Book contents
- Frontmatter
- Contents
- Preface
- 1 Introducing thermodynamics
- 2 A road to thermodynamics
- 3 Work, heat and the First Law
- 4 A mathematical digression
- 5 Thermodynamic potentials
- 6 Knowing the “unknowable”
- 7 The ideal gas
- 8 The two-level system
- 9 Lattice heat capacity
- 10 Elastomers: entropy springs
- 11 Magnetic thermodynamics
- 12 Open systems
- 13 The amazing chemical potential
- 14 Thermodynamics of radiation
- 15 Ideal Fermi gas
- 16 Ideal Bose–Einstein system
- 17 Thermodynamics and the cosmic microwave background
- Appendix A How pure is pure? An inequality
- Appendix B Bias and the thermal Lagrangian
- Appendix C Euler's homogeneous function theorem
- Appendix D Occupation numbers and the partition function
- Appendix E Density of states
- Appendix F A lab experiment in elasticity
- Appendix G Magnetic and electric fields in matter
- Appendix H Maxwell's equations and electromagnetic fields
- Appendix I Fermi–Dirac integrals
- Appendix J Bose–Einstein integrals
- Index
16 - Ideal Bose–Einstein system
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introducing thermodynamics
- 2 A road to thermodynamics
- 3 Work, heat and the First Law
- 4 A mathematical digression
- 5 Thermodynamic potentials
- 6 Knowing the “unknowable”
- 7 The ideal gas
- 8 The two-level system
- 9 Lattice heat capacity
- 10 Elastomers: entropy springs
- 11 Magnetic thermodynamics
- 12 Open systems
- 13 The amazing chemical potential
- 14 Thermodynamics of radiation
- 15 Ideal Fermi gas
- 16 Ideal Bose–Einstein system
- 17 Thermodynamics and the cosmic microwave background
- Appendix A How pure is pure? An inequality
- Appendix B Bias and the thermal Lagrangian
- Appendix C Euler's homogeneous function theorem
- Appendix D Occupation numbers and the partition function
- Appendix E Density of states
- Appendix F A lab experiment in elasticity
- Appendix G Magnetic and electric fields in matter
- Appendix H Maxwell's equations and electromagnetic fields
- Appendix I Fermi–Dirac integrals
- Appendix J Bose–Einstein integrals
- Index
Summary
From a certain temperature on, the molecules “condense” without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there also some truth to it?
Albert Einstein, Letter to Ehrenfest (Dec. 1924). Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, New York (1982)Introduction
For over 50 years the low-temperature liquid state of uncharged, spinless He4 was the only system in which a Bose–Einstein (BE) condensation was considered experimentally realized. In that case, cold (<2.19K) liquid He4 passes into an extraordinary phase of matter called a superfluid, in which the liquid's viscosity and entropy become zero.
With advances in atomic cooling (to ≈ 10–9 K) the number of Bose systems which demonstrably pass into a condensate has considerably increased. These include several isotopes of alkali gas atoms as well as fermionic atoms that pair into integerspin (boson) composites.
Although an ideal Bose gas does exhibit a low-temperature critical instability, the ideal BE gas theory is not, on its own, able to describe the BE condensate wave state. In order for a theory of bosons to account for a condensate wave state, interactions between the bosons must be included. Nevertheless, considerable interesting physics is contained in the ideal Bose gas model.
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- Thermal PhysicsConcepts and Practice, pp. 246 - 254Publisher: Cambridge University PressPrint publication year: 2011