T-x curves

From this inequality, we deduce that the derivatives (dP/dx)T and (dT/dx)P must have opposite signs, i.e., if the P-x curve is / creasing, then the T-x curve is simultaneously... 

This figure is another example of a phase diagram, drawn here for a constant pressure of 70 kPa. The t - y, curve represents states of saturated vapor, with states of superheated vapor lying above it The t — x, curve represents states of saturated liquid, with states of subcooled liquid lying below iL The two-phase region lies between these curves. 

With reference to the txy diagram, we describe the course of a constant-pressure heating process leading from a state of subcooled liquid at point a to a state of superheated vapor at point d. The path shown on the figure is for a constant composition of 60 mole percent acetonitrile. The temperature of the liquid increases as the result of heating from point a to point b, where the first bubble of vapor appears. Thus point b is a bubble point, and the t - x, curve is the locus of bubble points. 

It should be borne in mind that establishment of the isobestic point at X = 522 nm should be performed extremely carefully, as both the t/X curves of Hb and of HbOa are quite steep in this region (Fig. 12). Accurate wavelength calibration of the spectrophotometer used is thus an absolute requirement. 

Figure 6.16. An asymmetric T x) curve obtained for a system for which pAAB is a function of Tand x. pA s= (—6 + 0.5a) + (0.1 +0.8 T. This system shows a UCST at a mole fraction of about x=0.4...

In the computations, which were only of an illustrative nature, it was assumed for simplicity that fo(J.v) depends linearly on the irradiation power density J. Taking into consideration the more complex dependences of fo on J presents no llindamental difBculties and can be carried out of analytical approximations of the tabulated fo(J,v) characteristics for several different irradiation levels. The t (x) curve shows how the automatic tracking servo system vary the design parameters Ng and Ng in the course of the day. The calculated t (x) dependences and also the J(r) curve used in the computation are shown in Fig. 8. 

As shown in Fig. 18.10, the Fraenkel-chain Gs(t,X) curves at different A values can be superposed on one another over the entropic region closely by allowing a vertical shift. Thus from these simulation results, one can... 

T, X curve entirely analogous to the T, Vm, (or T, p) curve for a pure fluid. A constant-temperature cross-section yields a similar p, x coexistence curve. One can take these constant-pressure or -temperature sections including two-phase regions without complication because these variables are fields , variables that have the same values in the conjugate phases on opposite sides of the coexistence surface. In contrast a section at constant x would have no simple interpretation because the curve representing the intersection of the constant-jc plane with the coexistence surface represents points on tie-lines that do not lie in the plane and that terminate at a second phase with a different value of x. 

Figure 2.26. Glass transition temperature as a function of cure conversion for an epoxy-anhydride system. Experimental points were measured in a heating subsequent to a partial cure. T — x and T — x curves [see Eq. (27)] are simulations by means of the optimised model for diffusion-controlled cure.

Fig. 9a. Lower part shifts of caused by an error of Ax = 0.01 in the determination of the oxygen content. As the slope of the T x) curve is not constant the errors in vary between -2 and +4K . Upper part T x). After Conder (2000).

The type of correlation between experimentally measured variable parameters in the system is changing as a result of phase transformations within that system. The indirect methods are used to identify the changes in those correlations. For example, the p-V-T-x curves (pressure as a function of temperature (p-T curves) pressure or temperature as a function of volume (p-V or T-V curves) pressure drop during salt dissolution as a function of solution composition (p-x curves)) show a break at the location of the phase transformation. Not only pressure or temperature or composition could be considered as variables. The properties of the solution or the whole system itself as well as heating or cooling period in thermal analysis can be used as variables to find the phase transitions. 

We shall consider in detail some versions of p-V-T-x curve methods using schemes of typical isothermal and isobaric sections (Figure 1.10) of phase diagrams for binary systems. 

Figure 1.10 Behavior of p-V-T-x curves at phase transformations during experiments. FI - fluid phase S - solid phase (The Experimental Determination of Solubilities, Vol 6, Hefter Tomkins).

Typical vapour and liquid (T-x) curves under equilibrium (free boiling) and non-equilibrium... 

---