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Solved problems for the chapter:

Linear Expansivity and its Applications

View the theory »

Thermal Expansion

1. Linear expansion

2. Cubic expansion

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:linear_expansivity_and_its_applications/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 .

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 )

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.

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 .

10.

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

11.

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 .

12.

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?

13.

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

14.

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 ?

15.

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 .

16.

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 .

17.

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

18.

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 .

19.

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?

20.

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 .

21.

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.

22.

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.

23.

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.

24.

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.

25.

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

26.

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

27.

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.

28.

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.

29.

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.

30.

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

31.

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.

32.

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

33.

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?

34.

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

35.

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

36.

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.