Statistical Mechanics exam question

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SUMMARY

The discussion centers on key concepts in statistical mechanics, specifically distinguishing between degenerate energy levels and degenerate gases. A degenerate energy level refers to multiple energy states sharing the same energy, while a degenerate gas occurs when all particles occupy a single energy level at low temperatures. The conversation also addresses the Gibbs paradox, the nature of gravitational potential energy, and the significance of the partition function. Additional questions explore the characteristics of Bose and Fermi gases and their behavior under various conditions.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with statistical mechanics concepts
  • Knowledge of Bose-Einstein and Fermi-Dirac statistics
  • Basic grasp of thermodynamic laws
NEXT STEPS
  • Study the implications of the Gibbs paradox in statistical mechanics
  • Research the properties of Bose-Einstein and Fermi gases
  • Learn about the partition function and its applications in thermodynamics
  • Explore the Sahas ionization formula and its role in astrophysics
USEFUL FOR

Students and researchers in physics, particularly those focusing on statistical mechanics, quantum mechanics, and thermodynamics. This discussion is beneficial for anyone preparing for exams or seeking to deepen their understanding of gas behaviors and energy levels.

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I have my main UG exam on Sat & i dnt have answer to these questions . Help me out



Q. Distinguish b/w degenerate energy level & a degenerate gas ?

Ans : Degenrate level : A single energy level can be degenerate with another energy level , no difference b/w their energies . Degenerate gas : All particles occupy a single level at a particular temp. for a fermi gas at T=ok gas is completely degenerate , A BE gas show strong degeneracy at T < To .

Q. Which feature of classical statistical is responsible for Gibbs paradox ?

Ans : Entropy

Q. Why can't gravitational potential energy be asssociated with law of equipartition of energy ?

Ans : As it is of quantized character . More explanation needed

Q. A bose gas, fermi gas , classical gas are at same temp ,pressure & hve same no. of molecules . Which one wud hve least volume , largest volume . Give reason

Q.What kind of energy is fermi energy ?

Q. How is Sahas ionisation formula used to estimate stellar temp ?

Q.Explain the principle of detailed balance in lasers ?

Q.Why the chemical potential of a photon gas is zero ?

Q.Why is that electrons are not ejected out spontaneously from the metal inspite of having tremendous zero point pressure ?

Q.Significance of partition function ?

Q.Write the expression for pressure exerted by radiation for 1. Normal radiation ,2. diffuse radiation in terms of energy density

Q. Calculate the mean no. of photons per unit volume at a temp of 300k ?
 
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Q. Distinguish b/w degenerate energy level & a degenerate gas ?

ANS: Degenerate level: the energy levels that have more than one energy states with
same energy are known as degenerate energy level.

whereas the gas which shows departure from the ideal gas behaviour
are known as degenerate gas.
 
Q. Distinguish b/w degenerate energy level & a degenerate gas ?

ANS: Degenerate level: the energy levels that have more than one energy states with
same energy are known as degenerate energy level.

whereas the gas which shows departure from the ideal gas behaviour
are known as degenerate gas.
 

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