Introduction to Thermodynamics and Statistical Physics phần 8 ppt

... ~cπ µ 3N πV ¶ 1/3 Eyal 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 × 2. 28 × 10 11 m 580 0 K = ... = 4π 3 ¡ 10 26 m ¢ 3 µ 1. 380 65 68 × 10 −23 JK −1 3K 1.05457266 × 10 −34 Js2.997924 58 × 10 8 ms −1 ¶ 3 × 0.24359 ' 2.29 × 10 87 . (3.1 28) 2. The...

Ngày tải lên: 08/08/2014, 15:21

... (1.11) where ¡ ¯ ∇σ ¢ k and (δ¯p) k are parallel t o ¯ ∇g 0 ,andwhere ¡ ¯ ∇σ ¢ ⊥ and (δ¯p) ⊥ are orthogonal to ¯ ∇g 0 . Using this notation Eq. (1 .8) can be expressed as Eyal Buks Thermodynamics and Statistical Physics ... (M),andwhichisgivenby Eyal Buks Thermodynamics and Statistical Physics 4 1.2. Lar g est Uncertainty Estimator Moreover, the second property requires...

Ngày tải lên: 08/08/2014, 15:21

... βU , (1 .85 ) andtheoneinEq.(1 .84 )as σ =logZ gc + βU + ηN . (1 .86 ) Using Eq. (1. 58) one can expressed the Lagrange multipliers β and η as β = µ ∂σ ∂U ¶ N , (1 .87 ) η = µ ∂σ ∂N ¶ U . (1 .88 ) The chemica ... 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 Statis...

Ngày tải lên: 08/08/2014, 15:21

... (−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 Bosons occupation ... (2 .88 ) c p = c V + N. (2 .89 ) Proof. See problem 3 of set 2 . Eyal Buks Thermodynamics and Statistical Physics 59 Chapter 2. Ideal Gas where {E l } are the eigenenergies of a p...

Ngày tải lên: 08/08/2014, 15:21

... 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 ... eigenstate and a giv en orbital. 3.3.2 Partition Function of the Gas The grandcanonical partition function of the gas is given b y Z gc = Y n ζ n . (3...

Ngày tải lên: 08/08/2014, 15:21

... (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 = 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 conjug...

Ngày tải lên: 08/08/2014, 15:21

... (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 Thermodynamics and Statistical Physics 1 58 Chapter5. ExamWinter2010A where D ... (−β~ω) 2(1− exp (−2β~ω)) . (5 .8) Eyal Buks Thermodynamics and Statistical Physics 1 48 Chapter6. ExamWinter2010B and the magnetic susceptibility is...

Ngày tải lên: 08/08/2014, 15:21

... 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 1 In ... N + O µ 1 N ¶ , (1.150) Eyal Buks Thermodynamics and Statist ical Physics 32 1 .8. Solutions Set 1 m = N X l=1 n l , (1.143) and n l is state number of oscillator l. a) Calcula...

Ngày tải lên: 08/08/2014, 15:21

... (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 a magnetic ... reservoir at t emperature τ h and conv erts it all into work is possible. In Fig. 2 .8( b) a refrigerat or is added Eyal Buks Thermodynamics and Statistical Physics 68 2.7...

Ngày tải lên: 08/08/2014, 15:21

... , (2.1 78) one finds F = U −τσ (2.179) = Nτ (−η −1) (2. 180 ) = Nτ ³ µ τ − 1 ´ (2. 181 ) = Nτ µ log n n Q − log Z int − 1 ¶ . (2. 182 ) (2. 183 ) Eyal Buks Thermodynam ics and Statistical Physics 80 Chapter ... τ µ ∂σ ∂V ¶ τ µ ∂V ∂τ ¶ p . Using Vp= Nτ and Eq. (2. 185 ) one finds c p = c V + τ N V N p = c V + N. (2. 188 ) Eyal Buks Thermodynam ics and Statistical Physics 81 Ch...

Ngày tải lên: 08/08/2014, 15:21