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PHYS-C0220 - Termodynamiikka ja statistinen fysiikka, Luento-opetus, 9.1.2023-24.2.2023
This course space end date is set to 24.02.2023
Search Courses: PHYS-C0220
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Topic outline
Kurssin keskeiset käsitteet
1. Mikrokanoninen formalismi (BB 4.1-4.4 ja 14.5)
Mikrotila ja makrotila (
microstate, macrostate
)
Multiplisiteetti (
multiplicity
) eli systeemin mahdollisten mikrotilojen määrä,
\( \Omega \)
Lämpötilan mikroskooppinen, tilastollinen määritelmä
Mikrokanoninen joukko/ensemble (
microcanonical ensemble
)
Boltzmannin entropiayhtälö,
\( S = k_{\rm B} \ln \Omega (N,V,E) \)
2. Kanoninen formalismi (luvut 4, 5, 14, 19)
Kanoninen joukko/ensemble (
canonical ensemble
)
Boltzmannin kerroin (
Boltzmann coefficient
),
\( e^{-\beta E} \)
Partitiofunktio/tilasumma (
partition function
),
\( Z = \sum_i e^{-\beta E_i} \)
Gibbsin entropiayhtälö,
\( S = -k_{\rm B} \sum_i p_i \ln p_i \)
Ekvipartitioteoreema (
equipartition theorem
)
Maxwellin ja Boltzmannin (vauhti)jakauma [
Maxwell-Boltzmann (speed) distribution
]
3. Entropia ja termodynaamiset potentiaalit (luvut 16, 18)
Eksergia (
exergy, availability
)
Helmholtzin funktio/vapaa energia (
Helmholtz function/free energy
),
\( F = U - TS \)
Gibbsin funktio/vapaa energia (
Gibbs function/free energy
),
\( G = H - TS \)
Termodynamiikan kolmas pääsääntö (
The Third Law of Thermodynamics
)
4. Partitiofunktio ja ideaalikaasu (luvut 20, 21)
Kanoninen partitiofunktio (
canonical partition function
)
Semiklassinen ideaalikaasu
Identtiset tai toisistaan erotettavat hiukkaset: tilastolliset ominaisuudet
Kvanttikonsentraatio (
quantum concentration
),
\( n_{\rm Q} \)
Kvanttitilavuus (
quantum volume
),
\( v_{\rm Q} \)
Terminen aallonpituus (
thermal wavelength
),
\( \lambda_{\rm th} \)
5. Kemiallinen potentiaali ja kvanttistatistiikat (luvut 22, 29)
Kemiallinen potentiaali (
chemical potential
)
Suurkanoninen ensemble ja partitiofunktio (
grand canonical ensemble, grand canonical partition function
Bosen-Einsteinin ja Fermin-Diracin jakaumat
6. Kvanttistatistiikkojen sovelluksia (luvut 23, 30)
Elektronikaasu
Fermienergia ja fermilämpötila
Lämpösäteily
Musta kappale
Planckin säteilylaki (
black body distribution
)
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