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 gb g2, ... , respectively; in any given macro state in which there are N, particles in energy level ?1, N2 particles in energy level ?2, ... , assume the thermodynamic probability to be given by the Bose-Einstein expression,

ΩBE = (g1 + N1)!(g2 +N2)!.../g1!N1!g2!N2!

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

In ΩBE a maximum,subject to the equations of constraint ∑Ni = N = const.and ∑Ni?i = U = const., and show that

                             Ni = gi/λe-β?i - 1

 

Request for Solution File

Ask an Expert for Answer!!
Engineering Mathematics: Discuss the method of lagrangian multipliers
Reference No:- TGS02045322

Expected delivery within 24 Hours

2015 ©TutorsGlobe All rights reserved. TutorsGlobe Rated 4.8/5 based on 34139 reviews.