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CEM383 Equation Sheet, Final Exam - 2004S= k B ln Ωln N!≈ N ln NWqE==N!∏n∑Nj=1n∑j=1=n∑j=1n iigegQ = qQ=jqjjgee!jNNN!−ee−ej−j−ejNkkBTBTkBTN=n∑j=1n j∑j=1E−einigiePi= =nNg ej=k−en∑jj=1BTkBTn j e jn i gi−∆Ek T= eB , ∆E= ein j g−jEHG=NkBT2⎛⎜⎝ed ln q ⎞⎟dT ⎠⎛ d ln q ⎞= NkBT⎜T+ 1⎟⎝ dT ⎠jV⎛ q ⎞= −NkBT⎜ln −1⎟⎝ N ⎠µ = −k T lniBqni