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Extra info for Liquid State
T h e n , for another conformai s u b stance with different ε1 and σ1, we m a y define ratios / = ε1/ε0 and 3 h = cr^/tfo and rewrite E q . 18) where t h e molar residual Helmholtz free energy A0* of t h e reference substance is to be obtained at a different t e m p e r a t u r e Τ If and a different molar volume Yjh. An even more elegant form of E q . 18) is obtained by using t h e Massieu function J = — A IT. T h e n t h e prefactor / disappears a n d we have L*(T,Y)=J0*(Tlf,Ylh). 19) Although t h e residual functions are m o r e compact a n d m o r e directly related to experimental quantities, most theoretical discussions of fluids and of t h e principle of corresponding states have tended to emphasize t h e coni slightly different configurational functions like A .
In the highly structured liquid water), E q . 36) is completely useless even as a qualitative guide. H i g h e r - o r d e r multipole interactions may be averaged similarly. T h u s , the dipole-quadrupole interaction, proportional to μθ/r* and a function 2 2 % the q u a d of angles, averages to an energy proportional to —μ θ \γ }ιΤ\ r u p o l e - q u a d r u p o l e interaction averages to an energy proportional to 4 10 — ö / r Ä T ; etc. F r o m the nature of Boltzmann statistics, the averaged electrostatic energy for a pair of neutral molecules is necessarily negative (attractive).
22541.... B(T) 3 A plot of t h e reduced second virial coefficient 5 / ( 2 π Λ ^ σ / 3 ) as a function of kT/ε for each of these three pair energies m i g h t seem an appropriate way of comparing t h e m . However, since t h e p a r a m e t e r s ε and a are to a considerable extent arbitrary, a m o r e meaningful comparison will be obtained if we use for reducing p a r a m e t e r s two " e x p e r i m e n t a l " quantities (Kihara, 1953), t h e Boyle t e m p e r a t u r e TB (at which Β = 0) and the "Boyle v o l u m e " VB = TB(dBjdT)T=T^.