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**Thermodynamic Fit Functions of the Two-Phase Fluid and Critical Exponents** ()

Two-phase fluid properties such as entropy, internal energy, and heat capacity are given by thermodynamically defined fit functions. Each fit function is expressed as a temperature function in terms of a power series expansion about the critical point. The leading term with the critical exponent dominates the temperature variation between the critical and triple points. With

*β*being introduced as the critical exponent for the difference between liquid and vapor densities, it is shown that the critical exponent of each fit function depends (if at all) on*β*. In particular, the critical exponent of the reciprocal heat capacity*c*^{﹣1}is*α*=1－2*β*and those of the entropy*s*and internal energy*u*are 2*β*, while that of the reciprocal isothermal compressibility κ^{﹣1}_{T}is*γ*=1. It is thus found that in the case of the two-phase fluid the Rushbrooke equation conjectured*α*+ 2*β*+*γ*=2 combines the scaling laws resulting from the two relations*c*=d*u*/d*T*and κ_{T}=dln*ρ*/d*p*. In the context with*c*, the second temperature derivatives of the chemical potential*μ*and vapor pressure*p*are investigated. As the critical point is approached, ﹣d^{2}*μ*/d*T*^{2}diverges as*c*, while d^{2}*p*/d*T*^{2}converges to a finite limit. This is explicitly pointed out for the two-phase fluid, water (with*β*=0.3155). The positive and almost vanishing internal energy of the one-phase fluid at temperatures above and close to the critical point causes conditions for large long-wavelength density fluctuations, which are observed as critical opalescence. For negative values of the internal energy,*i.e.*the two-phase fluid below the critical point, there are only microscopic density fluctuations. Similar critical phenomena occur when cooling a dilute gas to its Bose-Einstein condensate.Keywords

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Elsner, A. (2014) Thermodynamic Fit Functions of the Two-Phase Fluid and Critical Exponents.

*Engineering*,**6**, 789-826. doi: 10.4236/eng.2014.612076.Conflicts of Interest

The authors declare no conflicts of interest.

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