By Badger R.M.

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137,138 As suitable starting point PV L a 1 þ y þ y2 À y3 a ¼ Zhs À ¼ À ; 3 L RTV RTV L RT ð1 À yÞ (1:191) was selected, with Zhs being Carnahan and Starling’s141 expression for the compression factor of a hard sphere (hs) fluid. 60 J KÀ1 cmÀ3. These results indicate a À Á substantial contribution of @CVL @V T V L ðT; Ps ÞaLs to the change of CVL with temperature along the orthobaric curve. Definitely the most widely used equation for correlating compressed liquid volumes or densities is the Tait equation,140,148 which can be written as L ðT; Pref Þ ¼ À CTV ln V L ðT; P Þ À Vref BTV þ P ; BTV þ Pref (1:193) L where Vref is a suitably selected reference volume, and Pref is the corresponding reference pressure; alternatively, one may write rL ðT; P Þ ¼ rLref ðT; Pref Þ ; BTD þ P 1 À CTD ln BTD þ Pref (1:194) where rLref is a suitably selected reference density.

36) we obtain ! 36), the primary thermodynamic functions (or integrated forms of the fundamental equations for a change of the state of a phase, or fundamental equations, or cardinal functions, or thermodynamic potentials, or Euler equations) are X nU ¼ TðnSÞ À PðnV Þ þ mi ni (1:39) i in the energy representation, and nS ¼ Xm 1 P i ðnUÞ þ ðnV Þ À ni T T T i (1:40) 12 Chapter 1 in the entropy representation. 36), respectively, at constant values of the intensive properties 1 P m T, P and the mi, or ; and the i , respectively.

104) It follows that These relations establish the link between the natural independent variables S, V, P, T and the energy-based functions U, H, F, G. 105b) and are obtained. 110a) and X m G ¼ xi i : RT RT i (1:110b) Here, R ¼ LkB denotes the molar gas constant. 110a). We note that the parallelism existing between equations valid for constantcomposition solutions, and for the corresponding partial molar quantities in such solutions, greatly facilitates the formulation of equations by analogy. This approach is valid whenever the properties appearing in any equation referring to a constant-composition solution are linearly related.