De Broglie wavelength and ideal gas entropy derivation

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SUMMARY

The discussion centers on the derivation of ideal gas entropy, specifically addressing the assumption that the dimensions of the box (Lx, Ly, Lz) are significantly larger than the de Broglie wavelength of the atoms. This assumption is crucial as it ensures that the quantum effects become negligible, allowing classical statistical mechanics to apply. Additionally, the inquiry into the number of energy levels available in a box with dimensions equal to the de Broglie wavelength highlights the transition between quantum and classical regimes in thermodynamics.

PREREQUISITES
  • Understanding of ideal gas laws and entropy concepts
  • Familiarity with quantum mechanics, specifically de Broglie wavelength
  • Knowledge of statistical mechanics principles
  • Basic grasp of thermodynamic systems and energy levels
NEXT STEPS
  • Explore the implications of quantum mechanics on classical thermodynamics
  • Research the relationship between de Broglie wavelength and particle confinement
  • Study the derivation of entropy in quantum gases
  • Investigate energy quantization in confined systems
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Physicists, thermodynamic researchers, and students studying quantum mechanics and statistical mechanics who seek to deepen their understanding of entropy in ideal gases.

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When the ideal gas entropy is derived, we consider N atoms in a box of volume=Lx*Ly*Lz. Then, we make the assumption that Lx,Ly,Lz >>de Broglie wavelength of atoms. I am not sure why we need to make this assumption? Thanks!
 
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How many energy levels are available in a box of dimensions equal to the deBroglie wavelength?
 

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