Density and Pressure
Density
Density is mass per unit volume: ρ = m / V (kg/m³ or g/cm³).
The density of a material depends on how tightly packed its particles are. Solids are typically denser than liquids, which are denser than gases (with notable exceptions like ice floating on water because water is unusual).
Measuring density:
- Regular solid: measure mass on balance; calculate volume from dimensions (V = l × w × h for cuboid; V = 4/3 πr³ for sphere). Then ρ = m/V.
- Irregular solid: use displacement can — volume of displaced water = volume of object (Archimedes' principle).
- Liquid: measure known volume with measuring cylinder; measure mass. ρ = m/V.
Kinetic theory of matter
All matter is made of particles (atoms/molecules) in continuous motion. The three states:
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Arrangement | Regular, close | Random, close | Random, far apart |
| Movement | Vibrate about fixed positions | Slide past each other | Move rapidly, randomly |
| Density | High | Medium–high | Very low |
| Shape/Volume | Fixed shape, fixed volume | Fixed volume, no fixed shape | No fixed shape, fills container |
Temperature is a measure of the average kinetic energy of the particles.
Gas pressure and the gas laws
Pressure = force per unit area: p = F / A (Pa = N/m²).
Gas pressure arises from gas molecules colliding with the container walls. More frequent or more forceful collisions → higher pressure.
Boyle's law (constant temperature): p₁V₁ = p₂V₂ If you halve the volume, pressure doubles — particles hit the walls more often.
Charles's law (constant pressure): V₁/T₁ = V₂/T₂ (T in Kelvin) If temperature rises, particles move faster and hit harder/more often → if pressure is constant, volume increases to maintain the same collision rate.
Pressure law (constant volume): p₁/T₁ = p₂/T₂ (T in Kelvin) At fixed volume, higher T → more forceful/frequent collisions → higher pressure.
Absolute zero: −273 °C = 0 K. At absolute zero, particles have minimum kinetic energy and gas pressure would be zero. Convert: T(K) = T(°C) + 273.
Fluid pressure
For a fluid (liquid or gas) at rest: p = hρg where h = depth below surface, ρ = fluid density, g = gravitational field strength.
Pressure in a fluid:
- Increases with depth.
- Acts equally in all directions at a given depth.
- Does not depend on the shape of the container.
Atmospheric pressure ≈ 101,000 Pa at sea level; decreases with altitude (less air above).
Upthrust (Archimedes' principle)
Any object submerged in a fluid experiences an upward force (upthrust) equal to the weight of fluid displaced: U = ρ_fluid × V_displaced × g. If upthrust ≥ weight, the object floats.
⚠Common mistakes
- Using °C instead of K in gas law calculations — always convert to Kelvin first.
- Wrong rearrangement of p = F/A — F = pA (not p/A).
- Confusing mass and weight in density calculations — density uses mass (kg), not weight (N).
- Assuming all gases obey the ideal gas laws at all conditions — high pressures and low temperatures cause deviations (CCEA awards marks for noting this at Higher level).
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