
The flask is then cooled with ice. What happens to the contents of the flask?

a) heating the flask b) cooling the flask

13.

A mercury thermometer consists of a glass flask with a volume of and a capillary tube. What must be the inner radius of the capillary tube for a change in temperature to correspond to a 1 mm change in mercury length? The difference between the cubic expansivity of mercury and glass is .

14.

A 2.4000 m long metal rod is composed of (welded) 0.9000 m long iron rod, 0.8000 m long copper rod, and 0.7000 m long aluminum rod measured at 10 °C.

Calculate the new length of the rod if the temperature is increased by 300 K.
What is the new length if the rod is cooled by 100 K?

The linear expansivities of iron, copper, and aluminium are , and respectively.

Calculate the results to 4 decimal places.

15.

There are two rods at a room temperature . The first is made of aluminium and is 60.0 cm long, the second is made of iron and is 60.2 cm long.

At what temperature will the rods be of the same length?
What is this length?

The linear expansivity of aluminium is and that of iron is .

16.

The circumference of a copper ring at a temperature of 20 °C is equal to 2.000 m. To what temperature do we need to heat the ring to increase the area of the circle bounded by the ring by 2 % of the original area?

The linear expansivity of copper is .

17.

What must be the change in temperature of a 30 m long gold wire if it's to have an expansion of 1 mm?

What is the expansion of an aluminium wire of the same length and temperature change?

The table below shows the values of the linear expansivities of aluminum and gold:

Linear expansivity of aluminium	Linear expansivity of gold

18.

A copper ring has a diameter of 0.8 m. How much does the circumference of the ring increase if its temperature is increased by 300 K? The linear expansivity of copper is .

19.

For most materials, when the temperature increases, they expand and their density decreases, and when the temperature decreases, they contract, and their density increases. This rule does not apply to water. Answer the following questions:

At what temperature is water densest?
Why does ice float on water?
What is the temperature of the water at the bottom of Lake Bled during winter when there is a layer of ice on top?
How is it that the fish in the lake do not freeze in the winter when children are already skating on the lake?

20.

A blacksmith uses an aluminium ruler in his work. He uses it to measure the length of a pipe and then places the ruler right next to the forge furnace, where the temperature is high. The blacksmith then measures the length of the pipe again but the hot ruler shows a different length of pipe from the initial measurement. Does the ruler show a higher or lower pipe length on the second measurement?

21.

A bimetal is made of iron and gold. How will the left end of the strap bend (the right one is clamped) if heated? The table shows the linear expansivity of iron and gold:

Bimetal of iron and gold

22.

When the temperature of a long iron bar is increased by , it extends by . How much does a long iron bar extend if its temperature is increased by ?

23.

An aluminium plate has a round opening with a diameter of 9.82 cm. What is the diameter of the opening if the temperature of the plate is increased by 400 K? The linear expansivity of aluminium is .

24.

The table below shows the linear expansivities of steel and glass. Explain why it is easier to unscrew the steel lid on a glass jar of pickled fruit when you immerse the whole jar in warm water.

25.

There are two equally long steel bars. Their length, measured at , is . The first is placed in the freezer, where the temperature is , and the second in the oven with a temperature of . What is the difference between the lengths of the cooled and heated bars? The linear expansivity of steel is .

26.

What is the percent increase in the area of a copper plate if its temperature is increased by 300 K? The linear expansivity of copper is .

27.

A bimetal is made of iron and gold. How will the left end of the strap bend (the right one is clamped) if we cool it?

Bimetal of iron and gold

28.

A cylindrical plug with a diameter of 20.00 mm is to be inserted into a cylindrical opening with a diameter of 19.98 mm in an iron plate. How much do we need to heat the iron plate for the plug to go into the opening? The linear expansivity of iron is .

29.

A square-shaped plate is heated. The length of each side of the square increases by after heating. By what percentage does the area of the plate increase?

30.

What is the density of mercury at if its density at is equal to . The cubic expansivity of mercury is .

31.

The table below shows the expansions produced when the temperature of - length of each of the metals listed is increased by :

Metals	Expansion [mm]
Iron, Steel	0.012
Gold	0.014
Aluminum	0.023
Lead	0.029

Which two metals would you use to make a bimetallic strip that will bend the most?
Which two metals would you use to make a bimetallic strip that will bend the least?

32.

The temperature of an iron cube is increased by 500 K.

What is the percent increase in its volume?
What is the percent increase in the length of its edge?

The linear expansivity of iron is .

33.

What is the percentage change in the volume of a cube whose edge is stretched by of its original length?

34.

By how much does the length of an iron rod of original length change if it cools by ?

The linear expansivity of iron is given as . This means that each metre of iron rail extends by 0.012 mm when heated by 1 K .

35.

What tools or data do we need to be able to use an iron rod to measure the temperature of the heated liquid in a container?

Density of iron, the linear expansivity of iron, measuring scale, and the specific heat capacity of the liquid.
Change in temperature, the pressure in the container, and the thickness of the rod.
Length of the rod at the initial temperature, the specific heat capacity of iron, measuring scale.
Expansion of the iron, measuring scale, and the initial temperature of the iron rod.
Change of temperature of the rod, the specific weight of iron, the external pressure, the pressure inside the container, and measuring scale;
Change in length of the iron rod, the density of iron, the mass of the rod, and the volume of the rod.

36.

A bimetallic strip is used to control the temperature of an electrical appliance. It is made of two different metals fixed together. The diagram shows the shape of the bimetallic strip before and after heating.

Which statement is correct?

Metal P contracts more than metal Q on heating.
Metal Q contracts more than metal P on heating.
Metal P expands more than metal Q on heating.
Metal Q expands more than metal P on heating.

37.

The diagram shows electricity cables being put up on a warm day. The cables are left loose between the poles, as shown in the diagram.

Why are the cables left loose?

They will contract on cold days.
They will contract on very warm days.
They will expand on cold days.
They will expand on very warm days.

38.

The temperature of a bridge rises from 5 °C on a cold night to 25 °C at midday. What happens to the bridge?

It becomes heavier.
It becomes more dense.
Its length increases.
Its mass increases.

39.

A wooden wheel can be strengthened by putting a tight circle of iron around it.

Which action would make it easier to fit the circle over the wood?

cooling the iron circle only
heating the iron circle
heating the wooden wheel and cooling the iron circle
heating the wooden wheel but not heating or cooling the iron circle

40.

A glass bottle has a metal cap. The cap fits very tightly and is difficult to remove. The cap and the neck of the bottle are dipped in a bowl of hot water. The cap can be removed more easily. What happens to allow the cap to be removed more easily from the bottle?

The cap contracts.
The cap expands.
The glass bottle contracts.
The glass bottle expands

41.

What happens when a metal block is heated?

Its width, height, and length all increase.
Its width increases only.
Its height increases only.
Its length increases only.

42.

A strip of iron and a strip of brass are firmly attached to each other along their entire length. This combination is a bimetallic strip.

This bimetallic strip is heated and it bends as shown.

The bimetallic strip is now cooled and becomes straight again. What causes the bimetallic strip to become straight again?

The brass contracts more than the iron.
The brass expands more than the iron.
The iron contracts more than the brass.
The iron expands more than the brass.

43.

Four students are asked to state and explain the relative magnitudes of the thermal expansion of solids and gases. Which student is correct?

Gases expand more than solids because the molecules in a gas are in random motion.
Gases expand more than solids because the attractive forces between molecules are much weaker in gases.
Solids expand more than gases because the molecules are closer together in solids.
Solids expand more than gases because the molecules in a solid are in a regular pattern.

44.

Which row shows the relative order of thermal expansion of solids, liquids and gases?

45.

A long, thin bar of copper is heated gently and evenly along its length.

What happens to the bar?

It becomes less heavy.
It becomes longer.
It becomes shorter.
It bends at the ends.

46.

The metal lid on a glass jar is difficult to unscrew. The jar is placed in a warm oven until the jar and the lid reach the same temperature. The lid is now easily unscrewed. Which property accounts for this?

thermal capacity of the jar
thermal capacity of the lid
thermal conduction
thermal expansion

47.

The diagrams show four examples of thermal expansion. In three of the examples, thermal expansion is useful. In one of the examples, expansion is unwanted and has to be allowed for. In which example is thermal expansion unwanted?

48.

The distance between two electricity pylons is . An engineer fits a cable of length between the pylons. Why does the engineer choose a cable that is longer than the distance between the two pylons?

to allow for contraction of the cable in cold weather
to create a slope in the cable for electrons to flow down
to keep the current low and the voltage high
to reduce magnetic fields around the cable

49.

Why are small gaps left between the metal rails of a railway track?

to allow for expansion of the rails on a hot day
to allow for contraction of the rails on a hot day
to allow for expansion of the rails on a cold day
to allow for contraction of the rails on a cold day

50.

When a bridge is built, a gap is left between each concrete slab. Why are these gaps left?

Concrete expands on warm days.
Concrete contracts on warm days
The gaps expand on warm days.
The gaps contract on cold days.