tailieunhanh - Muller A History of Thermodynamics The Doctrine of Energy and Entropy phần 7

Tham khảo tài liệu 'muller a history of thermodynamics the doctrine of energy and entropy phần 7', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Full Degeneration and Bose-Einstein Condensation 193 4 ỴJĩ lg3 2 and V jU 3 F 4 5 2 - IS 5 so that the energy is large but the entropy vanishes. Bosons For bosons - with the lower sign - we must realize that the biggest value of g must be g 0 lest negative values of the distribution function appear. Therefore g 0 and f r qu exp -l characterize the Bose case of full degeneracy. rmeptoperties of the distribution are muchas expected necause itimplien sdat ferre arelexs particles with lamm naxeeP. However there is a problem since fequ is singular for c 0 To be sure the values of v and p 4 v are finite namely41 N __ 2 I k . __ I k 5A kl Y I 2x-T d ị and p yhĩĩ-T d T V sfriSOe 2d y s yej e . t JI so s but there is somellieig sttaego. Im Iced ami p axe ftmetioen ef T only e circumstance that wchoeacome to ompme et en equiiibriumcondition for saturated vapour ctr c ibti g with a boiling condensate. That observation may serve as a hint that the equation for the number N of atoms is incorrect because DMt possito depend on T. And indeed the equation holds only for thn number of perhcles with --II. white p he number of particles with c 0 has somehow slipped through the Riemann -integre1 hon lfisoueXi cfiidanshiy ssninguliU-. Therafore rhe7y-equation must be rewrittenas I3 s d. ol . l. ll l0CA yLiI Till- y tỵ T v2- And if 7 daf ri S1C number of Iioic1 es m rdc eepmir. Ap is the number of pqiclesmthe ee 0 . One says The Noparticles with 41 f 3 2 and f 5 2 are values of the Riemann zeta function which occurs in the integration of the distribution functionft rga 0. 194 6 Thứd Law of Thermodynamics c 0 form the Bose-Einstein condensate 2 For T 0 there will be more and more condensate whose entropy is zero. The entropy of a Bose gas for full degeneracy vanishes therefore for T 0. The observed decomposition of liquid helium into a normal fluid and a super-fluid is often seen to be a reflection of the Bose-Einstein condensation Ihcidca isappcaiing the reflection