1. Modified Copy of Lecture Note from
Thursday 15th February 2007
Topics: Heat Conductivity of Electrons
Comment:
Reproduced from last year in february 2008
PHYS page 1

2. Lecture Thursday 15th February 2007
Topics Last Lecture:
* Heat conductivity due to phonons
* phonons
* anharmonicity - heat expansion
* anharmonicity - PHONON SCATTERING
Topics today: (Lorentz number factor 2 ( i.e. 2 pi2/9 )differences )
Electronic motion Classical Electron Gas model (Drude)
Heat and electrical conductivity of electrons
a) HEAT CONDUCTIVITY - see phonons
b) electrical conductivity
Drift velocity from acceleration
Conductivity (relation to resistance)
Wiedemann-Franz law derived
Lorenz number
CLASSICAL ASSUMPTIONS:
a) the gas heat capacity (related to Boltzmann)
b) velocity squared replaced by kT
Conductivity (sigma)
New Aspect: in the literature, there is a strong disagreement about what
is "average velocity". It results in a factor 2 ( i.e. 2 pi2/9 ) difference in the
so called Lorentz number.
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3. Three components : velocity, mean free path, heat capacity
Heat conductivity from the model (one before last lecture):
Three components : velocity, mean free path, heat capacity
From PHYS264 Mean Free Path
PHYS page 3

4. From Today
N/V is called density n
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5. PHYS page 5

6. From Today
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7. factor 2 ( i.e. 2 pi2/9 ) difference from our derivation
From Hyperphysics
factor 2 ( i.e. 2 pi2/9 ) difference
from our derivation
In our PDF textbook:
factor 2 ( i.e. 2 pi2/9 ) difference
PHYS page 7

8. Solid State Physics [3C25] Tony Harker, Chiranijib Mitra and Andrew Horsfield (pages 117)
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9. factor 2 ( i.e. 2 pi2/9 ) larger than our derivation
There are the following groups:
1. Kittel's book -> Wikipedia -> Hyperphysics -> Tony Harker et al -> some new textbooks
factor 2 ( i.e. 2 pi2/9 ) larger than our derivation
2. Ashcroft&Mermin -> Burns -> Hemmer -> our derivation
The difference is in the value of "average velocity".
Wikipedia gives (2007) a nice review
of the three velocities:
Most probable,
Average speed and
Root Mean Square.
The "Physical" is the root mean square, clearly, it relates to average energy.
If we assume thet all particles have the velocity, this assumption must at least
conserve the total energy!
(It might be possible to argue for the average speed too .....)
PHYS page 9

10. The difference is in the value of "average velocity"
The difference is in the value of "average velocity". Wikipedia gives (2007) a nice review of the three velocities: Most probable, Average speed and Root Mean Square. The "Physical" is the root mean square, clearly, it relates to average energy. If we assume thet all particles have the velocity, this assumption must at least conserve the total energy! (But it might be possible to argue for the average speed too .....)
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11. PHYS page 11

12. PHYS page 12

13. PHYS page 13

14. And Kittel - with the factor 2 result
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15. ________________________________________________________________
And Kittel - with the factor 2 result
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PHYS page 15