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...

Ngày tải lên: 08/08/2014, 15:21

... 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....

Ngày tải lên: 08/08/2014, 15:21

... (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...

Ngày tải lên: 08/08/2014, 15:21