Edexcel IGCSE Physics · Spec 5.1-5.2
Density
What density is and how to measure it.
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Density
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Explained
Density, and how to measure it for an awkward shape
Density is mass per unit volume: how much matter is packed into a given space. The equation is density equals mass divided by volume, written with the Greek letter rho for density.
It is worth being clear that heavy and dense are different words. A tonne of feathers and a tonne of lead have the same mass, and the feathers occupy a vastly larger volume, so the lead is denser. Density compares substances fairly by taking the volume out of the comparison.
Units, and the factor that catches people out
The SI unit is kilograms per cubic metre. Grams per cubic centimetre is also used and is often more convenient in the laboratory.
Converting between them is not a factor of a thousand. One metre is 100 cm, so one cubic metre is 100 cubed, which is 1 000 000 cubic centimetres. Combined with 1000 g in a kilogram, the conversion works out at 1 g per cubic centimetre being 1000 kg per cubic metre.
Water is 1 g per cubic centimetre, or 1000 kg per cubic metre. Keeping that one value in mind tells you immediately whether an answer is sensible, and it is also what decides floating: anything less dense than water floats in it, anything denser sinks.
Measuring a regular solid
Find the mass on a balance. Measure the dimensions with a ruler or vernier callipers and calculate the volume from them, so length times width times height for a cuboid. Then divide.
Take each measurement more than once and in more than one place, because a block that looks square may not be, and average the readings.
Measuring an irregular solid
Here the volume cannot be calculated, so it is measured by displacement.
Find the mass first, on a balance, while the object is dry. Weighing it wet adds the mass of the water clinging to it.
Then either lower it into a measuring cylinder partly filled with water and record the rise in level, or lower it into a eureka can filled to the spout and collect the water that overflows in a measuring cylinder. Either way, the volume of water displaced equals the volume of the object.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards four marks for describing how to find the volume of an irregular object, and the way it distributes them is instructive.
One mark for referring to a displacement method. One for using a measuring cylinder to measure the volume of water, allowing graduated cylinder but not beaker. One for repeating and averaging, which it also allows as repeating to identify anomalous results. And one for any further experimental detail relating to accuracy.
That fourth mark is the interesting one, because the mark scheme lists what would earn it: avoiding splashing, reading the measuring cylinder at eye level, standing the cylinder on a flat surface, ensuring the object is fully submerged, ensuring the eureka can is completely full before the object goes in, and checking there is no air trapped in the object.
Every one of those is a way the volume could come out wrong. Splashed water is volume that left without being counted. Reading at an angle misreads the scale. An object not fully under displaces less than its own volume. Trapped air displaces water that the object itself did not.
A quarter of the marks on this question, then, are for anticipating a specific error rather than for knowing the method. It also ignores filling the pot with water, so not every plausible sounding detail counts. On the separate question of measuring the mass, the credited answer is simply a top pan balance, with mass balance, electronic balance and digital balance all allowed.
Measuring a liquid
Find the mass of an empty measuring cylinder. Pour in a known volume of the liquid and find the mass again. The difference is the mass of the liquid alone.
Weighing the cylinder empty first is the whole method. Forgetting it means the glass is included in the mass, and the density comes out far too high.
Density and the particle model
The same substance usually has a different density in each state, and the reason is spacing rather than particle size.
Solids are densest, because their particles are packed closely in a regular arrangement. Liquids are slightly less dense, because the particles are still touching but irregularly arranged. Gases are far less dense, typically about a thousandth as much, because the particles are far apart with mostly empty space between them.
Heating a fluid makes its particles spread further apart, so the same mass occupies a larger volume and its density falls. That is the step that drives convection, and it is why this topic reappears in the heat transfer questions.
Water is the famous exception, being less dense as ice than as liquid, which is why ice floats and why ponds freeze from the top down.
Spec 5.1-5.2
What you need to know
- Define density as mass per unit volume
- Use the equation density equals mass over volume
- Describe how to measure density
Active recall
Quick check
Answer each question before opening the answer.
What is the equation for density?
Density = mass ÷ volume (ρ = m ÷ V).
What are the units of density?
kg/m³ (or g/cm³).
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