tailieunhanh - Basic Theoretical Physics: A Concise Overview P41

Basic Theoretical Physics: A Concise Overview P41. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | Electron Equilibrium in Neutron Stars 417 where without lack of generality it is assumed that only vk is negative. Of course we choose the smallest possible integral values for the . The concentration ratios ci then result from and according to the principle that the entropy should not change in course of the equilibrium reaction. In this way from the related free enthalpy condition one obtains the Law of Mass Action cV cV2 vk ck c f T p where from the ideal gas equation see the preceding subsection for the yield function f T p with a pressure unit p0 the following general expression results k k -vi gi T f T p ncv n - tiVpo For further simplification we have written g ff T p g 0 T kBT ln P Po which agrees with _ . . 5kBT Sj kB ln ----- . 2p By varying pressure and or temperature one can thus systematically shift the reaction yield in accordance with . increasing the pressure leads to an increased fraction of components with negative vi . As an application and generalization we shall presently treat the osmotic pressure and the decrease in boiling and solidification temperatures of a liquid by addition of sugar and de-icing salt. Firstly however an unusual topic. Electron Equilibrium in Neutron Stars Consider the quantitative answer to the following question How many electrons or protons are there in a neutron star Firstly we need to know the fraction Nelectrons Nprotons 1 Nneutrons . the ratio is extremely small although different from zero. Of course all absolute numbers would be extremely large3. 3 How large is Ne One can estimate this number by inserting typical values for the radius of a neutron star 10 km and of a neutron 10 13 cm . 418 54 Applications II Phase Equilibria in Chemical Physics The above result is then obtained. Consider the relevant astrophysical equilibrium reaction which is the equilibrium inverse 3-decay process pp ee nn vve Here pp stands for the proton4 nn for the neutron ee for the electron and