States of Matter
States of Matter — American System Physics Revision Notes & Topical Questions
5 min read 6 parts Lesson 1 of 5 1 quiz
Lesson summary
States of Matter: Density, Changes of State and Gas Pressure — AMERICAN SYSTEM PHYSICS notes: Calculate density, interpret heating and cooling curves and latent heat, and explain pressure in fluids and gases using particles.Density is mass per unit volume, ρ = m/V, in kg/m3 (or g/cm3).
- boiling point
- Liquid pressure
- hydraulic system
- pressure law
- Worked example 1
- Worked example 2
Section 1 of 6Density
Density is mass per unit volume, ρ = m/V, in kg/m3 (or g/cm3).
Water is about 1.0 g/cm3 = 1000 kg/m3, so 1 g/cm3 = 1000 kg/m3; also 1 m3 = 106 cm3 and 1 cm3 = 1 ml.
An object floats if its density is less than that of the liquid and sinks if greater.
Diffusion
Volume of a cuboid = l × w × h; volume of a cylinder = πr2h; the volume of an irregular solid is found from the rise in water level in a measuring cylinder. Diffusion is the net spreading of particles from higher to lower concentration due to random motion, faster in gases and at higher temperature.
Section 2 of 6Changes of state and latent heat
Condensation is gas to liquid with energy released.
Boiling point
The boiling point is the temperature at which a liquid boils at a given pressure (100 °C for pure water at standard atmospheric pressure).
The energy for a change of state is E = ml (J, kg, J/kg); for fusion E = mlf.
Temperature stays constant during a change of state because the supplied energy increases particle potential energy (separating particles) rather than their kinetic energy.
| Feature | Evaporation | Boiling |
|---|---|---|
| Temperature | any temperature | only at the boiling point |
| Where | surface only | throughout the liquid (bubbles) |
| Rate | usually slow | rapid |
| Effect on liquid | cools the remaining liquid | temperature stays constant while energy is supplied |
| Energy source | surroundings / the liquid itself | external heater |
| Factor | Why evaporation increases |
|---|---|
| Higher temperature | more particles have enough energy to escape |
| Larger surface area | more particles at the surface |
| Air movement | removes escaped particles so fewer return |
| Lower humidity | less vapour in the air to re-enter |
Cooling curve practical
- melt stearic acid (or salol) in a boiling tube in a hot water bath;
- remove the tube, place a thermometer or probe in the liquid and start a stopwatch;
- record the temperature every 30 s while stirring gently until well below freezing;
- plot temperature against time.
- The flat section gives the melting/freezing point;
- there the energy released as the substance solidifies (latent heat) balances the energy lost to the surroundings.
Heating curve from ice to steam
- ice below 0 °C warms as vibrations increase;
- at 0 °C a flat section as ice melts;
- water warms from 0 to 100 °C as particles move faster;
- at 100 °C a long flat section as water boils and particles separate completely;
- steam above 100 °C warms again.
Section 3 of 6Pressure in fluids and gases
Pressure is force per unit area. Liquid pressure is caused by the weight of liquid above a point, acts equally in all directions and increases with depth and density: Δp = ρgΔh.
What the symbols mean: p = pressure due to the liquid (Pa) · ρ = density of the liquid (kg m−3) · g = 9.81 N kg−1 · h = depth (m)
Pressure in fluids and gases
Hydraulic system
A hydraulic system uses an almost incompressible liquid to transmit pressure,
- so a small force on a small piston gives a large force on a large piston.
- (hydraulic brakes and jacks)
Atmospheric pressure is about 1.0 × 105 Pa at sea level and falls with altitude because there is less air above; it is measured with a barometer,
- while gas pressure differences use a manometer.
Useful conversions: 1 kPa = 1000 Pa and 1 m2 = 10 000 cm2.
Gas pressure arises because particles move randomly at high speed and change momentum when hitting a wall, exerting a force; the total force per unit area from many collisions is the pressure.
Compressing a gas at constant temperature makes the same particles hit a smaller area more often, so pressure rises: Boyle's law pV = constant.
Pressure law
Heating gas in a sealed rigid container makes particles hit the walls more often and harder; this is the pressure law, p/T = constant (T in kelvin),
- and is why aerosol cans must not be heated and tyre pressure rises after a long drive.
Heated at constant pressure (balloon, free syringe), a gas expands with volume proportional to kelvin temperature.
Combined: p1V1/T1 = p2V2/T2.
Extrapolating a pressure-temperature graph to zero pressure gives about −273 °C, absolute zero, where an ideal gas would exert no pressure.
Surface tension and viscosity are properties of liquids; crystalline solids have regular lattices; thermal expansion is an increase in size with temperature.
Section 4 of 6Worked examples
A metal block measures 2.0 cm × 3.0 cm × 5.0 cm and has mass 81 g. Find its density. [3]3 marks
V = 30 cm3; ρ = 81/30 = 2.7 g/cm3 = 2700 kg/m3 (aluminium).
A stone is lowered into a measuring cylinder; water rises from 42 cm3 to 58 cm3. The stone's mass is 40 g. Find its density. [2]2 marks
V = 16 cm3; ρ = 40/16 = 2.5 g/cm3.
Find the mass of air in a room 5.0 m × 4.0 m × 2.5 m (ρ = 1.2 kg/m3). [2]2 marks
V = 50 m3; m = 1.2 × 50 = 60 kg.
A sealed gas at 300 K and 120 kPa is heated to 400 K at constant volume. Find the new pressure. [2]2 marks
p2 = 120 × 400/300 = 160 kPa.
A hydraulic lift has pistons of 0.01 m2 and 0.5 m2. What load does 200 N on the small piston lift? Also find the pressure change under 10 m of water (g = 10 N/kg). [3]3 marks
Area ratio is 50, so F = 200 × 50 = 10 000 N. Δp = 1000 × 10 × 10 = 100 000 Pa.
Why does temperature stay constant during boiling while energy is supplied? [2]2 marks
The energy increases particle potential energy as particles separate completely, not their kinetic energy.
Section 5 of 6Key terms
| Term | Meaning |
|---|---|
| Density | Mass per unit volume, ρ = m/V; unit kg/m3. |
| Diffusion | Net spreading of particles from higher to lower concentration through random motion. |
| Condensation | Change from gas to liquid, with energy released. |
| Boiling point | Temperature at which a liquid boils at a given pressure; 100 °C for water at standard pressure. |
| Liquid pressure | Pressure caused by the weight of liquid above a point; increases with depth and density. |
| Pressure law | For a fixed mass of gas at constant volume, p/T is constant (T in kelvin). |
| Hydraulic system | Uses an incompressible liquid to transmit pressure so small forces make large ones. |
Section 6 of 6Exam technique
1
Mixing density units — 1 g/cm3 = 1000 kg/m3.
2
Saying temperature rises during a change of state — it is constant on the flat section.
3
Confusing evaporation and boiling — evaporation happens at the surface at any temperature.
4
Using Celsius in gas laws — convert to kelvin.
5
Thinking gas pressure comes from particles expanding or gravity — it comes from collisions.
Marked practiceQuizzes for this lesson
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