TAILIEUCHUNG - Thermodynamics Systems in Equilibrium and Non Equilibrium Part 9

Tham khảo tài liệu 'thermodynamics systems in equilibrium and non equilibrium part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 190 Thermodynamics - Systems in Equilibrium and Non-Equilibrium entropy variations as the entropy change due to the lattice volume change is directly calculated from the use of the Maxwell relation. It is helpful to have a visual sense of the application of the Maxwell relation on magnetization data to obtain entropy change as we will discuss in the following section. A summarized version of the following section is given in Amaral Amaral 2010 . Visual representation Let us consider a second-order phase transition system. M is a valid thermodynamic parameter . the system is in thermodynamic equilibrium and is homogeneous. Numerically integrating the Maxwell relation corresponds to integrating the magnetic isotherms in field and dividing by the temperature difference AC _ H Mi Mi ASM A H foH M Ti 1 H - M T H dH Ti 1 - T 33 which has a direct visual interpretation as seen in Fig. 15 a . If the transition is first-order there is an ideal discontinuity in the M vs. H plot. Still apart from expected numerical difficulties the area between isotherms can be estimated Fig. 15 b . b Fig. 15. Schematic diagrams of a a second-order and b first-order M vs. H plots showing the area between magnetic isotherms. From Eq. 33 these areas directly relate to the entropy change. The CC relation is presented in Eq. 34 a AT A M A He AS 34 where AM is the difference between magnetization values before and after the discontinuity for a given T A He is the shift of critical field from AT and AS is the difference between the entropies of the two phases. The use of the CC relation to estimate the entropy change due to the first-order nature of the transition also has a very direct visual interpretation Fig. 16 a From comparing Figs. 15 b and 16 a we can see how all the magnetic entropy variation that can be accounted for with magnetization as the order parameter is included in calculations using the Maxwell relation Fig. 16 b . The Mean-Field Theory in the Study of Ferromagnets and .

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