Density Required Practical, Internal Energy & Particle Motion in Gases
The particle model of matter explains why solids, liquids, and gases have vastly different densities (ρ = m / V) and compressibilities based on the spacing, arrangement, and kinetic energy of their particles. In gases, rapidly moving particles collide randomly with the walls of their container; each collision exerts a force at right angles to the wall, creating an outward gas pressure (p = F / A). Examiners regularly test the 6-mark required practical for measuring the density of regular solids, irregular solids (using a displacement Eureka can), and liquids, as well as explaining how heating or compressing a gas increases its pressure (including Boyle's Law, pV = constant, for Triple Science).
- Density Formula (ρ = m / V)
- Density is the mass per unit volume of a substance. Formula: Density, ρ (kg/m³ or g/cm³) = Mass, m (kg or g) / Volume, V (m³ or cm³). Note that 1 g/cm³ = 1,000 kg/m³ (the density of pure liquid water). An object floats in a fluid if its average density is less than the density of the fluid.
- Required Practical: Density of Regular Solids, Irregular Solids & Liquids
- 1. Regular solid (cuboid/cylinder): Measure mass (m) on an electronic balance; measure length, width, and height using a millimetre ruler or Vernier callipers/micrometer and calculate V = l x w x h; calculate ρ = m / V. 2. Irregular solid: Measure mass (m) on balance; find volume (V) by submerging in a water-filled displacement (Eureka) can and measuring displaced water volume in a measuring cylinder. 3. Liquid: Weigh empty measuring cylinder (m₁), add volume V of liquid (read bottom of meniscus at eye level), reweigh (m₂), find liquid mass m = m₂ - m₁, and calculate ρ = m / V.
- States of Matter & Conservation of Mass
- Solid: regular lattice arrangement, particles vibrate about fixed positions, strong forces between particles, fixed shape and volume. Liquid: random arrangement, particles still touching and slide past each other, weaker forces, fixed volume but takes shape of container. Gas: random arrangement, particles far apart moving rapidly in all directions, negligible forces between particles, fills any container. Changes of state (melting, boiling/evaporating, freezing, condensing, sublimating) are physical changes: mass is conserved because no particles are created or destroyed.
Density Required Practical, Internal Energy & Particle Motion in Gases: Wave Equation (v = fλ) & Force Vector (F = ma) Simulator
Adjust physical variables on the sliders below to see real-time changes in wave geometry, resultant forces, and acceleration.
F_net = 80 N − 25 N = 55 NAcceleration: a = F_net ÷ m = 55 ÷ 10 = 5.50 m/s²Key Concepts & Exam Definitions (6)
- Density Formula (ρ = m / V)
- Density is the mass per unit volume of a substance. Formula: Density, ρ (kg/m³ or g/cm³) = Mass, m (kg or g) / Volume, V (m³ or cm³). Note that 1 g/cm³ = 1,000 kg/m³ (the density of pure liquid water). An object floats in a fluid if its average density is less than the density of the fluid.
- Required Practical: Density of Regular Solids, Irregular Solids & Liquids
- 1. Regular solid (cuboid/cylinder): Measure mass (m) on an electronic balance; measure length, width, and height using a millimetre ruler or Vernier callipers/micrometer and calculate V = l x w x h; calculate ρ = m / V. 2. Irregular solid: Measure mass (m) on balance; find volume (V) by submerging in a water-filled displacement (Eureka) can and measuring displaced water volume in a measuring cylinder. 3. Liquid: Weigh empty measuring cylinder (m₁), add volume V of liquid (read bottom of meniscus at eye level), reweigh (m₂), find liquid mass m = m₂ - m₁, and calculate ρ = m / V.
- States of Matter & Conservation of Mass
- Solid: regular lattice arrangement, particles vibrate about fixed positions, strong forces between particles, fixed shape and volume. Liquid: random arrangement, particles still touching and slide past each other, weaker forces, fixed volume but takes shape of container. Gas: random arrangement, particles far apart moving rapidly in all directions, negligible forces between particles, fills any container. Changes of state (melting, boiling/evaporating, freezing, condensing, sublimating) are physical changes: mass is conserved because no particles are created or destroyed.
- Particle Motion & Pressure in Gases
- Gas molecules are in constant, random motion at high speeds. Temperature is directly proportional to the average kinetic energy of the molecules. As gas molecules collide with the inside walls of their container, their momentum changes and they exert a force at right angles (normal) to the surface. Gas pressure is the total force exerted by these collisions per unit area of the wall (p = F / A).
- Boyle's Law: Pressure & Volume at Constant Temperature (Triple)
- For a fixed mass of gas held at constant temperature, the pressure is inversely proportional to the volume: Pressure, p (Pascals, Pa) x Volume, V (m³) = constant (or p₁V₁ = p₂V₂). Halving the volume of a container doubles the number of particles per unit volume, so particles collide with the walls twice as frequently, doubling the pressure.
- Work Done on a Gas (Triple Higher Tier)
- Work is the transfer of energy by a force. Compressing a gas rapidly (e.g., using a bicycle pump) does mechanical work on the gas. This increases the internal energy store of the gas; because the gas particles bounce off the inward-moving piston faster, their average kinetic energy increases, increasing the temperature of the gas.
Quick-Fire Flashcards (6)
Click any card to check the answer, then mark it as Known to track your progress.
State the equation for density with standard SI units.
Why must you weigh an irregular object before submerging it in the Eureka can rather than after?
Why are changes of state (such as melting or boiling) classified as physical changes rather than chemical reactions?
What is the difference between boiling and evaporation?
State Boyle's Law in words and as an equation (Triple Science).
Explain why a helium balloon expands as it rises high into the upper atmosphere (Triple Science).
Exam-Style Questions & Mark Schemes (4)
Write or think through your answer first, then click Check Mark Scheme to see the exact points examiners award marks for.
- Q1
Describe in detail how a student can accurately determine the density of an irregularly shaped stone using a displacement can (Eureka can), a measuring cylinder, and an electronic balance. Include two precautions to improve accuracy. [6 marks]
Click “Check Mark Scheme” to compare your answer, 1. Place the dry stone on a zeroed electronic top-pan balance and record its mass (m) in grams [1 mark]. 2. Place a displacement (Eureka) can on a flat, level bench and fill it with water until excess water overflows from the spout; wait until the spout completely stops dripping [1 mark]. 3. Place an empty, dry measuring cylinder of suitable resolution directly underneath the spout [1 mark]. 4. Tie a thin piece of cotton/thread around the stone and lower it gently into the Eureka can until it is completely submerged (without splashing or letting your fingers enter the water) [1 mark]. 5. Wait for the spout to stop dripping, then read the volume of displaced water (V) in cm³ by viewing the bottom of the meniscus at eye level (to avoid parallax error) [1 mark]. 6. Calculate the density of the stone using the equation Density = Mass / Volume (ρ = m / V) in g/cm³ [1 mark].
- Q2
An aerosol deodorant can carries a warning label: 'Do not incinerate or expose to temperatures above 50°C'. Use the particle model of gases to explain why heating a sealed aerosol can could cause it to explode. [4 marks]
Click “Check Mark Scheme” to compare your answer, 1. Heating the aerosol can transfers thermal energy to the gas particles inside, increasing their average kinetic energy so the particles move faster [1 mark]. 2. Because the volume of the metal can is fixed and the particles move faster, they collide with the inside walls of the can more frequently (more collisions per second) [1 mark]. 3. Each collision with the wall also occurs with a greater force (harder collisions / greater change in momentum) [1 mark]. 4. Since pressure = force / area, the total outward force on the fixed surface area of the can increases, raising the gas pressure until the metal walls rupture and explode [1 mark].
- Q3
A scuba diver's air tank has an internal volume of 0.012 m³ and is filled with air at a pressure of 2.0 x 10⁷ Pa. Calculate the volume that this mass of air would occupy at normal atmospheric pressure (1.0 x 10⁵ Pa), assuming the temperature remains constant, and explain in terms of particles why compressing the air into the small tank increased its pressure. (Triple Science) [5 marks]
Click “Check Mark Scheme” to compare your answer, 1. State Boyle's Law at constant temperature: p₁ x V₁ = p₂ x V₂ (or p x V = constant) [1 mark]. 2. Substitute values: (2.0 x 10⁷ Pa) x 0.012 m³ = (1.0 x 10⁵ Pa) x V₂ -> 240,000 = 100,000 x V₂ [1 mark]. 3. Solve for V₂: V₂ = 240,000 / 100,000 = 2.4 m³ [1 mark]. 4. Particle explanation: Compressing the same number of air molecules into a much smaller volume increases the concentration (density) of gas particles [1 mark]. 5. With less distance to travel between walls, the particles collide with the internal walls of the tank much more frequently, exerting a much greater total outward force per unit area [1 mark].
- Q4
A solid brass cylinder has a radius of 2.0 cm, a height of 10.0 cm, and a mass of 1.07 kg. Calculate the density of the brass in g/cm³ (to 2 decimal places) and in kg/m³. (Volume of a cylinder = πr²h). [4 marks]
Click “Check Mark Scheme” to compare your answer, 1. Calculate the volume of the cylinder in cm³: V = π x r² x h = 3.1416 x (2.0)² x 10.0 = 125.66 cm³ [1 mark]. 2. Convert mass from kg to g: m = 1.07 kg x 1,000 = 1,070 g [1 mark]. 3. Calculate density in g/cm³: ρ = m / V = 1,070 g / 125.66 cm³ = 8.51 g/cm³ [1 mark]. 4. Convert to kg/m³ (multiply by 1,000): ρ = 8,510 kg/m³ [1 mark].
Common Exam Questions (4)
How do you measure the density of an irregular solid object (like a stone or chess piece) in the required practical?
1. Measure the mass (m) of the dry irregular object using a zeroed electronic top-pan balance. 2. Fill a displacement can (Eureka can) with water right up to the spout on a level surface and wait until it stops dripping. 3. Place an empty measuring cylinder under the spout and gently lower the object into the water on a thin thread until completely submerged. 4. The volume of water displaced into the measuring cylinder equals the volume (V) of the object. 5. Calculate density using ρ = m / V.
Why are solids and liquids generally much denser than gases?
In solids and liquids, the particles are packed closely together (touching), so there is a large mass of particles in a given unit volume. In a gas, the particles are very far apart with mostly empty space between them, so there are far fewer particles (much less mass) in the same volume (typically ~1,000 times less dense).
Why does the pressure of a fixed mass of gas in a sealed rigid container increase when its temperature is increased?
Score all 3 marks: 1. Increasing the temperature increases the average kinetic energy of the gas particles, so they move faster. 2. The particles collide with the internal walls of the container more frequently (more collisions per second) and each collision is harder (greater change in momentum / greater force per collision). 3. Since pressure = total force / area, a greater total force exerted on the same wall area increases the gas pressure.
How does doing work on a gas (such as pumping up a bicycle tyre rapidly) affect its temperature? (Triple Higher Tier)
Pushing the bicycle pump piston inwards does mechanical work on the gas (work is done against the gas pressure force). This transfers energy mechanically into the internal kinetic energy store of the gas particles, increasing their average kinetic energy and causing the temperature of the gas to rise.
Need more questions on Density Required Practical, Internal Energy & Particle Motion in Gases, or want to organise your own notes?
Type a specific exam question you are stuck on, pick one of the prompts below, or paste your class notes to build a custom set of flashcards and practice questions on this page.
Related study guides
Particle Model, Density & Pressure
The kinetic particle model explains the properties of solids, liquids, and gases in terms of the arrangement, motion, and potential energy of their particles. Heating a substance increases its internal energy, either raising its temperature (governed by specific heat capacity) or changing its state at constant temperature (governed by specific latent heat).
Specific Heat Capacity, Specific Latent Heat & Thermal Insulation
When a substance is heated, the thermal energy transferred either increases the average kinetic energy of its particles (raising its temperature according to Specific Heat Capacity, ΔE = mcΔθ) or increases the potential energy of its particles by overcoming intermolecular forces during a change of state (at constant temperature according to Specific Latent Heat, E = mL). Materials with a high specific heat capacity, such as water (4,200 J/kg°C), store large amounts of thermal energy per kilogram for every degree of temperature rise. Examiners frequently test multi-step calculations combining electrical power (E = Pt) with ΔE = mcΔθ, heating curve plateaus, and the metal block Specific Heat Capacity required practical.
Moments, Principle of Moments, Levers, Gears & Pressure in Fluids
In Triple Science GCSE Physics, a force or system of forces can cause an object to rotate about a pivot; the turning effect of a force is called the moment of the force (M = Fd). When a balanced object is in rotational equilibrium, the Principle of Moments states that the total clockwise moment about any pivot equals the total anticlockwise moment about that pivot, a principle applied in levers and interlocking gear wheels to act as force multipliers. This topic also covers pressure in fluids (liquids and gases), where pressure acts normal to any surface (p = F / A) and increases with depth and fluid density according to p = hρg, generating the upward force of upthrust.