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Unformatted text preview: I One way is to calculate averages for a path between two states (1 and 2) and to integrate over the reversible path. I Integrating the internal energy along a line of constant density: A Nk B T 2 A Nk B T 1 = Z 2 1 E Nk B T d = Z T 2 T 1 E Nk B T d T T . (37) I Integrating the pressure along an isotherm: A Nk B T 2 A Nk B T 1 = Z 2 1 PV Nk B T d = Z V 2 V 1 PV Nk B T d V V . (38) I This has to be done accurately for many closely spaced points, and is hence rather expensive. Notes I In FrenkelLadd method [FrenkelLadd, J. Chem. Phys. 81, 3188 (1984)] absolute internal energy is calculated by constructing a potential function which depends on parameter : U = U ( r , ) . I Then A = k B T ln R d r exp (U ( r , ) / k B T ) = R d r U exp (U / k B T ) R d r exp (U / k B T ) = U . (39) I U needs to be constructed so that for = the answer is accessible through analytic methods (e.g., ideal gas or harmonic lattice). Notes...
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 Winter '12
 Kotakoski

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