Chapter 14 (I)

Chapter 14 (I) - Chapter 14 Application of MaxwellBoltzmann...

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Chapter 14 Application of Maxwell- Boltzmann Statistics to an Ideal Gas — The Classical Statistical Treatment As mentioned in Chapt 13, Maxwell-Boltzmann statistics is a good model for a real gas under most conditions (the classical limit condition holds for real gases under most conditions except very low temperatures). , , ! / kT j j MB n j j N j MB j j e Z N g N f N g ε ω = = = (14.1)
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14.1 All TD properties expressed from Z 1. Entropy S ). 1 ln (ln ] / ) ln( [ ] / ) ln( [ ] ) ln( [ ] ) ln( [ ] ln ln [ ] ! ln ln [ ln / + + = + = + = = = + = = ∑∑ N Z Nk T U kT U Z N N N k kT N Z N N N k e Z N Nj N k g N Nj N k N Nj N g N k Nj g N k k S jj j j j j kT j j j j j j j j j j j j j ε ω (14.1)
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2. Helmholtz function F F = U TS = NkT(lnZ-lnN+1). (14.3) 3. Chemical potential μ e μ /kT =N/Z, μ =kTln(N/Z)= kT(lnZ-lnN). (14.4) 4. Internal energy U . ) ln ( ) ( . 1 ) ( ) ( , , 2 2 / 2 2 / / / / / V V j kT j j j kT j j j kT j j V kT j j j kT j j j kT j j j j j T Z NKT T Z kT Z N U e g kT kT e g kT dT d e g T Z e g Z e g Z N e Z N g N U j j j j j j = = = = =
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Chapter 14 (I) - Chapter 14 Application of MaxwellBoltzmann...

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