Source: https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-7-molecular-kinetic-theory-model-2

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# Molecular Kinetic Theory Model 2

Physics: Cambridge International A Level, topic 9.2.7

## Average molecular kinetic energy

The average molecular energy can be used to find the pressure of radiation.

### Kinetic energy

![Kinetic energy](https://image-v2.cdn.app.senecalearning.com/2018-08/10c34f1d-1668-49f7-b48b-36a4254c771a/particles-gas-.jpg)

- We assume that a gas is homogeneous (the same everywhere) and isotropic (has the same value when measured in different directions).
- This means that the average speed of a molecule in the x-direction must be the same as the y and the z-directions. So we can write:
 - $$\langle{c_x}\rangle=\langle{c_y}\rangle=\langle{c_z}\rangle$$
- This means that the average kinetic energy in each direction is the same.

### Momentum

![Momentum](https://image-v2.cdn.app.senecalearning.com/2018-09/34c2285d-c2d1-47c6-975e-adec798bbaf0/rubix-cube-.jpg)

- We consider a cube of length l which contains a gas.
- If we only look at the x-direction, we can say that the time taken for a particle to travel from one end to the other is:
 - $$t=\frac{l}{\langle{c_x}\rangle}$$
- If a particle collides with the wall of the box and is absorbed, we can write the change in momentum as:
 - Change in momentum = mass x velocity 
 - $$P=m\langle{c_x}\rangle$$

### Force

![Force](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/2.1.1%20-%20Matter/ball-wall%20-%20Edited-min.jpg)

- We can write the force exerted on the wall when it absorbs a particle as:
 - Force = change in momentum ÷ change in time 
 - $$F=\frac{P}{t}$$
- We can substitute in the equations for momentum and time to get:
 - $$F=\frac{m\langle{c_x}^2\rangle}{l}$$

### Pressure

![Pressure](https://image-v2.cdn.app.senecalearning.com/2018-08/5413b9a9-7d12-4cf8-83c4-84eb2d40c619/pressure-862180_1920.jpg)

- The pressure on the wall of the box when it absorbs one particle is given by the equation:
 - Pressure = force ÷ area 
 - $$p=\frac{F}{A}$$
- We can use the value for force and that the area is length squared to get:
 - $$p=\frac{m\langle{c_x}^2\rangle}{l^3}$$
- Since volume is length cubed we get:
 - $$p=\frac{m\langle{c_x}^2\rangle}{V}$$

### Pressure 2

![Pressure 2](https://image-v2.cdn.app.senecalearning.com/2018-08/5413b9a9-7d12-4cf8-83c4-84eb2d40c619/pressure-862180_1920.jpg)

- We have found the pressure for one particle if N particles hit the wall the pressure would be:
 - Total pressure = number of particles x pressure from one particle.
 - $${p_t}=Np$$
- We can substitute the pressure in to give:
 - $${p_t}=N\frac{m\langle{c_x}^2\rangle}{V}$$

### Kinetic equation

![Kinetic equation](https://image-v2.cdn.app.senecalearning.com/2018-08/10c34f1d-1668-49f7-b48b-36a4254c771a/particles-gas-.jpg)

- Recalling that the velocity is the same in all directions, we can write an equation for the total velocity squared as:
 - $$\langle{c}^2\rangle= \langle{c_x}^2\rangle+\langle{c_y}^2\rangle+\langle{c_z}^2\rangle$$
- Because the velocities are equal, we can simplify to give:
 - $$\langle{c_x}^2\rangle=\frac{1}{3}\langle{c_t}^2\rangle$$
- So the equation for pressure can be written as:
 - $$pV=\frac{1}{3}Nm\langle c^2\rangle$$

## Kinetic Energy of a Molecule

Using the results we obtained from the molecular kinetic theory derivation, we can find the temperature dependence of the kinetic energy of a molecule.

### Ideal gas law

![Ideal gas law](https://image-v2.cdn.app.senecalearning.com/2018-08/de57a36a-c449-4ba7-b287-647c333c56fc/gas-smoke-cloud-.jpg)

- Recall that the ideal gas law in terms of the Boltzmann constant, $$k$$ is:
 - $$pV=NkT$$
- And the equation of the molecular kinetic theory is:
 - $$pV = \frac{1}{3} Nm\langle c^2\rangle$$
- Equating the two gives:
 - $$NkT=\frac{1}{3}Nm\langle c^2\rangle$$

### Kinetic energy of a molecule

![Kinetic energy of a molecule](https://image-v2.cdn.app.senecalearning.com/2019-01/353eadef-301c-4c53-9aed-176e484510ce/gas-particle-model-exam-examphysics-.png)

- We can cancel a factor of $$N$$ from each side to give:
 - $$kT=\frac{1}{3}m\langle c^2\rangle$$
- Finally, multiplying each side by $$\frac{3}{2}$$, we obtain an expression for the average kinetic energy for a molecule:
 - $$\frac{1}{2}m\langle c^2\rangle = \frac{3}{2}kT$$
- The average kinetic energy for a molecule is proportional to the temperature.

## Molecular Kinetic Theory - Developments Over Time

Ideas about the underlying structure of materials have changed considerably over time.

### Early ideas

![Early ideas](https://image-v2.cdn.app.senecalearning.com/courseImages/biology/5.2.4%20-%20Control%20of%20body%20temperature/fire-2197606_640-min.jpg)

- The idea that the atom, or atoms that are too small to directly view, move around is ancient. This dates from Lucretius in approx 50 BCE.
- This idea was largely ignored because of the predominance of Aristotelian ideas about elements such as fire, earth, air and water.

### Particle nature of matter

![Particle nature of matter](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/2.2.1.2%20-%20changing%20states%20in%20the%20particle%20model%20-%20solid,%20liquid%20and%20gas.png)

- The modern theory of the particle nature of matter was attributed to Bernoulli.
- This was prior to the ideas of conservation of energy and how collisions between particles could be elastic.
- The model did not predict anything in itself.

### More complex ideas

![More complex ideas](https://image-v2.cdn.app.senecalearning.com/2018-03/5365635b-685a-4c71-822e-d9ef03ad9eab/(s)%20_Diagram%20-%201.1.6_%20Random%20bombardment%20of%20particles%20%20%20.png)

- Clausius developed a much more complex set of ideas.
- The observation of Brownian motion is the first direct evidence of the existence of particles.
- The kinetic theory of gases became universally accepted because of Einstein and Smoluchowski’s theoretical model, which made specific predictions about Brownian motion and diffusion.

## Test yourself on Molecular Kinetic Theory Model 2

- How can we calculate the force of a particle when it is absorbed by a wall?
- How can we calculate the pressure of one particle when it is absorbed by a wall?
- If a gas is isotropic and homogeneous how does the velocity in each direction relate?
- What is the constant of proportionality for the relationship between the average molecular kinetic energy and the temperature?
- What did Bernoulli's model of matter predict?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/1b5bc325-d783-4d2c-99cd-5a7d913debfc/section/092de65c-8360-4afe-ab3a-fa97135684fa/session)

- Previous topic: [9.2.6 Molecular Kinetic Theory Model](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-6-molecular-kinetic-theory-model.md)
- Next topic: [9.2.8 Thermal Energy Transfer](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-8-thermal-energy-transfer.md)

## Physics: Cambridge International A Level contents

### 1 Physical Quantities & Units
- 1.1 Physical Quantities & Units
  - [1.1.1 Use of SI Units](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-1-1-use-of-si-units.md)
  - [1.1.2 SI Prefixes, Standard Form & Converting Units](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-1-2-si-prefixes-standard-form-and-converting-units.md)
  - [1.1.3 End of Topic Test - Units & Prefixes](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-1-3-end-of-topic-test-units-and-prefixes.md)
  - [1.1.4 Avogadro's Constant](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-1-4-avogadros-constant.md)
  - [1.1.5 Scalars & Vectors](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-1-5-scalars-and-vectors.md)
- 1.2 Errors & Uncertainty
  - [1.2.1 Measuring Length, Time & Volume](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-1-measuring-length-time-and-volume.md)
  - [1.2.2 Measuring Temperature](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-2-measuring-temperature.md)
  - [1.2.3 Circuit Measurements](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-3-circuit-measurements.md)
  - [1.2.4 Limitation of Physical Measurements](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-4-limitation-of-physical-measurements.md)
  - [1.2.5 Uncertainty](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-5-uncertainty.md)
  - [1.2.6 Estimation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-6-estimation.md)
  - [1.2.7 Displaying Data](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-7-displaying-data.md)
  - [1.2.8 End of Topic Test - Measurements & Errors](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/1-2-8-end-of-topic-test-measurements-and-errors.md)

### 2 Kinematics
- 2.1 Equations of Motion
  - [2.1.1 Motion in a Straight Line](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/2-1-1-motion-in-a-straight-line.md)
  - [2.1.2 Graphs of Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/2-1-2-graphs-of-motion.md)
  - [2.1.3 Bouncing Ball Example](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/2-1-3-bouncing-ball-example.md)
  - [2.1.4 End of Topic Test - Motion in a Straight Line](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/2-1-4-end-of-topic-test-motion-in-a-straight-line.md)
  - [2.1.5 Acceleration Due to Gravity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/2-1-5-acceleration-due-to-gravity.md)

### 3 Dynamics
- 3.1 Momentum & Newton's Laws of Motion
  - [3.1.1 Mass & Inertia](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-1-1-mass-and-inertia.md)
  - [3.1.2 Newton's Laws](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-1-2-newtons-laws.md)
  - [3.1.3 Momentum](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-1-3-momentum.md)
  - [3.1.4 End of Topic Test - Newton's Laws & Momentum](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-1-4-end-of-topic-test-newtons-laws-and-momentum.md)
  - [3.1.5 A-A* (AO3/4) - Newton's Third Law](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-1-5-a-a-ao34-newtons-third-law.md)
- 3.2 Non-Uniform Motion
  - [3.2.1 Projectile Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-2-1-projectile-motion.md)
- 3.3 Linear Momentum & Conservation
  - [3.3.1 Conservation of Momentum](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/3-3-1-conservation-of-momentum.md)

### 4 Force, Density & Pressure
- 4.1 Force, Density & Pressure
  - [4.1.1 Fields](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-1-fields.md)
  - [4.1.2 Force in Uniform Fields](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-2-force-in-uniform-fields.md)
  - [4.1.3 Friction](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-3-friction.md)
  - [4.1.4 Buoyancy](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-4-buoyancy.md)
  - [4.1.5 Terminal Speed](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-5-terminal-speed.md)
  - [4.1.6 End of Topic Test - Acceleration Due to Gravity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-6-end-of-topic-test-acceleration-due-to-gravity.md)
  - [4.1.7 Centre of Mass](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-7-centre-of-mass.md)
  - [4.1.8 Forces & Equilibrium](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-8-forces-and-equilibrium.md)
  - [4.1.9 End of Topic Test - Scalars & Vectors](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-9-end-of-topic-test-scalars-and-vectors.md)
  - [4.1.10 Moments](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-10-moments.md)
  - [4.1.11 End of Topic Test - Moments & Centre of Mass](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-11-end-of-topic-test-moments-and-centre-of-mass.md)
  - [4.1.12 Density](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-12-density.md)
  - [4.1.13 Pressure](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/4-1-13-pressure.md)

### 5 Work, Energy & Power
- 5.1 Work, Energy & Power
  - [5.1.1 Work & Energy](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-1-1-work-and-energy.md)
  - [5.1.2 Power & Efficiency](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-1-2-power-and-efficiency.md)
  - [5.1.3 Conservation of Energy](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-1-3-conservation-of-energy.md)
  - [5.1.4 End of Topic Test - Work, Energy & Power](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-1-4-end-of-topic-test-work-energy-and-power.md)
- 5.2 Gravitational Fields
  - [5.2.1 Newton's Law](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-2-1-newtons-law.md)
  - [5.2.2 Gravitational Field Strength](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-2-2-gravitational-field-strength.md)
  - [5.2.3 Gravitational Potential](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/5-2-3-gravitational-potential.md)

### 6 Deformation of Solids
- 6.1 Materials
  - [6.1.1 Bulk Properties of Solids](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/6-1-1-bulk-properties-of-solids.md)
  - [6.1.2 Energy in Materials](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/6-1-2-energy-in-materials.md)
  - [6.1.3 Young Modulus](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/6-1-3-young-modulus.md)
  - [6.1.4 End of Topic Test - Materials](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/6-1-4-end-of-topic-test-materials.md)

### 7 Waves
- 7.1 Simple Harmonic Motion
  - [7.1.1 Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-1-simple-harmonic-motion.md)
  - [7.1.2 Simple Harmonic Systems](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-2-simple-harmonic-systems.md)
  - [7.1.3 Energy in Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-3-energy-in-simple-harmonic-motion.md)
  - [7.1.4 Resonance](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-4-resonance.md)
  - [7.1.5 End of Topic Test - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-5-end-of-topic-test-simple-harmonic-motion.md)
  - [7.1.6 A-A* (AO3/4) - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-6-a-a-ao34-simple-harmonic-motion.md)
  - [7.1.7 End of Topic Test - Gravitational Fields](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-1-7-end-of-topic-test-gravitational-fields.md)
- 7.2 Waves
  - [7.2.1 Progressive Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-1-progressive-waves.md)
  - [7.2.2 Intensity of Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-2-intensity-of-waves.md)
  - [7.2.3 Wave Speed & Phase Difference](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-3-wave-speed-and-phase-difference.md)
  - [7.2.4 Longitudinal & Transverse Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-4-longitudinal-and-transverse-waves.md)
  - [7.2.5 End of Topic Test - Progressive Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-5-end-of-topic-test-progressive-waves.md)
  - [7.2.6 Electromagnetic Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-6-electromagnetic-waves.md)
  - [7.2.7 Doppler Effect](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-7-doppler-effect.md)
  - [7.2.8 Sound Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-8-sound-waves.md)
  - [7.2.9 Measuring Sound Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-9-measuring-sound-waves.md)
  - [7.2.10 End of Topic Test - Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-10-end-of-topic-test-waves.md)
  - [7.2.11 Ultrasound Imaging](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-11-ultrasound-imaging.md)
  - [7.2.12 Ultrasound Imaging 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/7-2-12-ultrasound-imaging-2.md)

### 8 Superposition
- 8.1 Superposition
  - [8.1.1 Stationary Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-1-stationary-waves.md)
  - [8.1.2 Stationary Waves 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-2-stationary-waves-2.md)
  - [8.1.3 End of Topic Test - Stationary Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-3-end-of-topic-test-stationary-waves.md)
  - [8.1.4 A-A* (AO3/4) - Stationary Waves](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-4-a-a-ao34-stationary-waves.md)
  - [8.1.5 Interference](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-5-interference.md)
  - [8.1.6 Interference 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-6-interference-2.md)
  - [8.1.7 End of Topic Test - Interference](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-7-end-of-topic-test-interference.md)
  - [8.1.8 Diffraction](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-8-diffraction.md)
  - [8.1.9 Diffraction Gratings](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-9-diffraction-gratings.md)
  - [8.1.10 End of Topic Test - Diffraction](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/8-1-10-end-of-topic-test-diffraction.md)

### 9 Thermal Physics
- 9.1 Circular Motion
  - [9.1.1 Circular Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-1-1-circular-motion.md)
  - [9.1.2 Circular Motion 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-1-2-circular-motion-2.md)
  - [9.1.3 End of Topic Test - Circular Motion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-1-3-end-of-topic-test-circular-motion.md)
- 9.2 Thermal Physics
  - [9.2.1 Temperature](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-1-temperature.md)
  - [9.2.2 Measuring Temperature](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-2-measuring-temperature.md)
  - [9.2.3 Ideal Gas Law](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-3-ideal-gas-law.md)
  - [9.2.4 Ideal Gases](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-4-ideal-gases.md)
  - [9.2.5 Boyle's Law & Charles' Law](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-5-boyles-law-and-charles-law.md)
  - [9.2.6 Molecular Kinetic Theory Model](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-6-molecular-kinetic-theory-model.md)
  - [9.2.7 Molecular Kinetic Theory Model 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-7-molecular-kinetic-theory-model-2.md)
  - [9.2.8 Thermal Energy Transfer](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-8-thermal-energy-transfer.md)
  - [9.2.9 Thermal Energy Transfer Experiments](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-9-thermal-energy-transfer-experiments.md)
  - [9.2.10 End of Topic Test - Thermal Energy & Ideal Gases](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-10-end-of-topic-test-thermal-energy-and-ideal-gases.md)
  - [9.2.11 First Law of Thermodynamics](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/9-2-11-first-law-of-thermodynamics.md)

### 10 Communication
- 10.1 Communication Channels
  - [10.1.1 Communication Channels](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/10-1-1-communication-channels.md)
  - [10.1.2 Modulation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/10-1-2-modulation.md)
  - [10.1.3 Attenuation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/10-1-3-attenuation.md)
- 10.2 Digital Communication
  - [10.2.1 Digital & Analogue Signals](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/10-2-1-digital-and-analogue-signals.md)
  - [10.2.2 Representing Sound](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/10-2-2-representing-sound.md)

### 11 Electric Fields
- 11.1 Electric Fields
  - [11.1.1 Coulomb's Law](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-1-coulombs-law.md)
  - [11.1.2 Electric Field Strength](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-2-electric-field-strength.md)
  - [11.1.3 Electric Field Strength 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-3-electric-field-strength-2.md)
  - [11.1.4 Electric Potential](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-4-electric-potential.md)
  - [11.1.5 End of Topic Test - Electric Fields](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-5-end-of-topic-test-electric-fields.md)
  - [11.1.6 A-A* (AO3/4) - Electric and Gravitational Field](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-1-6-a-a-ao34-electric-and-gravitational-field.md)
- 11.2 Capacitance
  - [11.2.1 Capacitance](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-2-1-capacitance.md)
  - [11.2.2 Parallel Plate Capacitor](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-2-2-parallel-plate-capacitor.md)
  - [11.2.3 Energy Stored by a Capacitor](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-2-3-energy-stored-by-a-capacitor.md)
  - [11.2.4 Capacitor Discharge](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-2-4-capacitor-discharge.md)
  - [11.2.5 Capacitor Charge](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/11-2-5-capacitor-charge.md)

### 12 Current Electricity
- 12.1 Current Electricity
  - [12.1.1 Basics of Electricity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-1-basics-of-electricity.md)
  - [12.1.2 Mean Drift Velocity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-2-mean-drift-velocity.md)
  - [12.1.3 Current-Voltage Characteristics](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-3-current-voltage-characteristics.md)
  - [12.1.4 End of Topic Test - Basics of Electricity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-4-end-of-topic-test-basics-of-electricity.md)
  - [12.1.5 Resistivity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-5-resistivity.md)
  - [12.1.6 End of Topic Test - Resistivity & Superconductors](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-6-end-of-topic-test-resistivity-and-superconductors.md)
  - [12.1.7 Power and Conservation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-7-power-and-conservation.md)
  - [12.1.8 Microphones](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-8-microphones.md)
  - [12.1.9 Components](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-9-components.md)
  - [12.1.10 Relays](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-10-relays.md)
  - [12.1.11 Strain Gauges](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-1-11-strain-gauges.md)
- 12.2 DC Circuits
  - [12.2.1 Circuits](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-2-1-circuits.md)
  - [12.2.2 Potential Divider](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-2-2-potential-divider.md)
  - [12.2.3 Emf & Internal Resistance](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-2-3-emf-and-internal-resistance.md)
  - [12.2.4 End of Topic Test - Power & Potential](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/12-2-4-end-of-topic-test-power-and-potential.md)

### 13 Magnetic Fields
- 13.1 Magnetic Fields
  - [13.1.1 Magnetic Flux Density](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-1-magnetic-flux-density.md)
  - [13.1.2 End of Topic Test - Capacitance & Flux Density](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-2-end-of-topic-test-capacitance-and-flux-density.md)
  - [13.1.3 Moving Charges in a Magnetic Field](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-3-moving-charges-in-a-magnetic-field.md)
  - [13.1.4 Magnetic Flux & Flux Linkage](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-4-magnetic-flux-and-flux-linkage.md)
  - [13.1.5 Electromagnetic Induction](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-5-electromagnetic-induction.md)
  - [13.1.6 Electromagnetic Induction 2](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-6-electromagnetic-induction-2.md)
  - [13.1.7 Magnetic Flux Density](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-7-magnetic-flux-density.md)
  - [13.1.8 Magnetic Resonance Scanning](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-1-8-magnetic-resonance-scanning.md)
- 13.2 Alternating Currents
  - [13.2.1 Alternating Currents](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-2-1-alternating-currents.md)
  - [13.2.2 Operation of a Transformer](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-2-2-operation-of-a-transformer.md)
  - [13.2.3 End of Topic Test - Electromagnetic Induction & AC](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-2-3-end-of-topic-test-electromagnetic-induction-and-ac.md)
  - [13.2.4 Rectification](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/13-2-4-rectification.md)

### 14 Modern Physics
- 14.1 Quantum Physics
  - [14.1.1 The Photoelectric Effect](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-1-the-photoelectric-effect.md)
  - [14.1.2 The Photoelectric Effect Explanation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-2-the-photoelectric-effect-explanation.md)
  - [14.1.3 End of Topic Test - The Photoelectric Effect](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-3-end-of-topic-test-the-photoelectric-effect.md)
  - [14.1.4 Collisions of Electrons with Atoms](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-4-collisions-of-electrons-with-atoms.md)
  - [14.1.5 Energy Levels & Photon Emission](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-5-energy-levels-and-photon-emission.md)
  - [14.1.6 Wave-Particle Duality](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-6-wave-particle-duality.md)
  - [14.1.7 End of Topic Test - Absorption & Emission](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-7-end-of-topic-test-absorption-and-emission.md)
  - [14.1.8 Band Theory](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-8-band-theory.md)
  - [14.1.9 Diagnostic X-Rays](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-9-diagnostic-x-rays.md)
  - [14.1.10 X-Ray Image Processing](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-10-x-ray-image-processing.md)
  - [14.1.11 Absorption of X-Rays](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-11-absorption-of-x-rays.md)
  - [14.1.12 CT Scanners](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-1-12-ct-scanners.md)
- 14.2 Nuclear Physics
  - [14.2.1 Rutherford Scattering](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-1-rutherford-scattering.md)
  - [14.2.2 Atomic Model](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-2-atomic-model.md)
  - [14.2.3 Isotopes](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-3-isotopes.md)
  - [14.2.4 Stable & Unstable Nuclei](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-4-stable-and-unstable-nuclei.md)
  - [14.2.5 A-A* (AO3/4) - Stable & Unstable Nuclei](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-5-a-a-ao34-stable-and-unstable-nuclei.md)
  - [14.2.6 Alpha & Beta Radiation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-6-alpha-and-beta-radiation.md)
  - [14.2.7 Gamma Radiation](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-7-gamma-radiation.md)
  - [14.2.8 Particles, Antiparticles & Photons](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-8-particles-antiparticles-and-photons.md)
  - [14.2.9 Quarks & Antiquarks](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-9-quarks-and-antiquarks.md)
  - [14.2.10 Particle Interactions](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-10-particle-interactions.md)
  - [14.2.11 Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-11-radioactive-decay.md)
  - [14.2.12 Half Life](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-12-half-life.md)
  - [14.2.13 End of Topic Test - Radioactivity](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-13-end-of-topic-test-radioactivity.md)
  - [14.2.14 Nuclear Instability](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-14-nuclear-instability.md)
  - [14.2.15 Mass & Energy](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-15-mass-and-energy.md)
  - [14.2.16 Binding Energy](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-16-binding-energy.md)
  - [14.2.17 A-A* (AO3/4) - Nuclear Fusion](https://senecalearning.com/en-gb/revision-notes/international-a-level/physics/cambridge-international/14-2-17-a-a-ao34-nuclear-fusion.md)