Constant critical

Values of the critical temperature and pressure will be needed for prediction methods that correlate physical properties with the reduced conditions. Experimental values for many substances can be found in various handbooks and in Appendix D. Critical reviews of the literature on critical constants, and summaries of selected values, have been published by Kudchadker et al. (1968), for organic compounds, and by Mathews (1972), for inorganic compounds. An earlier review was published by Kobe and Lynn (1953). 

If reliable experimental values cannot be found, techniques are available for estimating the critical constants with sufficient accuracy for most design purposes. For organic compounds Lydersen s method is normally used, Lydersen (1955)  

Fedons (1982) gives a simple method for the estimation of critical temperature, that does not require a knowledge of the boiling point of the compound. 

Estimate the critical constants for diphenylmethane using Lydersen s method normal boiling point 537.5 K, molecular mass 168.2, structural formula  

Dashes represent bonds with atoms other than hydrogen. 

Values marked with an asterisk are based on too few experimental points to be reliable. 

The isotherm (plot of pressure versus volume) at the temperature Tc plays a special role in the theory of the states of matter. An isotherm behaves in accordance with the gas laws slightly below T. At certain pressure, a liquid condenses from gaseous state and is distinguishable from it by the presence of a visible interface. If, however, the compression takes place at a surface separating two phases does not appear and the volumes at each end of the horizontal part of the isotherm have merged to a single point, critical point of the gas. The temperature, pressure, and molar volume at the critical point are called the critical temperature T, critical pressure P, and critical molar volume of the substance respectively. Collectively, 

At and above T, the sample has a single phase that occupies the entire volume of the container. Thermodynamically such a phase is, by definition, a gas. However, the unusual physical properties of a substance close to its critical point warrant special terminology. The single phase that fills the entire volume ztT may be much denser 

---

The critical constants are obtained by applying Lydersen s method (1955) ... 

These properties are calcuiated directly from the critical constants. 

Pseudo Critical Constants and Acentric Factors for Petroleum Fractions... 

Using the principle of corresponding states requires knowledge of pseudo-critical constants of petroleum fractions these should be estimated starting from characteristic properties which are the normal boiling temperature and the standard specific gravity. 

This concept can be extended to mixtures if the pseudo-critical constants of the mixture and a mixture reduction group are defined. This gives the... 

For our needs, the saturation pressure of a mixture will be defined as the vapor pressure of a pure component that has the same critical constants as the mixture ( JT... 

The coefficient can also be estimated starting with the critical constants by the following formula ... 

When the critical constants for a pure substance or the pseudocritical constants for a petroleum fraction are known, the vapor pressure for hydrocarbons and petroleum fractions can be calculated using the Lee and Kesler equations ... 

Unlike the pressure where p = 0 has physical meaning, the zero of free energy is arbitrary, so, instead of the ideal gas volume, we can use as a reference the molar volume of the real fluid at its critical point. A reduced Helmlioltz free energy in tenns of the reduced variables and F can be obtained by replacing a and b by their values m tenns of the critical constants... 

Although the previous paragraphs hint at the serious failure of the van der Waals equation to fit the shape of the coexistence curve or the heat capacity, failures to be discussed explicitly in later sections, it is important to recognize that many of tlie other predictions of analytic theories are reasonably accurate. For example, analytic equations of state, even ones as approximate as that of van der Waals, yield reasonable values (or at least ball park estmiates ) of the critical constants p, T, and V. Moreover, in two-component systems... 

H. Mandel and N. Ewbank, Critical Constants of Diphenyl and Eerphenyl, Report No. NAA-SR-5129, Atomics International, Canoga Parks, Calif., Dec. 1960, p. 18. 

Parachor is the name (199) of a temperature-independent parameter to be used in calculating physical properties. Parachor is a function of Hquid density, vapor density, and surface tension, and can be estimated from stmctural information. Critical constants for about 100 organic substances have been correlated to a set of equations involving parachors and molar refraction (200). 

In the cycle calculations de.scribed below [2], film cooling was as.sumed. Further, as described in Appendix A, various a.s.sumptions were made for the critical constants, as follows. The constant C in Eq. (5.13) was taken as 0.045, and within W, the cooling efficiency tJcooi as 0.7 and the film cooling effectiveness ep as 0.4. All were assumed to be constant over the range of cooling flows considered. 

Calculation of Critical Constants from van der Waals Equation. 

Thus, from an investigation of the compressibility of a gas we can deduce the values of its critical constants. We observe that, according to van der Waals theory, liquid and gas are really two distant states on the same isotherm, and having therefore the same characteristic equation. Another theory supposes that each state has its own characteristic equation, with definite constants, which however vary with the temperature, so that both equations continuously coalesce at the critical point. The correlation of the liquid and gaseous states effected by van der Waals theory is, however, rightly regarded as one of the greatest achievements of molecular theory. 

Chueh s method gives consistently good results for mixtures except in the immediate vicinity of the critical region (T/TCml > 0.93). For the critical region, his procedure was modified by using true critical constants, rather than pseudocritical constants in Eq. (56). For this purpose, he has established a separate correlation of true critical volumes and temperatures (C3). 

---