- +44 141 628 6080
- info@tutorsglobe.com

Discuss the method of lagrangian multipliers

Response to the following problem:

Given N indistinguishable, quasi-independent particles capable of existing in energy levels ?_{1}, ?_{2},· .. , with degeneracies g_{b} g_{2}, ... , respectively; in any given macro state in which there are N, particles in energy level ?_{1}, N_{2} particles in energy level ?_{2}, ... , assume the thermodynamic probability to be given by the Bose-Einstein expression,

Ω_{BE} = (g_{1} + N_{1})!(g_{2} +N_{2})!.../g_{1}!N_{1}!g_{2}!N_{2}!

Using Stirling's approximation and the method of Lagrangian multipliers, render

In Ω_{BE} a maximum,subject to the equations of constraint ∑N_{i }= N = const.and ∑N_{i}?_{i} = U = const., and show that

N_{i} = g_{i}/λe^{-β?i - 1}

Expected delivery within 24 Hours

18,76,764

Questions

Asked

21,311

Experts

9,67,568

Questions

Answered

Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!

Submit Assignment
## Q : Performing operations in engineering notation

Perform the operations and express your answer in engineering notation.