Edexcel Physics IGCSE Topic 5: Solids, Liquids and Gases - Summary Notes

Density and Pressure

Density:
- Definition: Mass per unit volume.
- Units: kilograms per metre cubed (kg/m³).
- Formula: $\rho = \frac{m}{V}$ where $\rho$ is density, $m$ is mass, and $V$ is volume.
Finding the Density of a Liquid:
- Measure the mass of the measuring cylinder (tare the balance to avoid zero error).
- Fill the cylinder with the liquid and measure the new mass.
- The difference in masses is the mass of the liquid.
- Read the volume from the cylinder at eye level to avoid parallax error.
- Calculate density using the formula.
Finding the Density of a Solid:
- Measure the mass of the solid using a balance.
- If the solid is regularly shaped:
  - Measure dimensions using a ruler.
  - Use a mathematical formula to find the volume.
- If the solid is irregularly shaped:
  - Immerse it in water and measure the volume of water displaced (this is the volume of the solid).
- Calculate the density using the formula.
Pressure:
- Definition: Force per unit area.
- Units: Pascals (Pa).
- Formula: $p = \frac{F}{A}$ where $p$ is pressure, $F$ is force, and $A$ is area.
- Example: Bed of nails vs. single nail.
  - The force is the weight of the body.
  - The bed of nails distributes the force over a larger area, reducing pressure.
Pressure in Fluids:
- Acts equally in all directions.
- Causes a force at right angles to any surface.
- Created from the movement of particles colliding with a surface.
Pressure Beneath a Liquid Surface:
- Increases with depth, density of the liquid, and gravitational field strength.
- Formula: $p = \rho gh$ where $p$ is pressure, $\rho$ is density, $g$ is gravitational field strength, and $h$ is depth.
- Explanation:
  - Deeper in the fluid = more particles above = greater weight.
  - Higher density = more particles per unit volume = greater weight.
  - Weight depends on gravitational field strength.

Change of State

Heating a System:
- Increases internal energy.
- Causes either an increase in temperature or a change of state.
Temperature Increase:
- Energy goes towards making molecules vibrate more.
- Increases their kinetic energy.
Change of State:
- Energy goes towards freeing molecules from each other rather than increasing kinetic energy.
- Temperature stays constant during the change of state.
- Melting: Molecules in a solid vibrate enough to move away from fixed positions, turning into a liquid.
- Boiling: Molecules in a liquid gain enough energy to break their bonds and become separate molecules, turning into a gas.
Graph of Temperature vs. Time (Ice to Steam):
- A to B: Ice rising in temperature.
- B to C: Ice melting into water (temperature constant).
- C to D: Water rising in temperature.
- D to E: Water boiling into steam (temperature constant).
- E to F: Steam rising in temperature.
- Horizontal lines indicate a change of state where energy is used to separate particles (breaking intermolecular forces), not to increase temperature.
Evaporation:
- Escape of high-energy molecules from the surface of a liquid.
- Remaining molecules have lower average kinetic energy, reducing temperature (cooling effect).
- Increasing temperature, surface area, or providing a draught increases the rate of evaporation.
Evaporation vs. Boiling:
- Evaporation can happen at any temperature, boiling occurs at the boiling point.
- Evaporation occurs at the surface, boiling occurs throughout the liquid.
States of Matter:
- Solids:
  - Molecules close together in a regular pattern.
  - Strong intermolecular forces of attraction.
  - Molecules vibrate but can't move about.
- Liquids:
  - Molecules close together in a random arrangement.
  - Weaker intermolecular forces of attraction than solids.
  - Molecules move around each other.
- Gases:
  - Molecules far apart in a random arrangement.
  - Negligible/very weak intermolecular forces.
  - Molecules move quickly in all directions.

Specific Heat Capacity and Ideal Gases

Specific Heat Capacity:
- Definition: The amount of energy required to raise the temperature of 1kg of a substance by 1°C.
- Units: Joules per kilogram degree Celsius (J/kg°C).
- Formula: $\Delta Q = m \times c \times \Delta T$ where $\Delta Q$ is the change in thermal energy, $m$ is mass, $c$ is specific heat capacity, and $\Delta T$ is the temperature change.
Ideal Gas Molecules:
- Move rapidly and randomly due to collisions with other gas molecules.
- Gases exert pressure on a container due to collisions between gas molecules and the wall.
- Collisions cause a change in momentum, which exerts a force (force equals the change in momentum over time).
Gas Pressure and Temperature (Constant Volume):
- If temperature increases, pressure increases because molecules move faster and collide harder and more frequently with the walls.
- Absolute zero: The temperature at which pressure is zero (-273°C).
- Kelvin scale: Defines absolute zero as 0K, with an increment of one Kelvin equal to one degree Celsius.
- Conversion: Temperature in Kelvin = Temperature in degrees Celsius + 273
- Formula for fixed mass and volume: $\frac{p1}{T1} = \frac{p2}{T2}$ or $\frac{p}{T} = constant$
Gas Pressure and Volume (Constant Temperature):
- If volume increases, pressure decreases because molecules collide less frequently with the walls and over a greater area.
- Formula for fixed mass and temperature: $p1V1 = p2V2$ or $pV = constant$ (Boyle’s Law).
Temperature and Kinetic Energy:
- The temperature in Kelvin of a gas is proportional to the average kinetic energy of the molecules.
- Higher temperature means greater average kinetic energy and faster average speed of molecules.