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Theme B — The Particulate Nature of Matter

B.1.2 Density — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

B.1.2 Density — IB PHYSICS SL notes: Calculate density, mass and volume using ρ = m/V and relate density to particle spacing and measurement methods.Density = the mass per unit volume of an object, ρ = m/V.ρ is in kg m−3, m in kg and V in m3.Alternative units — g cm−3, with 1 g c…

  • Same volume
  • Typical values
  • Larger to smaller unit
  • Squared and cubed conversions
  • Rearranging
  • Two factors

Section 1 of 9Definition

Density
Density the mass per unit volume of an object, ρ = m/V.
  • ρ is in kg m−3, m in kg and V in m3.
Alternative units
  • Alternative units g cm−3, with 1 g cm−3 = 1000 kg m−3.
Same volume
  • Same volume the object with the lower density has the lower mass;
    • a bucket of feathers is lighter than a bucket of sand.
Intensive
  • Intensive density does not depend on how much of the material there is.
Typical values
  • Typical values air 1.2 kg m−3, water 1000, ice 920, aluminium 2700, iron 7900 and mercury 13 600 kg m−3.

Section 2 of 9Volumes and unit conversions

1Cuboid
  • V = l × w × h.
2Cylinder
  • V = πr2h.
3Sphere
  • V = (4/3)πr3.
4Larger to smaller unit
  • Larger to smaller unit multiply; smaller to larger unit — divide.
5Squared and cubed conversions
  • Squared and cubed conversions square or cube the conversion factor too.
  • 1 cm3 = 1 × 10−6 m3 and 1 mm3 = 1 × 10−9 m3.
  • 1 litre = 1 × 10−3 m3.
6Rearranging
  • Rearranging m = ρV and V = m/ρ.

Section 3 of 9Density and particle arrangement

Density and particle arrangement
Two factors
  • Two factors the mass of each particle and how closely they are packed.
Solids and liquids
  • Solids and liquids similar densities because their particles are in contact.
Gases
  • Gases densities hundreds to thousands of times lower, because of the large spacing.
Heavier atoms
  • Heavier atoms lead and gold give greater densities for similar packing.
Heating
  • Heating the volume increases while the mass is constant, so the density decreases;
    • this is the basis of convection.
Water
  • Water maximum density near 4 °C, and ice floats because its open hydrogen-bonded lattice is less dense.

Section 4 of 9Measuring density

1
For a regular solid, measure the mass on a balance and calculate the volume from the dimensions.
2
For an irregular solid, measure the mass and lower it into water in a measuring cylinder or eureka can.
3
The rise in water level equals the volume, if the object sinks and does not absorb water.
4
For a liquid, weigh an empty measuring cylinder, add a known volume, weigh again and divide the mass difference by the volume.
Uncertainty
  • Uncertainty it comes from reading the scale and balance.
Cube
  • Cube a side uncertain by ±0.5% gives a volume uncertainty of ±1.5%.

Section 5 of 9Mass–volume graphs

Mass–volume graphs
Straight line through the origin
  • Straight line through the origin the gradient is the density.
Steeper line
  • Steeper line a denser material.
Liquid in a container
  • Liquid in a container total mass against liquid volume has gradient ρ and intercept equal to the mass of the container.
Uncertainties
  • Uncertainties fractional uncertainties add when quantities are multiplied or divided and are multiplied by the power when raised to a power.
Sphere
  • Sphere volume depends on r3, so a 2% uncertainty in radius gives 6% in volume and density.

Section 6 of 9Mixtures, pressure and floating

Mixtures
  • Mixtures the average density is total mass divided by total volume, not the mean of the densities.
    • (unless the volumes are equal)
Pressure in a fluid
  • Pressure in a fluid it increases with depth as Δp = ρgh.
Floating
  • Floating an object floats when its average density is less than the fluid's.
  • The buoyant force equals the weight of fluid displaced, ρVg.
Steel ship
  • Steel ship it floats because the hull holds a large volume of air, giving an average density below that of water.

Section 7 of 9More from the specification

1
Volumetric mass density across Earth
  • Volumetric mass density across Earth measuring mass per unit volume explains buoyancy of crustal tectonic plates floating over Earth's mantle.
2
Density
  • Density mass per unit volume, rho = m divided by V, in kilograms per cubic metre.
3
Measuring density
  • Measuring density find the mass on a balance and volume by dimensions or displacement.
4
Temperature effect
  • Temperature effect most substances expand on heating, so their density falls.
5
Specific heat capacity
  • Specific heat capacity energy to raise 1 kg by 1 K, linking density and thermal behaviour of materials such as copper.
6
Latent heat
  • Latent heat energy for a change of phase at constant temperature.
7
Surface temperature
  • Effective temperature of the star's radiating surface.
8
Potential energy
  • Energy stored by the configuration of a system.
9
Luminosity
  • The total power of radiation emitted by a star.
10
Capacity
  • Charge a cell can supply, in A h or C.
11
Wavelength
  • Distance between a point on one wave and the same point on the next wave
12
Fusion
  • Joining of light nuclei into a heavier one.
13
Apparent brightness
  • The power received per unit area at the observer
14
Thermal equilibrium
  • Constant temperature because energy is absorbed and lost at equal rates
15
Phase change
  • Change of matter from one state to another
16
Thermal conductivity
  • Material constant relating the rate of conduction to the temperature gradient and area
17
Temperature
  • Measure of the average kinetic energy of the particles.
18
Thermal
  • A convection current in the air.
19
Radiation
  • Transfer by electromagnetic waves, requiring no medium
20
Copper
  • Metal widely used for electrical wires.
21
Conduction
  • Transfer of thermal energy by lattice vibrations and free electrons
22
Molecule
  • Tiny particle of the fluid, too small to be seen.

Section 8 of 9Key terms

TermMeaning
DensityMass per unit volume, ρ = m/V
VolumeSpace occupied by an object, in m3
Intensive propertyProperty that does not depend on the amount of material
Eureka canContainer used to measure the volume of an irregular solid by displacement
Average densityTotal mass divided by total volume
Fractional uncertaintyUncertainty divided by the measured value

Section 9 of 9Exam technique

1
Mixing cm3 with kg — convert volumes to m3.
2
Using the mean of two densities for a mixture — divide total mass by total volume.
3
Forgetting to cube conversion factors — 1 cm3 is 10−6 m3, not 10−2.
4
Saying density depends on the amount of material — it is the same for any sample.
5
Using the diameter in V = πr2h — use the radius.

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