# 数学代写|信息论代写information theory代考|CSCIT2023

#### Doug I. Jones

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## 数学代写|信息论代写information theory代考|Solid-Gas Transition

The line SG in Fig. 2.9 is the line along in which solid and gas coexist. The slope of this curve is given by:
$$\left(\frac{d P}{d T}\right)_{e q}=\frac{\Delta S_s}{\Delta V_s}$$
In the process of sublimation ( $s$, the entropy-change and the volume change for both are always positive. We denoted by $\Delta V_s$ the change in the volume of one mole of the substance, when it is transferred from the solid to the gaseous phase. This volume change is always positive. The reason is that a mole of the substance occupies a much larger volume in the gaseous phase than in the liquid phase (at the same temperature and pressure).

The entropy-change $\Delta S_s$ is also positive. This entropy-change is traditionally interpreted in terms of transition from an ordered phase (solid) to a disordered (gaseous) phase. However, the more correct interpretation is that the entropy-change is due to two factors; the huge increase in the accessible volume available to each particle and the decrease in the extent of the intermolecular interaction. Note that the slope of the SG curve is quite small (but positive) due to the large $\Delta V_s$.

## 数学代写|信息论代写information theory代考|Liquid-Gas Transition

The line LG in Fig. 2.9 is the line along which liquid and gaseous phases coexist. In this case the slope of the curve is also positive. Both the entropy and the volume change in the vaporization processes are positive. Again, traditionally the entropy of vaporization is interpreted in terms of order-disorder. This interpretation is unfortunately incorrect. It is difficult to argue that gas is more disordered than liquid. The correct interpretation is again the change in the accessible volume per particle, and the weakening of the average intermolecular interactions in the process of the evaporation, hence $\Delta S_v>0$.

It is worthwhile to mention an empirical law known as the Trouton Law. It states that the entropy of vaporization at one atmospheric pressure of many liquids is almost constant;
$$\Delta S_v \approx 85-87 / \mathrm{Jmol}^{-1} K^{-1}$$
Table 2.1 shows a few values of the entropy of vaporization. Note that the values of $\Delta S_v$ for liquids with strong interactions, such as water, ethanol, and methanol, are much larger than the values for the other liquids.

As one can see from this Table 2.1, the Trouton Law is not really a law. Table 2.1 shows that in many cases the transition from the liquid to the gaseous phase the dominant factor that determines the change in entropy is the change in the accessible volume. However, when there exist very strong intermolecular interactions, the entropy of vaporization $\Delta S_v$ becomes very large due to the weakening of the average interactions among the particles in the process of vaporization. As can be seen in Table 2.1 the values of $\Delta S_v$ are much larger for liquids with stronger interactions (hydrogen bonds, see Sect. 2.5 below).

# 信息论代写

## 数学代写|信息论代写information theory代考|Solid-Gas Transition

$$\left(\frac{d P}{d T}\right)_{e q}=\frac{\Delta S_s}{\Delta V_s}$$

## 数学代写|信息论代写information theory代考|Liquid-Gas Transition

2.9中的LG线是液相和气相共存的线。这种情况下，曲线的斜率也是正的。蒸发过程中的熵和体积变化都是正的。传统上，蒸发熵是用有序无序来解释的。不幸的是，这种解释是不正确的。很难说气体比液体更无序。正确的解释是每个粒子可达体积的变化，以及蒸发过程中平均分子间相互作用的减弱，因此$\Delta S_v>0$。

$$\Delta S_v \approx 85-87 / \mathrm{Jmol}^{-1} K^{-1}$$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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