Statistical thermodynamics - system of oscillators

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SUMMARY

The discussion focuses on calculating the probability distribution of energy quanta in a system of 10 oscillators characterized by a \(\beta\) parameter of ln(3/2). The probability function is defined as \(p(Q) \propto e^{-\beta Q}\), leading to the formulation \(p(Q) = N e^{-\beta Q}\). Participants emphasize the importance of determining the normalization constant \(N\) to ensure the probability distribution is correctly defined. This approach is essential for understanding statistical thermodynamics in oscillatory systems.

PREREQUISITES
  • Understanding of statistical thermodynamics principles
  • Familiarity with the concept of oscillators in physics
  • Knowledge of probability distributions and normalization constants
  • Basic proficiency in mathematical functions, particularly exponential functions
NEXT STEPS
  • Research the derivation of the normalization constant \(N\) for probability distributions
  • Study the implications of the \(\beta\) parameter in statistical mechanics
  • Explore the concept of energy quanta in quantum harmonic oscillators
  • Learn about the canonical ensemble in statistical thermodynamics
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Students and professionals in physics, particularly those studying statistical thermodynamics, as well as researchers interested in the behavior of oscillatory systems in thermal equilibrium.

henryc09
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Homework Statement


A system of 10 oscillators, characterised by a \beta^ parameter of ln(3/2) is in equilibrium with a heat bath. Determine the probability that the system should possesses Q quanta.

Homework Equations


p(Q) proportional to e^(-Beta*Q)

The Attempt at a Solution


I have seen a similar question to work out the average <Q> for a system which is one oscillator, but I'm not sure how to attack this problem
 
Physics news on Phys.org
You said p(Q) is proportional to e-βQ, which means p(Q)=Ne-βQ. You should start by figuring out the normalization constant N.
 

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