Understanding Non-Equilibrium Thermodynamics - Springer 2008 Episode 3 pdf

... take the form 3. 2 Thermoelectric Effects 73 With this notation, (3. 13) and (3. 14) take the more familiar forms q = −λ∇T +  π + µ e z e  i, (3. 15) E −∇  µ e z e  i = ε∇T + ri , (3. 16) with, as ... temperature distribution along the 3. 1 Electrical Conduction 71 Substitution of (3. 1) and (3. 2) in (3. 3) yields ρ ds dt = ∇·  µ e Tz e i  + 1 T  E −∇ µ e z e  · i, (3. 4) from whic...

Ngày tải lên: 12/08/2014, 08:22

... and tools from equilibrium thermodynamics but transposed at a local scale because non-equilibrium states are usually in- homogeneous. The objective is to cope with non-equilibrium situations where basic ... eradicate the non-homogeneity. 30 1 Equilibrium Thermodynamics: A Review dN k = r  j=1 ν jk dξ j (k =1, 2, ,n), n  k=1 ν jk M k =0 (j =1, 2, ,r). (1. 73) In Sects. 1.7.1–1.7 .3,...

Ngày tải lên: 12/08/2014, 08:22

... by dρ dt = −ρ∇·v , (3. 34) ρ dc 1 dt = −∇ · J 1 , (3. 35) ρ dv dt = −∇p, (3. 36) ρ du dt = −∇ · q −p∇·v . (3. 37) 3. 3 Thermodiffusion: Coupling of Heat and Mass Transport 81 vanish. Expression (3. 44) of σ s suggests ... ε>0). The global efficiency may be derived from (3. 23) or (3. 31) by using an aver- age for both generators, namely η np = η p Q p + η n Q n Q p + Q n , (3. 33) where Q...

Ngày tải lên: 12/08/2014, 08:22

... the reac- tions take place under isothermal and well stirred, i.e. spatially homogeneous 6 .3 Thermal Convection 1 53 this is only true for two-dimensional rolls and it is not so for three-dimensional patterns ... A 1 A 3 , dA 3 dt = −bA 3 + A 1 A 2 , (6 .35 ) where r = Ra/(Ra) c and b =4/(1 + 4k 2 ). The coefficient A 1 describes the velocity of the fluid particles, A 2 the temperature...

Ngày tải lên: 12/08/2014, 08:22

... (7. 23) Box 7 .3 Non-Equilibrium Temperature vs. Local Equilibrium Temperature In analogy with the classical theory, we define the non-equilibrium temper- ature θ by θ −1 (u, q )=  ∂s ∂u  q . (7 .3. 1) Expanding ... (7. 23) , the generalized Gibbs’ equation (7.15) takes the form ds = θ −1 du − τ ρλT 2 q · dq. (7 .3. 3) The integrability condition of (7 .3. 3) demands that ∂θ −1 ∂q = −...

Ngày tải lên: 12/08/2014, 08:22

... connection be- tween dynamics and thermodynamics should be underlined. EIT enlarges the range of applicability of non-equilibrium thermodynamics to a vast do- main of phenomena where memory, non-local, ... (8 .31 ) and energy (8 .33 ) and comparing with the general evolution equation for the entropy ρ ˙s = −∇·J s + σ s , (8 .38 ) one obtains the following results for the entropy flux and...

Ngày tải lên: 12/08/2014, 08:22

... is of prime importance in non-equilibrium thermodynamics. In addition, it was proved that the entropy used in rational thermodynamics is not unique. Meixner (1973a, 1973b) has shown that there exists ... given by a gas thermome- ter or a thermocouple. Recent investigations (Muschik 1977; Casas-V´azquez and Jou 20 03; Crisanti and Ritort 20 03) have brought out that a precise de - niti...

Ngày tải lên: 12/08/2014, 08:22

... engines, 10, 88, 101, 1 03, 1 13, 114, 1 23, 131 heat flux, 35 , 37 , 38 , 45, 47, 50, 54, 55, 64, 73, 76, 80, 93, 170, 181 heat of reaction, 31 33 Helmholtz’s free energy, 23, 24, 27, 36 , 267, 270, 276, ... 202, 2 03, 2 13, 225, 231 , 268, 278, 290, 291, 2 93, 297 chemical reactions, 5, 14, 23, 29, 31 , 38 , 39 , 46, 54, 63, 65, 79, 83, 91, 96 classical irreversible thermodynamic...

Ngày tải lên: 12/08/2014, 08:22

Ngày tải lên: 12/08/2014, 08:22