Physics Revision #1

Density and Pressure

Density Definition:
- The density of a substance is defined as the mass per unit volume.
- Measured in kilograms per cubic meter (kg/m³).
- Density Formula:
  $density = \frac{mass}{volume}$

Finding Density

Density of a Liquid:

To find the density of a liquid:
- Step 1: Measure the mass of the measuring cylinder on a balance.
- Step 2: Fill the cylinder with liquid and measure the new mass.
- Step 3: Calculate the mass of the liquid:
- Mass of liquid = New mass - Mass of measuring cylinder.
- Alternatively, use the tare function on the balance to avoid zero error.
- Step 4: Read the volume from the cylinder, ensuring that it is read straight-on to avoid parallax error.
- Step 5: Use the density formula to calculate density.

Density of a Solid:

To find the density of a solid:
- Step 1: Measure the mass of the solid on a balance.
- For Regularly Shaped Solids:
- Measure dimensions using a ruler or other measuring tool.
- Use an appropriate mathematical formula to find the volume.
- For Irregularly Shaped Solids:
- Immerse in water to measure the volume of water displaced, which equals the volume of the solid.
- Step 2: Use the density formula to calculate density.

Pressure

Pressure Definition:
- Pressure is defined as the force applied per unit area.
- Measured in Pascals (Pa).
- Pressure Formula:
  $pressure = \frac{force}{area}$

Pressure Example:

Example of pressure with a bed of nails:
- Force applied: Weight of the body.
- Total area:
- A single nail versus multiple nails (bed of nails).
- Observation:
- On a bed of nails, the pressure is lower because the area is greater.

Characteristics of Pressure in Fluids:

The pressure at a point in a gas or liquid at rest acts equally in all directions and causes a force at right angles to any surface.
Pressure in a fluid is produced by particle movement and collisions.
Pressure Variation with Depth:
- Pressure beneath a liquid surface increases with:
- Depth, density of the liquid, and gravitational field strength.
- Pressure Formula at Depth:
  $p = pgh$
- Where:
  - p = pressure,
  - p = density of the liquid,
  - g = gravitational field strength,
  - h = depth.

Summary of Fluid Pressure:

The increase in pressure with depth results from having more particles above the point, thus increasing their weight.
Higher density fluids have more particles per unit volume, resulting in greater weight.
Weight also depends on the gravitational field strength.

Change of State

Heating Effects:
- Heating a system increases its internal energy, causing either:
- An increase in temperature, or
- A change of state.

Temperature Increase:

When the temperature of a body rises:
- Energy increases molecular vibration and kinetic energy.

Change of State:

When a body changes state:
- Energy is used to separate molecules, keeping the temperature constant.
- Processes:
- Melting: Molecules in a solid vibrate enough to move away from fixed positions, transforming into a liquid.
- Boiling: Molecules in a liquid gain enough energy to break bonds and become gas.

Graph Representation of Heating Ice:

Graph Phases Explained:
- From A to B: Ice temperature rises.
- From B to C: Ice melts into water (temperature constant).
- From C to D: Water temperature rises.
- From D to E: Water boils into steam (temperature constant).
- From E to F: Steam temperature rises.

Evaporation:

Definition:
- Evaporation is the escape of higher energy molecules from liquid surfaces.
- After escape, remaining molecules have lower average kinetic energy, therefore the temperature drops (evaporation cools the liquid).
Applications:
- Useful for cooling mechanisms such as sweating.
Factors Increasing Evaporation Rate:
- Increase temperature, increase surface area, and provide airflow (draught).
Evaporation vs. Boiling:
- Evaporation occurs at any temperature and only at the surface.
- Boiling occurs throughout a liquid at the boiling point.

States of Matter Characteristics:

Solids:
- Molecules are close together in a regular pattern.
- Strong intermolecular forces of attraction.
- Molecules can vibrate but cannot move freely.
Liquids:
- Molecules are close together in a random arrangement.
- Weaker intermolecular forces compared to solids.
- Molecules can move around each other.
Gases:
- Molecules are far apart in a random arrangement.
- Negligible or very weak intermolecular forces.
- Molecules move rapidly in all directions.

Specific Heat Capacity

Definition:
- The specific heat capacity is the amount of energy required to raise the temperature of 1kg of a substance by 1°C.
- Measured in Joules per kilogram per degree Celsius (J/kg°C).
Specific Heat Capacity Formula:
- $\Delta Q = mc\Delta T$
- Where:
  - $\Delta Q$ = change in thermal energy,
  - $m$ = mass,
  - $c$ = specific heat capacity,
  - $\Delta T$ = temperature change.

Ideal Gas Molecules

Gas molecules move rapidly and randomly, colliding with each other.
Gases exert pressure on containers due to collisions with walls:
- Molecule rebounds change direction, hence their velocity and momentum change.
- Force Definition:
- Force is defined as the change in momentum over time.

Gas Pressure and Temperature Relationship:

At Constant Volume:
- If temperature increases, pressure increases due to faster and more forceful collisions with container walls.
Absolute Zero:
- The temperature at which pressure is zero is -273°C, known as absolute zero.
- The Kelvin scale defines this as 0K, with increments of 1 Kelvin equal to 1°C.
Conversion to Kelvin:
- $temperature in kelvin = temperature in degrees celsius + 273$

Gas Behavior Under Constant Conditions:

At Constant Temperature:
- If volume increases, pressure decreases because molecules collide less frequently with walls due to more area.
- Boyle's Law:
- $P1V1 = P2V2$
- or $PV = constant$
Temperature Relation:
The temperature in Kelvin of a gas is proportional to the average kinetic energy of the molecules.
Observation:
- Higher temperatures correspond to greater average kinetic energy and faster average molecular speed.

Absolute Zero: The lowest possible temperature. At this temperature the particles have no kinetic energy and so are completely stationary.

*Change in Thermal Energy: The product of the mass, specific heat capacity and temperature change of a substance.

Chemical Changes: Changes to the chemical structure of a substance. The substance does not usually restore its original properties when the changes are reversed.

Condensation: The changing from vapour state to a liquid state, when a substance is cooled.

Density: The mass per unit volume of an object.

Evaporation: The changing from liquid state to a vapour state, when a substance is heated.

Freezing: The changing from a liquid state to a solid state, when a substance is cooled.

Gas Temperature: The absolute temperature of a gas is directly proportional to the average kinetic energy of its molecules.

*Gas: A state of matter in which the particles are spread apart and have high kinetic energies. Any intermolecular forces acting between the particles are very weak.

Internal Energy: The energy stored by the atoms and molecules that make up a system. It is equal to the sum of the total kinetic and potential energies of the particles in the system.

Kelvin: The SI unit of temperature, based on an absolute temperature scale. To convert from degrees Celsius to degrees Kelvin, subtract 273 degrees. For a gas it is proportional to the average kinetic energy of the molecules.

*Liquid: A state of matter in which the particles are in contact, but can flow over each other. Intermolecular forces act between the particles.

Melting: The changing from solid state to liquid state, when a substance is heated.

Pascals: The unit of pressure, equal to a force of one Newton acting perpendicular to an area of one metre squared.

Physical Changes: Changes to the physical properties of a substance which can be reversed. Changes of state are physical changes since substances can restore their original properties when the changes are reversed.

Pressure in a Liquid Column: Equal to the product of the height of the column, the density of the liquid and the gravitational field strength.

Pressure of a Gas: The perpendicular force per unit area acting on the surfaces of a container as a result of the gas particles colliding with it. It acts equally in all directions.

Pressure: The force acting perpendicular to a surface, per unit area.

Pressure-Volume Relationship: When at a constant temperature, the volume of a fixed quantity of gas is inversely proportional to its pressure.

Pressure-Temperature Relationship: When at a constant volume, the pressure of a fixed quantity of gas is directly proportional to its absolute temperature.

Solid: A state of matter in which the particles are tightly packed together and can only vibrate about their fixed positions. Strong intermolecular forces act between the particles
Specific Heat Capacity: The amount of energy needed to increase the temperature of one kilogram of a given substance by one degree Celsius.

Temperature: A measure of the average kinetic energy of the particles in a substance. An increase in temperature will result in an increase in the particles' kinetic energies and velocities.