Introduction to Thermodynamics and Statistical Physics phần 3 pdf

... independen t, thus σ =6× µ − 2 3 ln 2 3 − 1 3 ln 1 3 ¶ =3. 8191 . 12. The random variable X obtains t he value n with proba b ility p n = q n , where n =1, 2, 3, ,andq =1/2. a) The entropy is given ... − 5 6 ¢ 2 =6. 3. Let W (m) be the probability for for taking n 1 steps to the right and n 2 = N − n 1 steps to the left, where m = n 1 − n 2 ,andN = n 1 + n 2 . Using Eyal Buks...

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... Z int ) ∂τ ¶ . (2. 134 ) Eyal Buks Thermodynamics and Statistical Physics 71 2.8. Problems Set 2 8. A lattice contains N sites, each is occupied by a single atom. The set of eigenstates of each atom, when ... .55) p 1 V γ 1 = p 2 V γ 2 . (2.109) Eyal Buks Thermodynamics and Statistical Physics 63 Chapter 2. Ideal Gas Fig. 2.6. Transforming work into heat. ∆σ = − Q τ , (2.1 23...

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... Law 1 03 3.2 PhononsinSolids 105 3. 2.1 OneDimensionalExample 105 3. 2.2 The3DCase 107 3. 3 FermiGas 110 3. 3.1 OrbitalPartitionFunction 110 3. 3.2 PartitionFunctionof theGas 110 3. 3 .3 EnergyandNumberofParticles ... SolutionsSet2 79 3. Bosonic and Fermionic Systems 97 3. 1 ElectromagneticRadiation 97 3. 1.1 ElectromagneticCavity 97 3. 1.2 PartitionFunction 100 3. 1 .3 CubeCa...

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... systems denoted as S 1 and S 2 .Letσ 1 = σ 1 (U 1 ,N 1 )and σ 2 = σ 2 (U 2 ,N 2 )betheentropyofthefirst and second system respectively Eyal Buks Thermodynamics and Statistical Physics 19 Chapter 1. ... to the total length of the chain, whereas in the other state the section has no contribution to the total length of the c hain. The total length of the c hain in Nα, and the...

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... 1(2.42) and employ the first order expansion log (1 + x)=x + O ¡ x 2 ¢ (2. 43) to obtain Eyal Buks Thermodynamics and Statistical Physics 53 2.1. A Particle in a Box n Q = µ Mτ 2π~ 2 ¶ 3/ 2 . (2.12) The ... (−βε n ) . (2.77) The total grandcanonical partition function is given by Z gc = Y n ζ n , (2.78) thus Eyal Buks Thermodynamics and Statistical Physics 58 2 .3. Fermi...

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... Gas D (∆E) 3 E =  E 3 − 3E 2 U +3EU 2 − U 3 ® =  E 3 ® − 3U  E 2 ® +2U 3 = − " 1 Z gc µ ∂ 3 Z gc ∂β 3 ¶ η − 3 Z 2 gc µ ∂Z gc ∂β ¶ η µ ∂ 2 Z gc ∂β 2 ¶ η + 2 Z 3 gc µ ∂Z gc ∂β ¶ 3 η # = − ∂ ∂β " 1 Z gc µ ∂ 2 Z gc ∂β 2 ¶ η − 1 Z 2 gc µ ∂Z gc ∂β ¶ 2 η # = ... (2.255) a) Using E q. (2.252) D (∆E) 2 E = − ∂ ∂β 3N 2β = 3 2 N β 2 = 2U 2 3N . (2.256) b) Using Eq. (2....

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... (3. 7) and µ 0 H =∇× A . (3. 8) The gauge condition (3. 6) and Eqs. (3. 7) and (3. 8) guarantee that Maxwell’s equations (3. 2), (3. 3), and (3. 4) are satisfied ∇ × E = − ∂ (∇× A) ∂t = −µ 0 ∂H ∂t , (3. 9) ∇ ... Buks Thermodynamics and Statistical Physics 105 Chapter 3. Bosonic and Fermionic Systems and therefore C V = ∂U ∂τ = 12π 4 5 N ³ τ Θ ´ 3 . (3. 81) Note that Eq....

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... =2× 1 8 × 4 3 πn 3 F = π 3 n 3 F (3. 170) n F = µ 3N π ¶ 1 /3 ε F = ~cπ L µ 3N π ¶ 1 /3 = ~cπ µ 3N πV ¶ 1 /3 Eyal Buks Thermodynamics and Statistical Physics 1 23 Chapter 3. Boso nic and Fermionic ... (ε) dε = L 3 π 2 ~ 3 c 3 Z ε F 0 ε 3 dε = (3. 171) = L 3 π 2 ~ 3 c 3 × ε 4 F 4 = 1 4 L 3 π 2 ~ 3 c 3 ε 3 F × ε F = = 1 4 L 3 π 2 ~ 3 c 3 3π 2...

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... (4. 53) ThelastresultistheNyquist’snoiseformula. Eyal Buks Thermodynamics and Statistical Physics 135 4.1. Classical Hamiltonian H = m ˙q 2 − m ˙q 2 2 + V (q) = p 2 2m + V (q) . (4.9) Hamilton-Ja cobi equations (4.7) and (4.8) read ˙q ... energy stored in the inductor, and the potential energy V = q 2 /2C is t he energy stored in the capacitor. The canonical conjugate momentum i...

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... (6 .30 ) and η =log µ Vτ 3 π 2 N~ 3 c 3 ¶ . (6 .31 ) b) The en tropy is evaluate using Eq. (1.86) σ =logZ gc + βU + ηN = N (1 + 3 + η) = N · 4+log µ Vτ 3 π 2 N~ 3 c 3 ¶¸ , (6 .32 ) and the Helmholtz free ... e −η V π 2 ~ 3 c 3 β 3 . (6.27) a) The a v erage energy U and average number of particle N are calcu- lated using Eqs. (1.80) and (1.81) respectively Eyal Buks...

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