Unformatted text preview: μ is the independent variable). Use it to ﬁnd the grand potential G and the number N , as functions of T,μ . Verify that N ( T,μ ) and μ ( T,N ) are inverse functions. c) For a quadratic potential, b = 2, add an external potentialfX , where X = ∑ i q x i , corresponding to a constant force f in the x direction. Evaluate the Gibbs partition function Z , and the Gibbs potential G ( T,N,f ). Evaluate X ( T,N,f ) by diﬀerentiating. 1...
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 Spring '11
 A.Sebastian
 Thermodynamics, mechanics, Work, Statistical Mechanics, Gibbs, Helmholtz free energy, canonical partition function, Polchinski

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