Inversion temperature zero-pressure limit

From either of these last two expressions it is evident that p.j,x. = 0 for an ideal gas, because each partial derivative is zero for such a substance. It is interesting that p,j X. does not equal 0 for a real gas at zero pressure except at the inversion temperatures (see below). This result suggests that our assumption that a real gas approaches the properties of an ideal gas at the limit of zero pressure is not entirely correct. 

We conclude that the Joule-Thomson coefficient is a function of both the temperature and the pressure, but, unlike the Joule coefficient, it does not go to zero as the pressure goes to zero. The inversion temperature, the temperature at which fi,T = 0, is also a function of the pressure. The value usually reported in the literature is the limiting value as the pressure goes to zero. 

For any gas, the sign of the Joule-Thomson effect depends on tanperature and pressure. The positive effect for each gas is observed only in the limited interval of temperatures and pressures. For each gas there are values of temperature and pressure at which the Joule-Thomson effect is equal to zero (no temperature changes occur at gas expansion in vacuum). These points (T, p,) are called points of inversion. At these points, the influence of forces of attraction is completely compensated for by the influence of repulsion forces consequently the gas temperature does not change. The set of inversion points forms an inversion curve in a p-T diagram. 

It can be seen from Equation (5.1) that the volume of steam required for deodorization is directly proportional to the system pressure and inversely proportional to the vapour pressure of the free fatty acid. Thus, a reduction in the former and an increase in the latter, brought about by increasing temperature, result in a reduction of time on temperature for a set steaming rate. This is correct for the simple reduction of fatty acid levels. However, oils vary in their content of pigments and oxidation products. Practical experience has shown that, whereas these products can be removed in the time required to reduce free fatty acid to the desired level from a good-quality feed oil, this is not so with oxidized oils. For such oils, an extended time at the selected temperature is required to allow thermal reactions to take place in which some of the oxidation products are further decomposed and the derivatives removed from the oil (Andersen, 1962 Brekke, 1980). If such oxidation products are not removed, the deodorized product will have a poorer taste and reduced oxidative stability. The limitations of this aspect of the deodorization process can be noted in the fact that to date the anisidine value, which is a measure of secondary oxidation products in the oil, is not reduced to zero. Commercial plants are currently designed for holding time on temperature of 30-120 min, but all are capable of extension. 

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