Compressibility and Expansion Coefficients of Liquids

The volumetric (P-V-T) behavior of gases under ordinary pressures is described approximately by the ideal gas law. For higher pressures, several more accurate equations of state were introduced. A calculation practice was introduced for ordinary calculations Gases are treated as though they were ideal. The volumes of solids and liquids are computed with the compressibility and the coefficient of thermal expansion. For ordinary calculations they are treated as though they had constant volume. 

E3.10 In the following table are presented a (coefficient of expansion), k (compressibility), and p (density) for liquid water and liquid CCI4. Use... 

Shah et al. carried out a Monte-Carlo simulation in the isothermal-isobaric (NPT) ensemble of [C4mim][PF6] [12]. The authors calculated the molar volume, cohesive energy density, isothermal compressibility, cubic expansion coefficient, and liquid structure as a function of temperature and pressure. A united atom force field was developed using a combination of ab initio calculations and literature parameter values were also developed. Calculated molar volumes were within 5% of experimental values, and a reasonable agreement was obtained between calculated and experimental values of the isothermal compressibility and cubic expansion coefficient. [PF6] anions were found to cluster preferentially in two favorable regions near the cation, namely around the C2 carbon atom, both below and above the plane of the imidazole ring [12],... 

The rapid variations (rise or fall) in the value of the thermodynamic response fimctions, namely the specific heat, the isothermal compressibility (both increase), and the coefficient of thermal expansion (which decreases with temperature when the latter is lowered below the freezing point), are some of the known spectacular anomalies of liquid water. These variations have till now eluded a fully satisfactory understanding [6]. Many computer simulation studies have been done and several theoretical approaches have been developed but they are still not universally accepted. 

The thermophysical and thermodynamic properties of liquid water as well as its chemical properties, all depend on the temperature and the pressure. The thermophysical and thermodynamic properties include the density p, the molar volume V = M/p, the isothermal compressibility/ct = P (dp/d P)t = —V (dV/dP)T, the isobaric expansibility ap = —p dp/dT)p = V dV/dT)p, the saturation vapour pressure p, the molar enthalpy of vapourization Ayf7, the isobaric molar heat capacity Cp, the Hildebrand solubility parameter 3h = [(Ay// —RT)/ the surface tension y, the dynamic viscosity rj, the relative permittivity Sr, the refractive index (at the sodium D-line) and the self-diffusion coefficient T>. These are shown... 

It is obvious that properties such as isothermal compressibility, isobaric expansion coefficient and heat capacity, which display an extremum near the critical density, cannot be intermediate between those of vapor and liquid. As an example, we show in Figs. 4a and 4b the isobaric heat capacity of supercritical water along an Isobar. The sharp spike in Fig. 4a, with temperature as the abscissa, is the equivalent of the broad maximum in Fig. 4b, with density as abscissa. 

Calculate the internal energy changes when the liquid phases of state 1 (n-hexane and aqueous solution) are compressed from p° to p and the aqueous solution of state 2 is decompressed from p2 to p°. Use an approximate expression from Table 7.4, and treat the cubic expansion coefficient of the aqueous solutions as being the same as that of pure water. 

Vilcu R, Miscdolea C (1967) Significant- structure theory of liquids. Heat capacities, compressibilities, and thermal- expansion coefficients of some molten alkali halides. J Chem Phys 46 906-909... 

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

The quantity (dV/dT)P is the coefficient of thermal expansion and [dV/dP)T is the coefficient of compressibility of the liquid. For many liquids, the internal pressure is in the range 2000 to 8000 atm. Because the internal pressure is so much greater than the external pressure,... 

All three quantities (V, H and S) show an upward jump at upon heating (apart from pathological liquids such as water as regards V). At Tg there is, however, no jump, so AV = 0, Mi = 0 and A5 = 0, but a bend, or a jump in their first derivatives. For V, H and S this means, respectively, jumps in the coefficient of expansion a, in the specific heat c and in the compressibility k. 

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

The approach to the critical point, from above or below, is accompanied by spectacular changes in optical, thermal, and mechanical properties. These include critical opalescence (a bright milky shimmering flash, as incident light refracts through intense density fluctuations) and infinite values of heat capacity, thermal expansion coefficient aP, isothermal compressibility /3r, and other properties. Truly, such a confused state of matter finds itself at a critical juncture as it transforms spontaneously from a uniform and isotropic form to a symmetry-broken (nonuniform and anisotropically separated) pair of distinct phases as (Tc, Pc) is approached from above. Similarly, as (Tc, Pc) is approached from below along the L + G coexistence line, the densities and other phase properties are forced to become identical, erasing what appears to be a fundamental physical distinction between liquid and gas at all lower temperatures and pressures. 

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