Temperature, Boyle critical

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... 

C A true rectangular hyperbola representing Boyle s law. The pressure doubles as the volume halves. As it is above the critical temperature, it is a gas and obeys the gas laws. 

To calculate the heat of evaporation of liquid radon to estimate the density of liquid radon, its critical volume, and the Boyle temperature. 

Typical dependence of Z on p/p, where p is the critical pressure, is illustrated in Figure 1 for a series of temperatmes such that T >T T. The temperatme T- is just above the critical temperature. The temperature T, at which the density dependence of Z is zero as plp — zero is termed the Boyle temperatme. For gases which are neither quantum fluids nor strongly polm, this temperatme is about 2.7 times the critical temperature for monatomic substances, decreasing to around 2.3 for polyatomic fluids. 

The temperature at which B changes sign is called the Boyle temperature Tg it occurs at roughly two-thirds of the critical temperature, Tg/T 2/3. The Boyle temperature is used in Figure 4.10 to make the plotted temperature dimensionless. To make B and C dimensionless, we use the Boyle volume which is defined by [20]... 

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. 

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

NAb = 0/2)bvdW We may work out the relation between critical and Boyle temperature,... 

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