Muller A History of Thermodynamics The Doctrine of Energy and Entropy phần 10

Tham khảo tài liệu 'muller a history of thermodynamics the doctrine of energy and entropy phần 10', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Table Equilibrium distribution function in a gas at rest . with u c 0 0 0 for a degenerate relativistic gas and limit values for weak and strong degeneration and for non-relativistic and ultra-relativistic case 1 Non-relativistic 1 kT Relativistic p c1 A Ultra-relativistic 1 kT non-degenerate lna l aexp - exp - fo Maxwell distribution aexp - ựl aexp - degenerate 1 exp exp fo l 1 iexp ựĩ Ặ l Maxwell-Jtittner distribution 1 iexp ir l strongly degenerate Fermi In a - 1 kT 1 for 0 2pkT In a -0 else 1 for 0 0 else Ina A2 _ kT _ 2 -1 1 for 0 p -y- In a 0 else strongly degenerate Bose c2 n In a - 0 kT p 0 exP 2ổr -l 1 expl -ji-b- - 1 1-1 p 0 7 7 0 exp IF-1 Planck distribution for p hv c White Dwarfs 295 The only remaining source of energy for a white dwarf is gravitational contraction - Helmholtz fashion. That keeps the star hot in the centre perhaps hot enough - a thousand times as hot as the sun - that it must be considered a relativistic gas. Note that the small electronic mass helps in this respect because the relativistic coldness -is more than 103 times smaller for electrons than for nuclei or atoms at the same temperature. Now large speeds make forsirrallde Broglie wave lengths sothạtqnantum effects should be kinah. Hewevee lhe lenge maviiaiionalprentute compresses the slag to nich a degree thft eeen Lie snikll kn t wave lengths interfere ami thus grodnee quarnurn deBenerkhon. Ttoforo an e white dwarf the elgelree eescanpeqhaps t l eg a relativistir gae quantum gas. Clianrhas lheai- 0Keanctl like alsenqrliirn as the basN IfH wv theory of white dwirfSe ln this wav lien pitwideil an applicatien fon Jtlttnerig formulae. Thagwhleqnntlnnoes tateinni deawttt u wiv1 In relativistic thermndenemics lke eonsevvaOrnn an massk cd lay the conservation of thenumbeio artides ndmnmeetem and nnoreo corherveheo are combined in a vedvrsavatiun. Weteve wk 0 and T . 0 where A B Na is the particle flux vector and TAB is the energy-momentum tensor. The .