Introduction to Thermodynamics and Statistical Physics phần 4 ppt

... Buks Thermodynamics and Statistical Physics 48 Chapter 2. Ideal Gas log Z gc = X n log ( 1 + λ exp (−βε n )) ' λ X n exp (−βε n ) = λZ 1 , (2 .44 ) where Z 1 = V µ Mτ 2π~ 2 ¶ 3/2 (2 .45 ) [see ... ssical lim it λ exp ( −βε) ¿ 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...

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... 130 4. 2.2 Example 131 4. 3 NyquistNoise 132 4. 4 ProblemsSet4 136 4. 5 SolutionsSet4 138 5. Exam Wint er 2010 A 147 5.1 Problems 147 5.2 Solutions 148 Eyal Buks Thermodynamics and Statistical Physics ... SolutionsSet3 117 4. Classical Limit of Statistical M echanics 127 4. 1 ClassicalHamiltonian 127 4. 1.1 Hamilton-Jacobi Equations 128 4. 1.2 Example 128 4. 1.3 Example...

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... number of flips required. Eyal Buks Thermodynamics and Statistical Physics 24 Chapter 1. The Principle of Largest Uncertainty Table 1.1. The microcanonical, canonical and grandcanonical distributions. energy ... 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...

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... spacing, k n = 2πn aN , (3.57) and n is in teger ranging from −N/2toN/2. 0 0.2 0 .4 0.6 0.8 -1 -0.8 -0.6 -0 .4 -0.2 0.2 0 .4 0.6 0.8 1 x The function |sin (πx/2)|. Eyal Buks Thermodynamics and Statistical Physics 105 Chapter ... Stefan-Boltzmann constant. Eyal Buks Thermodynamics and Statistical Physics 1 04 Chapter 3. Bosonic and Fermionic Systems Similarly to th e...

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... hni) 2 E . (3. 147 ) Eyal Buks Thermodynamics and Statistical Physics 120 Chapter 4. Classical Limit of Statistical Mechanics ¯p =(p 1 ,p 2 , , p d ) , (4. 4) namely H = H (¯q, ¯p) , (4. 5) and it is ... Thermodynamics and Statistical Physics 121 3.6. Solutions Set 3 thus µ = τ log · exp µ nπ~ 2 m e τ ¶ − 1 ¸ . (3.179) Eyal Buks Thermodynamics and Statistical Physi...

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... finds Z ∞ −∞ dωS q (ω)=  q 2 ® = Cτ , (4. 48) therefore S V (ω 0 )= 4Cω 3 0 L 2 πQ τ, (4. 49) or using Eqs. (4. 42) and (4. 46) S V (ω 0 )= 2Rτ π . (4. 50) Th us, Eq. (4. 44) can be rewritten as S q (ω)= 2Rτ π 1 L 2 (ω 2 0 − ... given by [see Eq. (4. 3)] p = L ˙q ,and the Hamiltonian (4. 6) is given by H = p 2 2L + q 2 2C . (4. 13) Hamilton-Ja cobi equations (4. 7) and (4. 8) read ˙q = p...

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... N B )log   µ V 2 V 1 ¶µ τ 2 τ 1 ¶ c V,A +c V,B N A +N B   , (5. 54) and the requirement ∆σ =0leadsto Eyal Buks Thermodynamics and Statistical Physics 153 5.2. Solutions is the internal partition function. ... integral ∞ X n x =0 ∞ X n y =0 ∞ X n z =0 → 4 8 ∞ Z 0 dnn 2 , (5. 34) thus, one has log Z gc =2 4 8 ∞ Z 0 dnn 2 log µ 1+λ exp µ −β π~cn L ¶¶ . (5.35) By employing the...

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... 0.8 20−n =5.6 × 10 4 . (1. 144 ) 8. Using N + + N − = N, (1. 145 a) N + − N − = M m , (1. 145 b) one has N + = N 2 µ 1+ M mN ¶ , (1. 146 a) N − = N 2 µ 1 − M mN ¶ , (1. 146 b) or N + = N 2 (1 + x) , (1. 147 a) N − = N 2 (1 ... 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 Thermodynamics...

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... Z int ) ∂τ ¶ . (2.1 34) 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 ... probability p n to find n molecules in a small volume v (namely, v<<V) contained in the vessel is given by p n = λ n n! e −λ , (2. 140 ) where λ = Nv/V. Eyal Buks Thermod...

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... Thermodynam ics and Statistical Physics 84 2.9. Solutions Set 2 (2. 244 ) and Maxwell’s relation µ ∂σ ∂V ¶ τ,N = µ ∂p ∂τ ¶ V,N , (2. 245 ) one finds µ ∂U ∂V ¶ τ,N = τ µ ∂p ∂τ ¶ V,N − p. (2. 246 ) In the ... Z int − 1 ¶ . (2.182) (2.183) Eyal Buks Thermodynam ics and Statistical Physics 80 Chapter 2. Ideal Gas 4. Using Eqs. (1.87), (1.70) and (1.71), and noting that ∂ ∂τ = −...

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