Volume-temperature relation

The quantities B, B, / , and ft are called second virial coefficients C, C, y, and / third virial coefficients and D, D, 3, and 3 fourth virial coefficients. These coefficients are functions of the temperature and are characteristic of the individual gas. These equations reproduce the pressure-volume-temperature relations of gases accurately only for low pressures or small densities. 

The virial coefficients can be determined from studies of the pressure-volume-temperature relations of gases. A graphical method for determining the fugacity may be illustrated by the use of the equation of state... 

Experiments have also been carried out on polystyrene with various amounts of plasticizers extrapolation to zero plasticizer content provided an insight into the course of the volume-temperature relation below Tg. Even at (Tg - 70 K) no indication of a transition was found. 

Martin, G. M., S. S. Rogers and L. Mandelkern Volume-temperature relations of amorphous polymers over extended temperature range. J. Polymer Sci. 20, 579-581 (1956). 

Pressure, Volume, Temperature Relations for a Liquid. In Chapter 2 it was shown that the behavior of gases could be expressed by a few simple laws which are, to a large extent, independent of the natm e of the gas. This is not true of liquids, and no simple law, analogous to the general gas law for gases, can be written governing the behavior of liquids. To be sure, expressions for the volume of a liquid as a function of temperature and pressure can be written. At constant pressure the volume of a liquid at any temperature T is given by... 

Douslin, D. R. Harrison, R. H. Pressure, Volume, Temperature Relations... 

Bridgman, P. W. (1912). Water in the liquid and five solid forms, under pressure. Proc. Am. Acad. Arts Sci. 47, 441-558. [50, 61] Bridgman, P. W. (1935). The pressure-volume-temperature relations of the liquid and the phase diagram of heavy water. J. Chem. Phys. 

Simha, R., Utracki, L. A., and Garcia-Rejon, A., Rressure-volume-temperature relations of a poly-e-caprolactam and its nanocomposite. Compos. Interfaces, 8, 345-353 (2001). 

Berg, J. I Simha, R Pressure-volume-temperature relations in liquid and glassy selenium. Journal of Non-Crystalline Solids, 22(1), pp. 1-22 (1976). 

Jain, R. K., Simha, R., Pres sure-volume-temperature relations in small-hydrocarbon liquids. The Journal of Physical Chemistry, 85(15), pp. 2182-2185 (1981). 

VOLUME-TEMPERATURE RELATIONS OF AMORPHOUS POLYMERS OVER AN EXTENDED TEMPERATURE RANGE. 

The volume anomaly AVq is the difference between the true volume and the volume which would exist in the absence of magneto-elastic interactions and can be obtained by extrapolation of the empirical volume temperature relation, from the high temperature phase. 

Effect of Crystallization on Pressure-Volume-Temperature Relations... 

At normal prepares (/ =0) and finite cooling rates, one obtains for constant internal equilibrium (A) the volume-temperature relation (curve a) according to the equation ... 

Figure 6.2 Specific volume-temperature relations for linear polyethylene. Open circles, specimen cooled relatively rapidly from the melt to room temperature before fusion experiments soiid circies, specimen crystallized at 130°C for 40 days, then cooled to room temperature prior to fusion (12).

R. E. Gibson and O. H. Loeffler, Pressure-Volume-Temperature Relations in Solutions, n. The Energy-Volume Coefficients of Aniline, Nitrobenzene, Bromobenzene and Chlorobenzene. J. Am. Chem. Soc., 61,2515-2522 (1939). 

Fig. 2.2 Specific volume-temperature relations for an unfractionated linear polyethylene sample. Slowly cooled from melt O isothermally crystallized at 130 °C for 40 days then cooled to room temperature .(4)...

Fig. 2.3 Specific volume-temperature relation for linear polyethylene samples. Samples initially crystallized at 131.3 °C for 40 days. Unfractionated polymer, Marlex-50 fraction M = 32 000 O. (From Chiang and Flory (5))...

Dreisbach presents tables on the pressure, volume, temperature relations of organic compounds, using Cox charts for families of compounds. In the last chapter of Gaydon s book, dissociation energies for 275 molecules are listed. 

Fig. 4.3. Specific-volume-temperature relations for the melting of linear polyethylene. Key , unfractionated polymer o, fraction M = 32000. (Reprodnced from [4], copyright 1961, American Chemical Society.)...

Fig. 11-1. Volume-temperature relations for a glass-fonning polymer and a material that crystallizes completely on cooling. is a melting point, and and T are glass transition temperatures of an uncrystallized material that is cooled quickly and slowly, respectively.

Fig. 11-2. Volume-temperature relation for an amorphous (upper line) polymer and semicrystalline (lower line) polymer.

As pointed above, Patterson and Woolley [114] performed measurements of density that cover a large temperature range, from 5 to 95 °C. Since they reported the apparent molar volumes at constant molahties, from 0.03 to 1.0 mol kg, it is possible to differentiate their F2 values with regard to temperature in this concentration region. This permits to describe in a more detail the volume-temperature relations in citric acid solutions. Thermal behaviour of these solutions is illustrated by arbitrarily choosing three solutions with the molahties 0.06 0.5 and 1.0 mol kg . It is observed that at constant m, the apparent molar volumes increase with... 

Some general, a rather qualitative description of such relations, for all citrates treated together, is presented here. The volume-temperature relations are based on numerical differentiation of experimental densities, and evidently accuracies of the first and second derivatives of densities with regard to temperature strongly depend on the accuracy of d(/w 7) values coming from different investigations. The first derivative of densities leads to the cubic expansion coefficients (thermal expansibilities) of aqueous solutions of citrates... 

FIGURE 6.5 Specific volume-temperature relation for crystallizable polymers. Numbers apply to Example 6.8. 

Sage, B. H., J. G. Schaafsma, and W. M. Lacey. Phase equilibria in hydrocarbon systems, V pressure volume-temperature relations and thermal properties of propane. lEC 26 1218-1224 (1934). 

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