kinetic molecular theory of gases

1. Kinetic theory &
the behaviour of
gases

2. Learning outcomes
 use a particle model to describe solids, liquids, gases & changes of
state
 explain gas pressure and thermal expansion in terms of kinetic theory
 describe how a barometer measures atmospheric pressure
 estimate the height of the atmosphere using a physical model
 recall and use the gas laws to make quantitative predictions
 relate the gas laws & absolute zero of temperature to the behaviour
of ideal gases
 illustrate how science works through historical case studies
 introduce microscopic atoms and molecules through reasoning based
on careful observation of macroscopic behaviour
 use apparatus for relevant demonstration and class experiments
 convert temperatures between Celsius & Kelvin scales

3. Misconceptions
Students often think that particles
• have the properties of bulk matter (particles change in size as
the temperature changes, particles can melt and solidify)
• have air in between them
• have thoughts and intentions e.g. ‘they prefer to move to places
that are less crowded’.
There is much confusion about the nature of particle
motion in solids, liquids and gases.

4. Teaching challenges
Atoms and molecules are far too small to be glimpsed
by even the most highly-powered optical microscope.
Diagrams of particle arrangements are often static.
• Dynamic animations showing the random thermal motion of
particles, at all temperatures and in all states of matter, usefully
overcome the misconceptions which static diagrams can foster.
Students find it difficult
• to appreciate that gas pressure acts equally in all directions
• to account for the consequences of pressure differences
• to convert between units of volume (cm3, m3)

5. All things are made
of atoms
“If, in some cataclysm, all of scientific knowledge were to be destroyed,
and only one sentence passed on to the next generations of creatures,
what statement would contain the most information in the fewest
words?
“I believe it is the atomic hypothesis (or the atomic fact, or whatever you
wish to call it) that all things are made of atoms - little particles that
move around in perpetual motion, attracting each other when they are a
little distance apart, but repelling upon being squeezed into one
another.
“In that sentence, you will see, there is an enormous amount of information
about the world, if just a little imagination and thinking are applied.”
Richard Feynman

6. Evidence for atoms
In pairs:
What evidence for atoms can you, or do you,
show your pupils?

7. Evidence for atoms
• crystals – regularity of surfaces, cleaving
• mixing different liquids
• change of volume: solid  gas, liquid  gas
• air occupies space and has mass
• diffusion: solid into solid, solid into liquid, gas into gas
• Brownian motion
See the Practical Physics website, ‘Molecules in motion’ collection

8. Many states of matter
solid, liquid, gas, plasma …
superfluids, liquid crystals, solid solutions, aerogels, foams, thin
films, colloids, immiscible liquid mixtures, gas dissolved in liquid,
condensed matter, biopolymers…..

9. Molecular models
• solid
• liquid
• gas
Discuss, first in pairs, then in groups:
How does each model account for observable
physical behaviour – shape, ability to flow,
elasticity, surface, changes of state?

10. Gases: bulk properties
quantity symbol SI unit
pressure p Pa (Nm-2
)
volume V m3
temperature T kelvin, K
density r kg m-3
pressure = force applied over a unit area.
Later: see SPT Forces, episode 8 Pressure
A
F
p 

11. An ideal gas
• huge number of point molecules (occupy negligible volume) in
continual random motion (and so ‘kinetic’)
• colliding elastically with each other and with container walls
• no forces between the molecules, except in collision
• time in collisions very small compared to time between collisions
• distance travelled between collisions (‘mean free path’) depends
on gas density
• average speed of molecules depends on gas temperature
• in a gas composed of different molecules, the average
molecular Ek is the same for all, so those with larger mass have
smaller speed

13. Gas pressure
t
v
m
t
mv
F






)
(
bombardment of the
container walls
change of momentum
with each collision
mv - (-mv) = 2mv

14. The speed of gas molecules
Ways of estimating an average speed in air
- from the speed of sound (340 ms-1 at s.t.p.)
- thought experiment: a molecule falls freely from the top of the
atmosphere
Direct measurement: Zartman (1931) experiment to find the
distribution of molecular speeds in a beam emitted from an oven
opening. Average speed of N2 at room temperature ~ 500 ms-1
as
v
u
as
u
v
2
0
2
2
2





15. Distribution of particle speed for 106 oxygen particles
at -100, 20 and 600 oC.

16. The size of a molecule
oil film experiment
Devised by John William Strutt, Lord Rayleigh, who also explained
why the sky looks blue, and many other things! Nobel prize-
winner 1904.

17. The size of atoms
‘If an apple were
magnified to the size
of Earth, the atoms in it
would each be about
the size of a regular
apple.’
Richard Feynman
AFM showing atoms within hexagonal
graphite unit cells. Image size 2 nm × 2 nm.

18. Models made real
metallurgy (e.g. sword-making) existed long before any theory of
metal structure. secret techniques to develop toughness & hardness,
found by trial and error (e.g. heat treatments, hot working)
late 19th C model (polycrystalline structure of metals - grains)
metallurgists studied polished and etched metal surfaces under a
microscope, X-ray crystallography from 1911
theory of cracks (dislocations and defects in metal lattice) limiting
strength, confirmed by electron microscopy after 1937
materials by design e.g. transistor 1947, pure glass fibre 1970,
1000s of steel alloys today. Determining properties using
computer simulations.

19. Galileo and Torricelli
Task:
Read chapters 3 & 4 from Joan Solomon (1989) The big
squeeze. ASE booklets series The Nature of Science.
Discuss: Could you use an extract from this in your
teaching?
………………………………………………………………...
How to make a water barometer in school, for a
participative demonstration.

20. Height of the atmosphere
weight of a column,
pressure of a column,
pressure of air and water columns are
equal, so
Vg
mg
W 


gh
A
Ahg
A
Vg
A
F
p 






w
a
w
a
w
w
a
a
h
h
h
h








21. Hydraulic machines
Hydraulic machines exploit these facts:
• pressure is the same throughout a fluid (at same height).
• liquids are incompressible.
How do hydraulic systems work?
In pairs:
Explore SPT Forces episode 8.
(25 min)

22. An empirical law
temperature constant re-plot to show inverse proportionality
Boyle’s law: pV = constant
[Clive Sutton (1992) Words, Science and Learning Open University Press pp 74-75]

23. Extrapolating from data
Another empirical law…
Charles’ law: T
V 
In oC, a linear relationship.
Direct proportionality if
temperature scale is redefined.
T in kelvins, where
K = oC + 273

24. Other gas laws
pressure law: (T in kelvins)
All three relationships combined:
where n is number of moles, gas constant R = 8.31 J K-1
This means
T
p 
nR
T
pV

 constant
2
2
2
1
1
1
T
V
p
T
V
p


25. Kinetic theory – a chronology
c.420 BC – atomic theory (Democritus: matter ultimately uncut-able)
1662 – Boyle’s law
1738 – Bernoulli Hydrodynamica (molecular collisions  gas pressure)
1787 – Charles’ law
1798 – atomic theory of heat
1827 – Brownian motion
1834 – ideal gas law
1849 – kinetic theory
k = 1.38 x 10-23 J K-1 (Boltzmann constant)
kT
v
m
2
3
2
1
c
macroscopi
c
microscopi
2



26. Gas properties
PhET simulation Gas properties
Pump gas molecules to a box and see what happens as
you change the volume, add or remove heat, change
gravity, and more.
Measure the temperature and pressure, and discover
how the properties of the gas vary in relation to each
other.

27. Phase diagrams
A phase diagram (p - T) shows
boundaries between phases
of matter.
• At the triple point, all 3 phases co-
exist.
• Beyond the critical point, there is
no distinction between gas and
liquid phases.
PhET: phase change simulation

28. Speed of sound
When a sound wave travels in a medium, particles in the medium
are subjected to varying stresses, with resulting strains.
The speed of sound is partly affected by the elasticity (stiffness) of
the medium, E, and partly by the density, , of the medium.
In a gas, the sound (pressure) wave is an adiabatic process (no
thermal transfers), so
strain
stress
,
(vol)
length
original
(vol)
length
in
change
strain
,
area
force
stress 

 E

E
v 
p
c
c
E
V
p
)
(


29. Physics of society?
measuring society e.g.
• Thomas Hobbes (1651) Leviathan. political philosophy (science)
based on ‘natural philosophy’
• Enlightenment (especially in France): social statistics to measure
society (large numbers: order emerges from random behaviour)
physics e.g.
• kinetic theory & phases changes (statistical mechanics)
• growth and form in nature – fractal patterns, chaos theory
physics-based modelling human behaviour e.g.
• modelling geography – e.g. growth of cities, transport networks
• modelling road traffic – changes of state
• financial forecasting
Philip Ball (2004) Critical mass: how one thing leads to another

30. Educational constructivism
Four valuable ideas:
• the importance of the pupil’s active involvement in thinking, if
anything like understanding is to be reached
• the importance of respect for the child and for the child’s own
ideas
• that science consists of ideas created by human beings
• that the design of teaching should give high priority to making
sense to pupils, capitalising and using what they know and
addressing difficulties that may arise from how they imagine
things to be
‘To make knowledge one’s own is crucial for satisfying learning,
though not at all a simple or quick process.”
Ogborn J (1997) ‘Constructivist Metaphors of Learning Science’,
Science and Education 6:121-133