How to measure the density of regular solids, irregular solids and liquids, and how to compare thermal insulators fairly, with the results, graphs and evaluation that exam questions ask for.
Objectives
Calculate density from mass and volume, and convert between g/cm³ and kg/m³.
Describe how to measure the density of a regular solid, an irregular solid and a liquid.
Plan a fair test to compare thermal insulators, naming the variables that must be controlled.
Use a table or a cooling graph to decide which material is the best insulator, and evaluate the method.
Density and thermal insulation practicals explained
Start here
Two of the most common practical questions in physics are about materials. How can you find out how much matter is packed into a space, which is density? And how can you find out which material keeps something hot for longest, which is thermal insulation?
Both practicals follow the same pattern. You choose what to change and what to measure, you keep everything else the same so that the test is fair, you repeat readings, and then you use your results to reach a conclusion and judge how reliable it is.
By the end you can describe the three density methods, plan a thermal insulation test, and answer the evaluation questions that go with them.
Density and the equation
Density tells you how much mass is packed into each unit of volume. The equation is density = mass ÷ volume, written ρ = m ÷ V. The symbol ρ is the Greek letter rho. The unit is kilograms per cubic metre, kg/m³, or grams per cubic centimetre, g/cm³.
The two units are linked: 1 g/cm³ is the same as 1000 kg/m³. Water has a density of 1.0 g/cm³, which is 1000 kg/m³. An object with a density greater than water sinks in water. An object with a smaller density floats.
If you are given a mass in kilograms and a volume in cubic centimetres, change one of them first so that the units match. Then divide.
A formula triangle with mass on top and density and volume underneath. Density equals mass divided by volume, and mass equals density times volume.
A regular solid
A regular solid has a shape you can measure, such as a cuboid. Find its mass by putting it on a balance. Then measure its length, width and height with a ruler, or with calipers for a more precise value. Multiply the three to get the volume.
For example, a metal block that is 4.0 cm long, 3.0 cm wide and 2.0 cm high has a volume of 4.0 × 3.0 × 2.0 = 24 cm³. If its mass is 65 g, its density is 65 ÷ 24 = 2.7 g/cm³, which is the density of aluminium.
Repeat each length measurement in different places and take a mean. Check that the balance reads zero before you start. The biggest source of error is usually the ruler, because a small reading error on a short length is a large percentage of the length.
A flow of four boxes: measure the mass on a balance, measure the length, width and height, work out the volume by multiplying them, then work out density as mass divided by volume.
An irregular solid and a liquid
A stone has no neat shape, so you find its volume by displacement. Fill a displacement can with water until it just overflows from the spout. Put a measuring cylinder under the spout. Lower the stone slowly on a thread into the can, and collect the water that is pushed out. The volume of that water equals the volume of the stone. You can also lower the stone into a measuring cylinder of water and subtract the starting reading from the final reading.
Read a measuring cylinder with your eye level with the bottom of the curved surface of the water, called the meniscus. Dry the stone and find its mass on the balance. If the stone has a mass of 130 g and displaces 50 cm³, its density is 130 ÷ 50 = 2.6 g/cm³.
For a liquid, put a measuring cylinder on a balance and set the reading to zero. Pour in a known volume, such as 50 cm³, and read the mass of the liquid straight from the balance. Divide the mass by the volume. If 50 cm³ of oil has a mass of 46 g, its density is 46 ÷ 50 = 0.92 g/cm³, which is less than water, so the oil floats on water.
Planning a thermal insulation test
An insulator slows the transfer of thermal energy. To compare materials, wrap identical containers of hot water in different materials such as bubble wrap, cotton wool, newspaper and foam, or pack the material between a small beaker and a larger one. Put a lid on each container with a hole for a thermometer.
The material is the independent variable, because it is what you change. The fall in temperature after a fixed time is the dependent variable, because it is what you measure. Everything else is a control variable and must be the same: the starting temperature of the water, the volume of water, the type and size of container, the thickness of the insulation, the lid, the room and the time.
Record the temperature at the start and then every two minutes for about ten minutes. Safety matters because you are using hot water. Use water at about 80 °C rather than boiling, stand the containers on a heatproof mat, wear eye protection and take care when carrying the kettle.
Results and evaluation
The best insulator is the one that lets the water cool the least in the same time. Work out the fall in temperature for each material by subtracting the final temperature from the starting temperature. If foam gives a fall of 12 °C and newspaper a fall of 19 °C, the foam is the better insulator and it is 7 °C better.
A graph of temperature against time for each material shows the same thing. The curve for the better insulator is flatter, because it loses energy more slowly. Insulators work because they have a low thermal conductivity, which means they are poor conductors of heat. Materials that trap small pockets of air are especially good, because air is a poor conductor and trapped air cannot circulate to carry heat away by convection.
To improve the investigation, repeat each material and take a mean, use a thermometer with a smaller scale division or a temperature probe, and use the same thickness of each material. Say what you changed and why it improves the results.
A graph of temperature against time for two beakers of hot water. The beaker with no insulation cools from 80 to 54 degrees in 10 minutes. The beaker wrapped in foam cools from 80 to 68 degrees, so its line is flatter and the foam is the better insulator.
Improving the method
Exam questions often ask what could go wrong and how to fix it. In the density practicals the main problems are reading errors and water clinging to the stone. In the insulation test the main problems are heat lost from the top of the beaker and a thermometer that only reads to the nearest degree.
Random errors change from one reading to the next, and repeating the readings and calculating a mean reduces their effect. A systematic error shifts every reading the same way, such as a balance that does not read zero when empty, and it is fixed by correcting the equipment, not by repeating.
When you suggest an improvement, say what you would do and why it helps. For example: read the meniscus with your eye level with the bottom of the curve, to avoid a parallax error. Or: use a lid on each beaker, to reduce the energy lost by evaporation and convection from the surface of the water.
Recap
Density is mass divided by volume. Measure the mass on a balance, find the volume by measuring lengths, by displacement or with a measuring cylinder, and divide. A material that is denser than water sinks in water.
In a thermal insulation test, change only the material, measure the fall in temperature after a fixed time, and control everything else. The smaller the fall, the better the insulator. Repeat the readings and use a graph to compare the cooling curves.
Key points
Density = mass ÷ volume, and 1 g/cm³ equals 1000 kg/m³.
Find the volume of a regular solid by multiplying its three lengths, of an irregular solid by displacement, and of a liquid with a measuring cylinder.
A material with a density greater than water sinks in water, and a material with a smaller density floats.
In the insulation test, the material is the independent variable, the fall in temperature is the dependent variable, and everything else is controlled.
The best insulator gives the smallest fall in temperature, and a flatter cooling curve.
Worked examples
Example 1
A metal block is 5.0 cm long, 4.0 cm wide and 2.0 cm high. Its mass is 108 g. Calculate its density.
Find the volume: 5.0 × 4.0 × 2.0 = 40 cm³.
Write the equation: density = mass ÷ volume.
Substitute: 108 ÷ 40 = 2.7 g/cm³.
Answer: 2.7 g/cm³
Common slips
Slip: Volume = 5.0 + 4.0 + 2.0 = 11 cm³ The volume of a cuboid is found by multiplying the three lengths, not adding them.
Slip: density = volume ÷ mass Density is mass divided by volume, not the other way round.
Slip: 108 × 40 = 4320 g/cm³ Divide the mass by the volume. Multiplying gives a number that is far too large.
Example 2
A student lowers a stone into a measuring cylinder containing 60 cm³ of water. The water level rises to 90 cm³. The stone has a mass of 78 g. Calculate the density of the stone.
Find the volume of the stone from the rise in water level: 90 − 60 = 30 cm³.
Write the equation: density = mass ÷ volume.
Substitute: 78 ÷ 30 = 2.6 g/cm³.
Answer: 2.6 g/cm³
Common slips
Slip: The volume of the stone is 90 cm³. The final reading includes the water. Subtract the starting reading to find the volume of the stone.
Slip: density = mass × volume Density is found by dividing the mass by the volume.
Slip: 78 ÷ 90 = 0.87 g/cm³ This uses the final reading instead of the stone volume. It would wrongly suggest the stone floats.
Example 3
Two identical beakers each hold 100 cm³ of water at 80 °C. Beaker A is wrapped in foam and beaker B is wrapped in newspaper. After 10 minutes the temperatures are 68 °C for A and 61 °C for B. State which material is the better insulator and calculate how much more the water in B cooled.
Work out the fall in temperature for A: 80 − 68 = 12 °C.
Work out the fall in temperature for B: 80 − 61 = 19 °C.
The smaller fall means less thermal energy escaped, so foam is the better insulator.
B cooled by more than A by 19 − 12 = 7 °C.
Answer: Foam is the better insulator. The water in B cooled by 7 °C more.
Common slips
Slip: A fell by 68 °C. The fall is the starting temperature minus the final temperature, not the final temperature.
Slip: B fell by 61 °C. Subtract the final temperature from the start to find the fall.
Slip: Newspaper is better because its final temperature is lower. A lower final temperature means the water lost more thermal energy.
Slip: B cooled by 80 − 61 − 68 = −49 °C Compare the two falls. Subtract the smaller fall from the larger fall.
Questions and answers
Density and thermal insulation practicals practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
State the equation for density.
Show answer
Answer: density = mass ÷ volume
Density compares mass with the space it takes up.
density = mass ÷ volume.
Question 2 Easy
A block has a mass of 160 g and a volume of 20 cm³. Calculate its density.
Show answer
Answer: 8.0 g/cm³
density = mass ÷ volume.
160 ÷ 20 = 8 g/cm³.
Question 3 Easy
Which piece of equipment is used to measure the mass of a solid in a density practical?
Show answer
Answer: a balance
Mass is measured on a balance.
A ruler measures length and a measuring cylinder measures volume.
Question 4 Easy
Where should your eye be when you read a measuring cylinder?
Show answer
Answer: level with the bottom of the meniscus
The bottom of the curved surface is the meniscus.
Your eye should be level with it.
Question 5 Medium
A stone of mass 130 g displaces 50 cm³ of water. Calculate the density of the stone.
Show answer
Answer: 2.6 g/cm³
The volume of the stone equals the volume of water displaced, 50 cm³.
130 ÷ 50 = 2.6 g/cm³.
Question 6 Medium
Convert a density of 2.5 g/cm³ into kg/m³.
Show answer
Answer: 2500 kg/m³
1 g/cm³ is 1000 kg/m³.
2.5 × 1000 = 2500 kg/m³.
Question 7 Medium
50 cm³ of a liquid has a mass of 46 g. Calculate its density and say whether the liquid floats on water.
Show answer
Answer: 0.92 g/cm³, so it floats
density = 46 ÷ 50 = 0.92 g/cm³.
This is less than the density of water, 1.0 g/cm³, so it floats.
Question 8 Medium
State two control variables in an investigation comparing thermal insulators.
Show answer
Answer: the starting temperature of the water and the volume of water
The test is fair only if just the material changes.
Starting temperature and volume of water are two examples.
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A student is given a small stone with an irregular shape. Describe a method the student could use to find the density of the stone. [4 marks]
Show answer and marking points
Answer: Find the mass of the stone on a balance. Fill a displacement can until water just runs out of the spout and place a measuring cylinder under the spout. Lower the stone gently into the can on a thread and collect the displaced water. Read the volume of the water in the measuring cylinder, which equals the volume of the stone, and calculate density = mass ÷ volume.
measure the mass of the stone with a balance (1)
use a displacement can or a measuring cylinder of water to find the volume of water displaced (1)
the volume of the water displaced equals the volume of the stone (1)
density = mass ÷ volume (1)
Exam-style question 24 marks
A student compares three materials as thermal insulators. She wraps each material round an identical beaker of hot water and measures the fall in temperature after 10 minutes.
(a) State two variables she must keep the same. [2 marks]
(b) Describe how her results would show which material is the best insulator. [2 marks]
Show answer and marking points
Answer: (a) Any two from: the starting temperature of the water, the volume of water, the thickness of the insulation, the type of beaker, the time. (b) Work out the fall in temperature for each material. The material with the smallest fall in temperature is the best insulator.
(a) one correct control variable (1)
(a) a second correct control variable (1)
(b) work out the fall in temperature for each material (1)
(b) the smallest fall means the best insulator (1)
Common mistakes
Adding the length, width and height to find the volume
Multiply them. Volume of a cuboid = length × width × height.
Using the final reading in the measuring cylinder as the volume of the stone
Subtract the starting reading from the final reading to find the volume of the stone.
Reading the meniscus from above or below
Put your eye level with the bottom of the curve of the liquid, or the reading will be wrong.
Forgetting to control the starting temperature or the volume of water in the insulation test
Only the material may change. Everything else, including the starting temperature and the volume, must stay the same.
Saying the insulator with the lower final temperature is the best
The best insulator has the smallest fall in temperature, so the highest final temperature.
Questions students ask
Is Density and thermal insulation practicals on the Foundation or Higher tier?
Density and thermal insulation practicals is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 5.
What is a common mistake on Density and thermal insulation practicals?
Adding the length, width and height to find the volume. Multiply them. Volume of a cuboid = length × width × height.
Where are the answers to the Density and thermal insulation practicals questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.