Density

A system is designed to store excess energy from the National Grid.

• Excess energy from the National Grid powers a motor that lifts a large cube.

• To transfer the energy back to the National Grid, the cube is allowed to fall.

• The falling cube turns a generator which produces electricity.

Figure 6 shows the cube before it is lifted and after it is lifted.

The cube has a density of 4200 kg/m³.

Determine the mass of the cube.

Use the Physics Equations Sheet.

Explain why the cube is made from a material with a high density.

The system is designed to store excess energy from the National Grid.

Explain how the efficiency of the system could be determined.

The system in Figure 6 on page 20 needs to be able to store excess energy as quickly as possible.

Explain one change to this system that would allow the same amount of energy to be stored more quickly.

Do not refer to efficiency in your answer.

Data-storage computers get very hot.

Scientists investigated using the sea to cool data-storage computers.

The computers were set up inside a large metal container.

Figure 8 shows the metal container before it was lowered into the sea.

Why is the container made of metal?

Tick (✓) one box.

The walls of the container are solid.

Figure 9 shows an arrangement of six particles in a solid.

The air inside the container is a gas.

Draw an arrangement of six particles in a gas in the box below.

How does the air in the container exert pressure on the container?

Tick (✓) one box.

As the container is lowered into the sea, the temperature of the air in the container decreases.

Complete the sentence.

Choose the answer from the box.

When the temperature of the air in the container decreases, the average speed of the

After the temperature of the air in the container had decreased, the computers were switched on.

The computers caused the temperature of the air to then increase.

Describe how the air pressure in the container changed as the temperature decreased and then increased.

The container has a length of 12 m.

The container has a cross-sectional area of 7.5 m².

Calculate the volume of the container.

Use the equation:

volume = length × cross-sectional area

Use the Physics Equations Sheet to answer questions 05.7 and 05.8.

Write down the equation that links density (ρ), mass (m) and volume (V).

The average density of the container and its contents is 1100 kg/m³.

Calculate the mass of the container and its contents.

Use your answer to Question 05.6

Energy can be stored using a Compressed Air Energy Storage (CAES) system.

When more electricity is generated than is needed, a CAES system uses the surplus electricity to compress air in a storage tank.

When there is a greater demand for electricity, the CAES system releases the compressed air to generate electricity.

Figure 7 shows a diagram of the CAES system.

The CAES system has two processes:

• compressing air to store energy. This process has an efficiency of 0.72

• releasing the air to generate electricity. This process has an efficiency of 0.86

Calculate the efficiency of the CAES system.

Give your answer to 2 significant figures.

The generator works when forces from the compressed air cause a turbine to rotate.

When particles of air collide with the turbine they transfer energy to the turbine.

In warm weather the temperature of the compressed air increases, increasing the pressure inside the storage tank.

Explain how the motion of the particles in warmer air causes an increase in the power transferred to the turbine.

The volume of the storage tank is 5.0 × 10⁵ m³.

The density of the compressed air is 48 kg/m³.

specific heat capacity of air = 1100 J/kg °C

The temperature of the compressed air increases from 12 °C to 27 °C.

Calculate the energy transferred to the compressed air in the storage tank.

Use the Physics Equations Sheet.

Give your answer in standard form.

The UK government wants the amount of carbon dioxide released into the atmosphere to be reduced.

Explain why efficient energy storage is important in reducing the amount of carbon dioxide released when generating electricity.

A piece of steel is heated until it has all melted.

Calculate the change in thermal energy when the temperature of the piece of steel is increased by 50 °C.

mass of steel = 4.0 kg

specific heat capacity of steel = 420 J/kg °C

Use the equation:

change in thermal energy = mass × specific heat capacity × temperature change

The internal energy of the steel increases as the steel is heated.

What is meant by ‘internal energy of the steel’?

Tick (✓) one box.

Solid steel cannot be poured.

Which statement about the particles in a solid gives the reason why?

Tick (✓) one box.

Complete the sentence.

Choose the answer from the box.

Which diagram shows how the arrangement of particles changes when a solid melts and becomes a liquid?

Tick (✓) one box.

The density of steel decreases as it melts.

How does the spacing of the particles change as the steel melts?

Complete the sentence.

Choose the answer from the box.

Steel is a mixture of iron and a small amount of carbon.

Table 1 shows the mass of carbon in 1.0 kg of different types of steel.

A 4.0 kg piece of steel contains 18 grams of carbon.

Determine which type of steel the 4.0 kg piece is made from.

You should include a calculation in your answer.

The 4.0 kg piece of solid steel was heated until it reached its melting point.

The additional energy required to melt the piece of steel was 280 000 J.

Calculate the specific latent heat of fusion of the steel.

Use the Physics Equations Sheet.

Figure 6 shows a swimmer wearing a wetsuit.

The wetsuit helps to keep the swimmer warm.

A student wrapped a thermometer in a piece of wetsuit material and placed the thermometer in water containing ice.

Figure 7 shows the apparatus.

After 30 seconds in the water the temperature of the thermometer had decreased by 7.5 °C

Calculate the average decrease in temperature each second.

The student recorded the temperature of the thermometer after 30 seconds for four materials. Each piece of material was the same size and thickness.

In each test the starting temperature of the thermometer was 21.0 °C

Table 2 shows the results.

Complete Figure 8 using the data in Table 2.

You should:

• label the y-axis

• draw the bars for materials Y and Z.

Which material is the best thermal insulator?

Give a reason for your answer.

Tick (✓) one box.

The student tested a new material with a greater thermal conductivity than material Z.

The piece of new material was the same size and thickness as the piece of material Z.

What was the temperature of the thermometer after 30 seconds?

Tick (✓) one box.

During the investigation 0.0150 kg of the ice melted. The temperature of the water and ice did not change.

specific latent heat of fusion of ice = 334 000 J/kg

Calculate the energy needed to melt the ice.

Use the equation:

energy to melt the ice = mass × specific latent heat

The student wanted to determine the density of a wetsuit material.

The student measured the length of one side of a cube of wetsuit material with:

• a micrometer

• a ruler.

Table 3 shows the results.

Complete the sentence.

Choose the answer from the box.

The results show that compared to the ruler the micrometer has a higher

Use the Physics Equations Sheet to answer questions 04.7 and 04.8.

Write down the equation that links density (ρ), mass (m) and volume (V).

The student calculated the volume of the cube of wetsuit material to be 0.186 cm³

The density of the cube was 0.300 g/cm³

Calculate the mass of the cube.

Give your answer in grams.

A student investigated how the pressure of a gas depends on its temperature. The volume of the gas did not change. Figure 6 shows the equipment used.

Pressure is sometimes measured in units called atmospheres.

What is 1 atmosphere in kilopascals (kPa)?

The student took four pressure readings for each temperature. Table 1 shows the pressure readings when the temperature was 50.0 °C

Calculate the uncertainty in the mean pressure.

Figure 7 shows a sketch graph of the results.

The student said that as the temperature increases the pressure increases. Give a better description of the relationship between temperature and pressure.

A pressure cooker is a sealed pot that uses steam to cook food. Figure 8 shows a pressure cooker.

When the water in the pressure cooker starts to boil:

• the amount of steam in the pressure cooker increases

• the temperature of the steam increases above 100 °C

Explain why these changes make the pressure in the cooker increase.

If the pressure inside the pressure cooker becomes greater than 200 kPa then some of the steam is released through the safety valve. The released steam expands as it moves into the atmosphere. Explain how a change in density of the steam is caused by a change in the arrangement of particles in the steam as it is released.

A student investigated the density of different types of rock.

Figure 1 shows a piece of limestone.

The student was not able to calculate the volume of the piece of limestone using measurements taken with a ruler.

What is the reason?

Tick (✓) one box.

Figure 2 shows some of the equipment given to the student.

Describe a method the student could use to determine the volume of the piece of limestone.

The mass of the piece of limestone was 155 g.

The volume of the piece of limestone was 62 cm³.

Calculate the density of the piece of limestone.

Use the equation:

Density can be measured in g/cm³.

What is another unit for density?

Tick (✓) one box.

Figure 3 gives the density of some other types of rock.

The student has a sample of an unknown type of rock.

The density of this rock is 2.4 g/cm³.

Draw a bar on Figure 3 to show the density of the unknown type of rock.

Complete the sentence.

Choose the answer from the box.

The data in Figure 3 suggests that the unknown type of

The student cannot be certain that the unknown type of rock is one of the types of rock in Figure 3.

Give a reason why.

Pumice is a type of rock that has holes in it. The holes contain air.

Which diagram shows the arrangement of particles in air?

Tick (✓) one box.

A student determined the density of a cube made of bronze. The student used a balance to measure the mass of the bronze cube. Figure 5 shows the balance before the cube was added.

What type of error is shown on the balance?

How could the student get a correct value for the mass of the cube from the balance?

The student measured the length of the bronze cube using Vernier callipers and then using a micrometer. Table 1 shows the results.

Complete the sentence.

The results in Table 1 show that the Vernier callipers and the micrometer have

The student wanted to determine the density of a bronze coin.

The student had several identical coins. The volume of each coin was very small.

The student added water to a measuring cylinder. Figure 6 shows the student reading the volume of water in the measuring cylinder.

Give two changes the student should make to increase the accuracy of the volume measurement.

Describe how the student could use a displacement method to determine an accurate value for the volume of a single coin.

Old penny coins were made from a disc of bronze. New penny coins are made from a disc of a different metal. Figure 7 shows a disc of metal.

Table 2 shows information about the discs used to make each coin.

The discs used to make the old and the new coins have the same cross-sectional area. Calculate value X in Table 2. Give your answer to 2 significant figures. The volume of a disc can be calculated using the equation: volume of a disc = cross-sectional area × thickness

Ice cream is made by cooling a mixture of liquid ingredients until they freeze.

Which statement describes the motion of the particles in solid ice cream? Tick (✓) one box.

How do the kinetic energy and the potential energy of the particles change as a liquid

Figure 6 shows a bowl used for making ice cream.

The walls of the bowl contain a liquid coolant. The bowl is cooled to –20 °C before the mixture is put in the bowl. The bowl causes the mixture to cool down and freeze.

Explain why the different thermal conductivities of metal and plastic are important in the design of the bowl.

The liquid coolant has a freezing point below –20 °C Explain one other property that the liquid coolant should have.

The initial temperature of the mixture was +20 °C. The mixture froze at –1.5 °C. A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it. specific heat capacity of the mixture = 3500 J/kg °C specific latent heat of fusion of the mixture = 255 000 J/kg

Calculate the mass of the mixture. Give your answer to 2 significant figures.

Some ceiling lights in the home are connected to the mains by a two-core cable.

Figure 6 shows a ceiling light.

Suggest why some ceiling lights do not have an earth wire.

Write down the equation that links charge flow, current and time.

There is a current of 2.95 A in one of the copper wires for 60 seconds.

Calculate the charge flow through the wire.

Use your equation from question 04.2

Figure 7 shows a current potential difference graph for a piece of copper wire.

Draw another line on Figure 7 for a wire with a different resistance.

Some fuses have a thin piece of copper that melts if the current is too large.

Draw the circuit symbol for a fuse.

Describe how the movement of the copper particles in the wire changes when copper melts.

Old copper wires are melted when they are recycled.

Calculate the energy needed to melt 500 kg of copper at its melting point.

Specific latent heat of fusion of copper = 200 kJ/kg

Use the Physics Equations Sheet.

A student wanted to determine the density of the irregular shaped object shown in Figure 11

Plan an experiment that would allow the student to determine the density of the object.

Another student did a similar experiment.

He determined the density of five common plastic materials.

Table 3 shows the results.

Figure 12 shows the results plotted in a bar chart.

Complete Figure 12

You should:

• Write the correct scale on the y-axis.

• Draw the bars for polyester, polystyrene and PVC.

The student is given a piece of a different plastic material.

The student determined the density of the material three times.

Table 4 shows the results.

Determine the uncertainty in the student’s results.

A student wanted to determine the density of the irregular shaped object shown in Figure 3

Plan an experiment that would allow the student to determine the density of the object.

Another student did a similar experiment. He determined the density of five common plastic materials. Table 1 shows the results.

Figure 4 shows the results plotted in a bar chart.

Complete Figure 4 You should:

• Write the correct scale on the y-axis.

• Draw the bars for polyester, polystyrene and PVC.

The student is given a piece of a different plastic material. The student determined the density of the material three times. Table 2 shows the results.

Determine the uncertainty in the student’s results.