Evaluate the internal energy departure function at N A 3 = 0.6 and /kT = 1

Evaluate the internal energy departure function at ρN_Aσ³ = 0.6 and ε/kT = 1 by performing the appropriate derivatives and integrations of the equation of state obtained by applying

at all temperatures and densities:

(a) The square-well potential with λ_sw = 1.5

(b) The Sutherland potential

(c) Compare these results to those obtained in problem 8.35 and explain why the numbers are not identical.

Data from problem 8.35:

An alternative to the pressure equation route from the molecular scale to the macroscopic scale is through the energy equation (Eqn. 7.50). The treatment is similar to the analysis for the pressure equation, but the expression for the radial distribution function must now be integrated over the range of the potential function. Suppose that the radial distribution function can be reasonably represented by:

at all temperatures and densities. Use Eqn. 7.50 to derive an expression for the internal energy departure function of fluids that can be accurately represented by the following:

(a) The square-well potential with λ_sw = 1.5

(b) The Sutherland potential

Evaluate each of the above expressions at ρN_Aσ³ = 0.6 and ε/kT = 1.

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