An alternative to the pressure equation route from the molecular scale to the macroscopic scale is through the energy equation (Eqn. 7.51). 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.

(a) Suppose that u(r) is given by the square-well potential (R = 1.5) and g(r) = 10 - 5(r/σ) for r > σ. Evaluate the internal energy departure function where ρσ³ = 1 and ε/kT = 1.

(b) Suppose that the radial distribution function at intermediate densities can be reasonably represented by: g ~ (1 + 2(σ/r)²) at all temperatures. Derive an expression for the attractive contribution to the compressibility factor for fluids that can be accurately represented by the Sutherland potential.

Transcribed Image Text:

P = PRT- 00 ²N² 6 dr 8(r) 47² dr 45₁(du) 7.51