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# 物理代写|热力学代写Thermodynamics代考|EML3007 How Can I Estimate Thermodynamics Properties?

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## 物理代写|热力学代写Thermodynamics代考|How Can I Estimate Thermodynamics Properties?

So far, we have discussed the properties of a perfect gas and a moderately dense gas and their mixtures, but many of the materials encountered in practice do not fall into those categories and yet their properties are often required in an engineering context. It is not practicable to seek to measure all of the properties of all materials that might be encountered in engineering practice over a wide range of conditions. There is, therefore, a very considerable body of literature devoted to the estimation of the properties of such materials that is well beyond the scope of this book. However, many of the better estimation methods, which have often been implemented in computer software for the prediction of properties, e.g. REFPROP (Lemmon et al. 2018), have their origins in statistical mechanical methods based around Equation 2.113. It is such methods we consider briefly here.

## 物理代写|热力学代写Thermodynamics代考|How Can the Principle of Corresponding States Be Used to Estimate Properties?

We first consider the principle of corresponding states because it underpins, in some form, the very many thermodynamic models used in engineering. Here, we will briefly describe its scientific basis for pure fluids and the extension to mixtures is discussed in Chapter 4 on the basis of very clear assumptions that provide a powerful predictive tool.
The principle of corresponding states establishes a connection between the configuration integrals of different substances and thereby allows each of the configurational thermodynamic properties of one fluid to be expressed in terms of those of another fluid. If one fluid can be selected as a reference fluid and the properties of all others related to it then the basis for powerful property prediction approaches can be created. Since configurational and residual thermodynamic properties are related in a very simple way, the same results apply also to the latter.

The theoretical basis of the two-parameter corresponding states principle is the assumption that the intermolecular potentials of two substances may be rendered identical by the suitable choice of two scaling parameters, one applied to the separation and the other to the energy. Thus, the intermolecular potential of a substance that conforms to the principle is taken to be
$$\phi(r)=\varepsilon F(r / \sigma),$$
where $\varepsilon$ and $\sigma$ are, respectively, scaling parameters for energy and distance, and $F$ is a universal function among all relevant materials. Substances that obey Equation $2.129$ are said to be conformal. One of the great strengths of the method is that the function $F$ need not be known. Instead, a reference substance is introduced, identified by the subscript 0, for which the thermodynamic properties of interest are known, and this is used to eliminate $F$ from the problem. The configurational (and hence, residual) properties of another conformal substance, identified by the subscript $i$, are thereby given in terms of those of the reference fluid. We shall also see that the parameters $\varepsilon$ and $\sigma$ may be eliminated in favor of measurable macroscopic quantities.

## 物理代写热力学代写Thermodynamics代考|How Can the Principle of Corresponding States Be Used to Estimate Properties?

$$\phi(r)=\varepsilon F(r / \sigma),$$

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