Chapter 14 – Matter very hot and cold
14.1 The magic ratio: ε/kT
Learning Outcomes:
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particles in matter have an average energy of thermal activity of the order kT
values of kT may be expressed in joule per particle, electron volt, or kJ mol–1
bonds are characterised by the energy e needed to break them.
at high temperatures, bonds break and matter comes apart. Atoms come apart into ions
and electrons. The ratio e /kT is small even for large e.
at low temperatures, thermal activity is feeble, and e /kT is large except for processes
with very small e. Matter condenses to solid or liquid, and complex structures form.
many processes start happening at an appreciable rate when e /kT is in the range 10 or
15 to 30.
Lesson 1 – Temperature and radiation
Objectives: To understand how objects can change as they heat up; to link this to infrared
radiation emitted;
Activities:
10P Temperatures everywhere would be a useful starting point to encourage pupils to
estimates values and get a feel for the ranges of temperatures we encounter. It may be an
opportunity to revisit the idea of absolute zero. Spend 10-15 mins on this simple starter
40P Hot glows reminds pupils about how objects glow as they get hot. While seemingly
simple, this is probably something that they have not thought about in much detail, particularly
how the colour changes with temperature. It is possible to adapt a webcam to see in IR, and
I’m going to do this! You can then see an object heating up and compare the visible light
emitted with the infra-red.
50P Slow motion syrup can be used to start to quantify these changes. Try plotting the time
taken to roll down the slope at different temperatures. An extension is to drop a marble through
syrup at different temperatures and compare the results. Remembering that speed of roll or
drop is proportional to viscosity, you should get en exponentially decreasing trend as this is an
example of the Boltzmann factor we are working towards. The Boltzmann factor is not explicitly
covered until section 14.2, so experiments can be left qualitative at this stage and revisited
later.
Out of class:
Piglet
20S Molecules and change
Pooh
45X Matter comes apart
Christopher Robin
Lesson 2 Potential wells and interatomic bonds
Objectives: To be able to describe the role of the potential well in interatomic bonds and how
this links to macroscopic behaviour
Activities:
If pupils would like more demonstration of changes at temperature, use 70P LCD films and
80P Silicone putty, but keep this brief.
Move on by showing the demonstration from Atomic microscope software as described in 100S
Introducing breakouts. Then have a go at 110E Staying bound; breaking out to introduce
the concept of a potential well and the situations it can be used to describe.
This will lead nicely into 120H Energy for one water molecule to escape which can be used
in the lesson rather than at home. It will provide essential practice in transferring between units
and going from many to just a few molecules. It also gives the first encounter of energy of a
particle being kT, thinking back to Chapter 13. It may be important to point out that the 3/2
factor used previously is not key when we are talking about orders of magnitude.
Out of class:
Piglet
25S Energy per particle
30S Likely events in time
Pooh
35S Values of energy ε=kT
Christopher Robin
Lesson 3: Energy and kT
Learning outcomes: To be able to use units kJ/mol and eV when describing energy of particles
and be able to relate this temperature using kT; to be able to decide when a change will
happen at an appreciable rate, relating energy required to kT.
Activities:
Show 10O Temperature and the energy per particle as a scene setter. Then show pupils
15S Rough values of the energy kT, but remove some of the numbers and ask them to fill in
the gaps to begin to relate the different units to each other. Ask for suggestions as the kinds of
situations each involves. It is also helpful as it emphasises that approximation is a useful tool in
being able to understand what is going on more easily.
If 35S was set as homework it will be essential to spend time going over it here, and attempting
it now if not. It sums up the key ideas from this section: that the average energy of a particle is
given by kT, that different units can be used to discuss energy changes.
Next look at 20O Different processes to begin to link energy required to kT and compare to
see if a breakout or change can happen.
Finally, set 50S Matter starting to come apart. Either start it now or use for homework, but
give time at the start of the next lesson to look at some examples from it.
Out of class:
Piglet
25S Energy per particle
30S Likely events in time
14.2
Learning outcomes:
Learning outcomes
Pooh
40S Particles spreading out
Christopher Robin
10T Einstein’s solid
20T Equipartition of energy
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The ratio of numbers of particles in two states differing by energy e is the Boltzmann
factor exp(–e/kT)
The origin of the Boltzmann factor is the small probability of repeatedly gaining extra
energy at random from a large collection of other particles.
To a first approximation the rate of a reaction with activation energy e is proportional to
exp(–e/kT), and can increase rapidly with temperature.
Reactions can also involve changes in the number of spatial or orientational
arrangements of particles.
Lesson 4 - The Boltzmann Factor exp(-ε/kT)
Learning objectives: To be able to explain how random movement of particles gaining and
losing energy can lead to an exponential distribution of energies.
Two class experiments that demonstrate and begin to quantify the energy distribution of
particles. 150E A race depending only on chance and 170S Getting lucky: climbing and
energy ladder by chance. Spend some time looking at how this model works, comparing it to
throwing dice. It is important to relate this to real life processes
Next, concentrate on 1 particle using 190S: Following one particle: exponential behaviour.
Add a Table to look at the results and use Excel to see if it is truly exponential. Pupils should
be familiar with this from Chapter 10. The graph in Modellus is plotting time spent in each state
against energy of state. Using a table, take the final numbers for count0 to count8 (this is the
time in each state) and plot with 1-8. This will give the familiar curve. Taking log of ‘count’ and
re-plotting ought to give a straight line!
This exercise is essential, as pupils need to understand that exponential behaviour arises out
of random movement of particles.
Out of class:
Piglet
70S Distribution of particles
Pooh
80X Exponential distributions
Christopher Robin
Lesson 5
Learning objectives: To know how to use the Boltmann factor exp(-e/kt) to describe the number
of particles having a certain energy at a given temperature.
Recap last lesson showing that the number of particles at a certain energy level is exponential.
Discuss what factors might affect this.
Try to derive the Boltzmann factor: we are trying to determine how many particles are likely to
reach energy level ε given initial temperature kT, just like in the Modellus model or dice game.
There will be more particles if ε is reduced, and more particles if kT is increased. This leads to
the Boltzmann factor: exp (-ε/kT).
Move on to 60X Thinking about the Boltzmann Factor to check understanding.
Look at the atmosphere example of p114-5
Follow up with 100S Density where jet planes fly
Pupils will also need practice at using the Boltzmann Factor and seeing what it means in terms
of the activation energy, and ‘things starting to happen’ at around 15-30 x kT. Use the A2 book
and the questions below
Out of class:
Piglet
90S The Boltzmann Factor
Pooh
Christopher Robin
Lesson 6: Activation Energy
Learning objectives: To be able to relate Boltzmann Factor to activation energy
Make a circus of these activities, the emphasis being on careful experimental results, and
relevant analysis of data. In each instance there is an empirical quantity that relates to a
process eg current, viscosity, and pupils have to show that the relationship between this and
temperature is exponential. Therefore they can find the value ε of the activation energy,
remembering the 15-30kT rule.
Use 240E Conduction in a semiconductor, 260E Chemical clock reactions, 270E Vapour
pressure in liquids, and 280E Flow rates of sticky liquids.
Each experiment should be done by one group only, and either feed back detailed results at
the end or at the start of the next lesson. This may take the whole hour, with suitable analysis,
and time needs to be given over to sharing and discussion of results.
Piglet
150S Electrons from hot
metals
Pooh
140D Contaminated surfaces
Christopher Robin
30T Flow in liquids
40T Why you can’t get to
absolute zero
Lesson 7: Review
Learning objectives: Review lesson
Try Software activities 220S Change of rate with change of temperature and 230S
Interactive graphs of Boltzmann Factor to draw everything together. Follow up with any of
the data handling activities: 110D, 120D and 130D.