Introduction to Thermodynamics and Statistical Physics phần 10 pptx

... + 2 exp (βJ) , (6.37) Eyal Buks Thermodynamics and Statistical Physics 159 Chapter6. ExamWinter2010B 2. The k vector is restricted due to boundary conditions to the values k = πn L , (6.21) where n ... transformation Eyal Buks Thermodynamics and Statistical Physics 151 Chapter5. ExamWinter2010A is given by ε (k)=~kc , (5.4) where c is the speed of ligh t and where k = q...

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... Stefan-Boltzmann constant. Eyal Buks Thermodynamics and Statistical Physics 104 Chapter 3. Bosonic and Fermionic Systems Similarly to th e EM case, the average total energy is given by U = X n }ω n exp ... (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 St...

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... 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 = p m (4 .10) ˙p ... 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 is given by [see Eq. (4.3)] p = L ˙q ,a...

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... system. Eyal Buks Thermodynamics and Statistical Physics 2 Con tents 6. Exam Wint er 2 010 B 155 6.1 Problems 155 6.2 Solutions 156 References 163 Index 165 Eyal Buks Thermodynamics and Statistical Physics ... Radiation Law 103 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 Partit...

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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. ... has to be chosen out of 5 options. Show that the probability to pass the test (namely to have at least 11 correct answers) using guessing only, is 5.6 × 10 −4 . Eyal Buks...

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... 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 and Statist ical Physics 29 1.8. Solutions Set ... Buks Thermodynamics and Statist ical Physics 43 Chapter 1. The Principle of Largest Uncertainty is determined by the Boltzmann factor. The energy change due to flippin...

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... . Eyal Buks Thermodynamics and Statistical Physics 59 Chapter 2. Ideal Gas where {E l } are the eigenenergies of a particle due to internal degrees of freedom, and where λ =exp(βµ )and =1/τ. As ... (−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. Fermions and Bo...

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... has log τ 2 τ 1 =log µ V 2 V 1 ¶ 1−γ . (2 .107 ) Thus τ 1 V γ−1 1 = τ 2 V γ−1 2 , (2 .108 ) or using Eq. (2 .55) p 1 V γ 1 = p 2 V γ 2 . (2 .109 ) Eyal Buks Thermodynamics and Statistical Physics 63 Chapter 2. Ideal ... cycle is due to the heat that is subtracted from the heat bath Eyal Buks Thermodynamics and Statistical Physics 67 Chapter 2. Ideal Gas where the work in bot...

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... 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 = − 1 τ 2 ∂ ∂β , (2.189) one finds ... b→candd→a, as shown in Fig. 2.12. Assume that the heat capacities C V and C p are temperature independent. Calculate the e fficiency η of this engine. Eyal Buks Thermodynam ics and...

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... simplicity we take E + = E − = 0. Thus, Eqs. (3 .101 ) and (3 .102 ) become Eyal Buks Thermodynamics and Statistical Physics 112 Chapter 3. Boso nic and Fermionic Systems b) Sho w that the variance ... Buks Thermodynamics and Statistical Physics 123 Chapter 3. Boso nic and Fermionic Systems thus T planet = r R Sun 2D T Sun , and for Mars T Mars = r 6.96 × 10 8 m 2 ×...

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