Matter: hot and cold

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14 Matter: very hot and very cold
Revision Guide for Chapter 14
Contents
Student's Checklist
Revision Notes
Boltzmann factor........................................................................................................................ 4
Thermal activation processes.................................................................................................... 4
Values of the energy kT ............................................................................................................. 6
Summary Diagrams (OHTs)
Climbing a ladder by chance ..................................................................................................... 7
Temperature and average energy per particle .......................................................................... 8
Average energy per particle for various processes ................................................................... 9
Variation of Boltzmann factor with temperature ...................................................................... 10
Examples of activation processes ........................................................................................... 12
Advancing Physics A2 1

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Matter: very hot and very cold
Student's Checklist
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I can show my understanding of effects, ideas and
relationships by describing and explaining cases involving:
the ratio of the numbers of particles in a body that exist in states at different energy, and the
change in the ratio when the temperature changes
Revision Notes: Boltzmann factor
Summary Diagrams: Climbing a ladder by chance; Temperature and average energy per
particle; Average energy per particle for various processes; Variation of Boltzmann factor with…read more

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Matter: very hot and very cold
the Boltzmann factor exp(­ / kT)
Revision Notes: Boltzmann factor; Activation processes
Summary Diagrams: Variation of Boltzmann factor with temperature; Examples of activation
processes
Advancing Physics A2 3…read more

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Matter: very hot and very cold
Revision Notes
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Boltzmann factor
For a large number of particles in thermal equilibrium at temperature T, the ratio of numbers
of particles occupying distinct states which differ by energy is given by the Boltzmann factor
e­ /kT , where k is the Boltzmann constant.
The value of the Boltzmann constant is k = 1.38 × 10­23 J mol­1 K­1.…read more

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Matter: very hot and very cold
Activation
energy gap
particles
The Boltzmann factor e ­ / kT is an approximation to the fraction of particles in a large system
at temperature T having a larger than average energy of at least . If the temperature is
increased, the number of energetic particles increases, and the process occurs more rapidly.
Thermionic emission
To escape from a metal surface, a conduction electron must cross an energy barrier: the work
function of the surface.…read more

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Matter: very hot and very cold
proportional to the Boltzmann factor e­ / kT, where is the energy needed to free an electron.
Hence the conductivity of an intrinsic semiconductor is approximately proportional to e­ / kT:
= 0 e - / kT .…read more

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Matter: very hot and very cold
Summary Diagrams (OHTs)
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Climbing a ladder by chance
Climbing a ladder of energy by chance
One particle may acquire energy several times With many particles, a fraction f acquire energy
in succession at each step of ladder
fraction f 3
gets lucky three times
energy fraction f2
gets lucky twice energy fraction f
gets lucky once
energy
By chance, particles may get extra energy from the random thermal motion of particles in the
surroundings…read more

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Matter: very hot and very cold
Temperature and average energy per particle
Temperature and energy = kT
temperature energy = kT photons hf = kT
1 MeV 100 GJ mol­1
supernova 6 billion K nuclear binding gamma rays
energy
= 1.0 pm
100 keV 10 GJ mol­1
hard x-rays
10 keV = 0.1 nm 1 GJ mol­1
interior of Sun 1 keV 100 MJ mol­1
6 million K ionisation of inner soft x-rays
electrons of atoms = 2.…read more

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Matter: very hot and very cold
Average energy per particle for various processes
Processes and energy ~
~ kT per particle
1000 100 000
x-ray
photons
inner electrons in atoms liberated emitted
plasmas
form 10000
100
ultraviolet
photons
emitted
outer electrons in atoms liberated ceramics
10 1000
evaporate
ionic bonds broken
covalent bonds broken metals melt
metallic bonds broken
visible
1 photons 100
emitted
water
hydrogen bonds broken evaporates
1/10 10
soft matter
van der Waals bonds broken exists
kT at room temperature
1/40 2.…read more

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Matter: very hot and very cold
Variation of Boltzmann factor with temperature
Boltzmann factor: the minority with energy /kT
Boltzmann 1 + e­1 exp(­/kT)
factor as a
power of ten +
10­4 + e­10
logarithmic
scale +
10­8 where the action is: e­20
+
+
10­12 /kT from 15 to 30
+ e­30
+
10­16 ­40
+ e
1 5 10 15 20 25 30 35 40
/kT (linear scale)
Hot at this end of the scale Cold at this end of the scale
The…read more

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