2.1.2

Molecular Kinetic Theory Model 2

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Average molecular kinetic energy

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

Kinetic energy

Kinetic energy

  • 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:
    • vx=vy=vZ{v_x}={v_y}={v_Z}
  • This means that the average kinetic energy in each direction is the same.
Momentum

Momentum

  • 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=lvxt=\frac{l}{{v_x}}
  • 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=mvxP=m{v_x}
Force

Force

  • We can write the force exerted on the wall when it absorbs a particle as:
    • Force = change in momentum ÷ change in time
    • F=PtF=\frac{P}{t}
  • We can substitute in the equations for momentum and time to get:
    • F=mvx2lF=\frac{m{v_x}^2}{l}
Pressure

Pressure

  • The pressure on the wall of the box when it absorbs one particle is given by the equation:
    • Pressure = force ÷ area
    • p=FAp=\frac{F}{A}
  • We can use the value for force and that the area is length squared to get:
    • p=mvx2l3p=\frac{m{v_x}^2}{l^3}
  • Since volume is length cubed we get:
    • p=mvx2Vp=\frac{m{v_x}^2}{V}
Pressure 2

Pressure 2

  • 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.
    • pt=Np{p_t}=Np
  • We can substitute the pressure in to give:
    • pt=Nmvx2V{p_t}=N\frac{m{v_x}^2}{V}
Kinetic equation

Kinetic equation

  • Recalling that the velocity is the same in all directions, we can write an equation for the total velocity squared as:
    • vt2=vx2+vy2+vz2{v_t}^2= {v_x}^2+{v_y}^2+{v_z}^2
  • Because the velocities are equal, we can simplify to give:
    • vx2=13vt2{v_x}^2=\frac{1}{3}{v_t}^2
  • So the equation for pressure can be written as:
    • pV=13Nmv2pV=\frac{1}{3}Nmv^2

Molecular Kinetic Theory - Developments Over Time

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

Early ideas

Early ideas

  • 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

  • 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

  • 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.
Jump to other topics
1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics1.1.2Graphs of Motion1.1.3Uniform Acceleration Equations1.1.4Projectile Motion1.1.5Bouncing Ball Example
1.2

Forces

1.2.1Friction1.2.2Terminal Speed1.2.3Newton's Laws1.2.4Exam-Style Question - Forces1.2.5End of Topic Test - Newton's Third Law
1.3

Momentum & Impulse

1.3.1Momentum1.3.2Momentum 21.3.3End of Topic Test - Newton's Laws & Momentum
1.4

Work, Energy & Power

1.4.1Work & Energy1.4.2Conservation of Energy1.4.3Power & Efficiency1.4.4IB Multiple Choice- Work, Energy & Power
2

The Particulate Nature of Matter

2.1

Thermal Concepts

2.1.1Molecular Kinetic Theory Model2.1.2Molecular Kinetic Theory Model 22.1.3Thermal Energy Transfer2.1.4Thermal Energy Transfer Experiments2.1.5Thermal Equilibrium2.1.6Thermal Conductivity2.1.7Heat Energy Transfer
2.2

Modelling a Gas

2.2.1Ideal Gases2.2.2Ideal Gases 22.2.3End of Topic Test - Thermal Energy & Ideal Gases2.2.4Exam-Style Question - Ideal Gases
3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves3.1.2Simple Harmonic Motion
3.2

Travelling Waves

3.2.1Wave Speed & Phase Difference3.2.2Longitudinal & Transverse Waves3.2.3Electromagnetic Waves3.2.4Electromagnetic Waves 23.2.5Sound Waves
3.3

Wave Characteristics

3.3.1Polarisation
3.4

Wave Behaviour

3.4.1Reflection & Absorption3.4.2Reflection of Light3.4.3Refraction3.4.4Refractive index
3.5

Standing Waves

3.5.1Standing Waves3.5.2Standing Waves 23.5.3End of Topic Test - Standing Waves3.5.4IB Multiple Choice - Waves
3.6

Simple Harmonic Motion

3.6.1Simple Harmonic Motion3.6.2Simple Harmonic Systems3.6.3Energy in Simple Harmonic Motion3.6.4End of Topic Test - Simple Harmonic Motion3.6.5End of Topic Test - Simple Harmonic Motion
3.7

Single Slit Diffraction

3.7.1Diffraction
3.8

Interference

3.8.1Interference3.8.2Interference 23.8.3Diffraction Gratings3.8.4End of Topic Test - Diffraction
3.9

Doppler Effect

3.9.1Doppler Effect
4

Fields

4.1

Circular Motion

4.1.1Circular Motion4.1.2Centripetal Force4.1.3IB Multiple Choice - Circular Motion
4.2

Newton's Law of Gravitation

4.2.1Newton's Law4.2.2Orbits of Planets & Satellites4.2.3Escape Velocity & Synchronous Orbits4.2.4End of Topic Test - Gravitational Fields
4.3

Fields

4.3.1Fields4.3.2Gravitational Field Strength4.3.3Gravitational Potential4.3.4Electric Field Strength4.3.5Electrostatic & Gravitational Forces4.3.6Electric Potential4.3.7IB Multiple Choice - Gravitational Fields
4.4

Fields at Work

4.4.1Radial Field Strength4.4.2Orbits of Planets & Satellites4.4.3Escape Velocity & Synchronous Orbits4.4.4End of Topic Test - Gravitational Fields4.4.5Uniform Electric Fields4.4.6IB Multiple Choice - Electric Field & Potential
4.5

Electric Fields

4.5.1Electric Charge4.5.2Conservation of Charge4.5.3Coulomb's Law4.5.4Current4.5.5Potential Difference4.5.6IB Multiple Choice - Electric Charge
4.6

Magnetic Effect of Electric Currents

4.6.1Magnetism4.6.2Magnetic Field4.6.3Magnetic Force4.6.4Moving Charges in a Magnetic Field4.6.5IB Multiple Choice - Magnetism
4.7

Heating Effect of Currents

4.7.1Circuits4.7.2Resistance4.7.3Power and Conservation4.7.4IB Multiple Choice - DC Circuits
4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction4.8.2Electromagnetic Induction 24.8.3Magnetic Flux & Flux Linkage4.8.4End of Topic Test - Electromagnetic Induction
4.9

Power Generation & Transmission

4.9.1Alternating Currents4.9.2Operation of a Transformer
4.10

Capacitance

4.10.1Capacitance4.10.2Parallel Plate Capacitor4.10.3Energy Stored by a Capacitor4.10.4Capacitor Discharge4.10.5Capacitor Charge4.10.6Magnetic Flux Density4.10.7End of Topic Test - Capacitance & Flux Density
5

Nuclear & Quantum Physics

5.1

Discrete Energy & Radioactivity

5.1.1Atomic Spectra5.1.2Atomic Structure5.1.3Photons5.1.4Discrete Energy Levels5.1.5Alpha, Beta & Gamma Radiation5.1.6Scientific Practices - Unstable Nuclei5.1.7Radioactive Decay5.1.8IB Multiple Choice - Atomic Physics
5.2

Nuclear Reactions

5.2.1Mass & Energy5.2.2Nuclear Fission
5.3

The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons5.3.2Particle Interactions5.3.3Classification of Particles5.3.4Wave-Particle Duality5.3.5Wave Functions & Probability5.3.6IB Multiple Choice - Quantum Physics
5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay5.4.2Nuclear Radius5.4.3IB Multiple Choice - Nuclear Physics
6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units6.1.2SI Prefixes, Standard Form & Converting Units6.1.3End of Topic Test - Units & Prefixes
6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements6.2.2Uncertainty6.2.3Estimation6.2.4End of Topic Test - Measurements & Errors
6.3

Vectors & Scalars

6.3.1Scalars & Vectors6.3.2Vector Problems

Practice questions on Molecular Kinetic Theory Model 2

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    How can we calculate the force of a particle when it is absorbed by a wall?Multiple choice
  2. 2
    How can we calculate the pressure of one particle when it is absorbed by a wall?Multiple choice
  3. 3
    If a gas is isotropic and homogeneous how does the velocity in each direction relate?Multiple choice
  4. 4
    What did Bernoulli's model of matter predict?Multiple choice
  5. 5
    What did Aristotle think the elements were?Multiple choice
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Molecular Kinetic Theory Model

Thermal Energy Transfer