How Does Changing Energy and Oscillators Affect \(\Omega\) in Thermal Physics?

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SUMMARY

The discussion focuses on the impact of changing energy and the number of oscillators on the number of microstates (\(\Omega\)) in thermal physics. When the total energy of a system of 100 oscillators, each with an average of 10 quanta, is doubled, \(\Omega\) increases by a factor of \(2^{99}\). Additionally, adding one more oscillator to the system without altering the total energy results in an increase of \(\Omega\) by a factor of 11. The calculations were verified using the formula \((q+N-1)!/(N-1)!q!\).

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  • Understanding of thermal physics concepts, specifically microstates and macrostates.
  • Familiarity with statistical mechanics and the role of oscillators in energy distribution.
  • Proficiency in combinatorial mathematics, particularly factorial calculations.
  • Knowledge of the equation for calculating microstates in a system of oscillators.
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Students and professionals in physics, particularly those specializing in thermal physics and statistical mechanics, as well as educators seeking to enhance their understanding of microstate calculations and energy distribution in oscillatory systems.

nahanksh
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Homework Statement


Consider a collection of 100 oscillators, each with an average of 10 quanta.
a) By what factor would \Omega(microstate) change if the total energy were increased by a factor of 2?
b) By what factor would \Omega change if one more oscillator were added to the original system without changing the total energy?


Homework Equations





The Attempt at a Solution


I tried to use (q+N-1)!/(N-1)!q! but it doesn't work...

The answer for a) is '2^99' and for b is 'a factor of 11'

Could someone help me out here?

Thanks a lot !
 
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I have just tried to substituted the value into the equation and it seems the answer is approximately correct a) 2^96.6 b) 10.9 (with N=100, q=1000).
Maybe I misinterpret the question.
 

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