Isothermal compressibility thermodynamic definition

In order to introduce basic equations and quantities, a preliminary survey is made in Section II of the statistical mechanics foundations of the structural theories of fluids. In particular, the definitions of the structural functions and their relationships with thermodynamic quantities, as the internal energy, the pressure, and the isothermal compressibility, are briefly recalled together with the exact equations that relate them to the interparticular potential. We take advantage of the survey of these quantities to introduce what is a natural constraint, namely, the thermodynamic consistency. 

Preliminary to such a search we examine several thermodynamic properties of fluids at or close to criticality, that clearly show why and how fluctuations dominate under such conditions, (i) Consider first the isothermal compressibility, kj = —(dV/dP)T/V. At the critical point the isotherm dP/dV)r has zero slope thus, Ki grows indefinitely as T —> Tc. (ii) Using Eq. (1.3.13) and the definition for K one finds that (dV/dT)p = -(dV/dP)TidPldT)v = KiV dP/dT)y, wherein (dP/dT)v does not vanish. Therefore, the coefficient of thermal expansion, = i /V) dV/BT)p also grows without limit as the critical point is approached, (iii) According to the Clausius-Clapeyron equation in the form AH = T(Vg — Vi)(dP/dT), the heat of vaporization of the fluid near the critical point becomes very small, since Vg — Vi 0, whereas dP/dT remains finite. 

Table 2.4 lists the values of ten state functions of an aqueous sucrose solution in a particular state. The first four properties (T, p, ha, b) are ones that we can vary independently, and their values suffice to define the state for most purposes. Experimental measurements will convince us that, whenever these four properties have these particular values, each of the other properties has the one definite value listed—we cannot alter any of the other properties without changing one or more of the first four variables. Thus we can take T, p, ha, and B as the independent variables, and the six other properties as dependent variables. The other properties include one (F) that is determined by an equation of state three (m, p, and Xb) that can be calculated from the independent variables and the equation of state a solution property (77) treated by thermodynamics (Sec. 12.4.4) and an optical property ( d)- In addition to these six independent variables, this system has innumerable others energy, isothermal compressibility, heat capacity at constant pressure, and so on. 

Preliminary to such a search we examine several thermodynamic properties of fluids at or close to criticality that clearly show why and how fluctuations dominate under such conditions. (1) Consider first the isothermal compressibility, k/= —(dV/dP) / At the critical point the isotherm (dP/dV)j-has zero slope thus, kj grows indefinitely as T —> (2) Using Eq. (1.3.8) and the definition for x/ one... 

---