# Matter: hot and cold

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### Page 1

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…

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…

### Page 2

14 Matter: very hot and very cold

Student's Checklist

Back to list of Contents

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…

Student's Checklist

Back to list of Contents

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…

### Page 3

14 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

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

### Page 4

14 Matter: very hot and very cold

Revision Notes

Back to list of Contents

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 ,…

Revision Notes

Back to list of Contents

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 ,…

### Page 5

14 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…

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…

### Page 6

14 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 .

Conductance variation with temperature

for…

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 .

Conductance variation with temperature

for…

### Page 7

14 Matter: very hot and very cold

Summary Diagrams (OHTs)

Back to list of Contents

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…

Summary Diagrams (OHTs)

Back to list of Contents

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…

### Page 8

14 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…

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…

### Page 9

14 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…

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…

### Page 10

14 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…

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…

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