Boyle point

Figure 1 shows second virial coefficients for four pure fluids as a function of temperature. Second virial coefficients for typical fluids are negative and increasingly so as the temperature falls only at the Boyle point, when the temperature is about 2.5 times the critical, does the second virial coefficient become positive. At a given temperature below the Boyle point, the magnitude of the second virial coefficient increases with... 

In the Sceptical Chymist Boyle points out that in nature there are always many possible explanations, and it is fallacious to argue the case for one explanation by the exclusion of another. He could present the mechanical view only as one possibility among many. It is, he says,... 

There was a problem, though, which Boyle pointed out, taking his objection from Van Helmont How do we know that what is produced by our analysis was previously present in the substance being analyzed Analysis on its own... 

This temperature is called the Boyle point or Boyle temperature TBoyle. Below this temperature, the value of Z at first decreases, approaches a minimum and then increases as the pressure is increased continuously. Above 50 C, the value of Z shows a continuous rise with increase in pressure. 

We use this relation to calculate values of A B/T), Using the experimental value of B at 323 K, the temperature nearest to the Boyle point, we calculate values of BjT and so of B at other temperatures, and compare these with the directly measured values. 

The temperature at which Eq. (7-22) is zero is called the Boyle point. The term Boyle point is used because, at temperatures near Tg, Boyle s law is obeyed over a wider than usual range of values of the pressure. 

Comparison of Eqs. (7-65) and (7-23) yields the conclusion that a van der Waals gas has an inversion temperature equal to two times its Boyle point. It is generally true that Tf > Tg, however, the ratio Tf/Tj, varies from gas to gas. 

Above the Boyle point (Sec. 7-1), 5 is positive and p jp > 1 below the Boyle point, B is negative and p jp < 1. As an example of the magnitude of this ratio, nitrogen gas near 300°K has B 5Q cc/mole, so that gBp/RT gPisoo where p is expressed in atmospheres. This correction becomes important only at relatively high pressures. 

Analogy with the Boyle point Flory (1953) has pointed out a far-reaching analogy between the 0-point for polymer molecules in solution and the Boyle point for nonideal gas molecules. This is useful in understanding the nature of the 0-point, which is crucial to much that is to follow on steric stabilization. 

The point at which this occurs is known as the Flory or theta point and is in some ways analogous to the Boyle point for a nonideal gas. Under these conditions. 

The measurements of Douslin et al. are particularly valuable because the virial coefficients of the two pure substances Bn and B22 and the interaction virial coefficient B were measured over such a range of temperature that it was possible to make a direct determination of the Boyle-point parameters and F = (rdi5/dr)T=TB. Bn, B22, and B12 were found to follow the same theorem of corresponding states when T and F were used as the reduction parameters, whereas this was not so when the more usual critical parameters, T and F were employed. The experimental values of T and F are given in Table 2 together with the values calculated by assuming the Lorentz-Berthelot combining rules ... 

The reduced temperatures that correspond roughly to the melting, boiling, and critical points are 0.52, 0.87, and 1.29, respectively. At these temperatures the reduced second virial coefficients are —8.1, —3.2, and —1.6. Typical values of bo are similar to molar volumes of liquids, hence for simple substances the second virial coefficient varies between —1000 and — 200cm mol" from the melting point to the critical point. The Boyle point, the temperature at which B = 0, lies at T 3.4, or roughly four times the boiling point. 

Flory s analysis focuses on the thermodynamic interactions between polymers, and defines the theta point at the critical polymer concentration for phase separation (equal to the critical concentration of chain units within a single chain upon collapse transition), similar to the Boyle point of the non-ideal gas. We can perform Virial expansion on the osmotic pressure of dilute polymer solutions, as... 

First, Boyle points out in Sennertian fashion that the reduction of the camphor reveals the inadequacy of the scholastics views on mixture, since most of them claim that mixmre necessitates the loss of the ingredients forms. Since the camphor is regained intact upon a mere affusion of water, it must have been lurking there all along in the form of... 

For many years it had been believed that fire would break down materials into their elements, but Boyle pointed out that the number of products obtained varied with the method by which the fire was applied. Thus, when wood was heated in a retort, it yielded oil, spirit, vinegar, water and charcoal, but when heated in the open, it gave only ashes and soot. 

Theories for dilute solutions have been dealt with by Yamakawa and Lifshitz et They are covered in several reviews of which that by Casassa is specially useful. Finally, in view of the significance of chain conformation in many of these theories Chapter 9 of this volume could be consulted. In this connection the so called theta temperature, T, plays a central role. It is ddined as that temperature for which A = 0 (in the limit M- oo) and is analogous to the Boyle point in gases. ... 

Twelve coefficients for the Martin-Hou equation of state can be computed using analytical relations if the critical parameters, Boyle point temperature. 

See Problem 7.1. The Boyle-point temperature is defined as that temperature at which a = 0 for P = 0. From Figure A.4 estimate the Boyle-point temperature for gases that follow that chart. What is the practical significance of the Boyle point ... 

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