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## 物理代写|热力学代写thermodynamics代考|COMPRESSIBILITY FACTOR AND GENERALIZED

The equations of state for the real gases, in general, are quite difficult to use. For most of the engineering problems, the compressibility chart provides a simple means to account for the dense gas effects. For an ideal gas $\frac{p \tilde{v}}{R_0 T}=1$ and for a dense gas, we write
$$\frac{p \tilde{v}}{R_0 T}=Z$$
where $Z$ is no longer equal to unity. $Z$ is called the compressibility factor and varies with the state variables, that is, $Z(p, T)$. Different gases at the same $p$ and $T$ give different values of $Z$. However, if $p$ and $T$ are normalized with respect to the values at the critical state, that is, reduced temperature $T_R=\frac{T}{T_C}$ and reduced pressure $p_R=\frac{p}{p_C}$, then $Z\left(T_R, p_R\right)$ is a universal function valid for all gases. This is known as the theorem of corresponding states. The theorem states that “Any pure gas at the same reduced pressure and temperature should have the same compressibility factor”.
$Z$ is plotted against $p_R$ for various constant values of $T_R$ and is shown in Figure 2.2. The figure replaces the equation of state and we can find the $p, v$ and $T$ data from it for any gas.

The general procedure is to first calculate for the given $p$ and $T$, the reduced pressure and temperature by normalizing with the critical pressure and temperature. The value of $Z$ is obtained from the compressibility chart (Figure 2.2) and thereafter the value of the reduced molar volume $\tilde{v}_R$ is calculated. If, however, $\tilde{v}_R$ is given, then a value of $\tilde{v}_R=\tilde{v}_R Z$, known as a pseudo reduced molar volume is used and plotted in the generalized chart instead of the reduced volume $\tilde{v}R$ as it is more convenient. With $\tilde{v}_R$ and $p_R\left(\right.$ or $T_R$ ), we can find the other missing state variable directly from the generalized compressibility charts in which constant $\tilde{v}{R^{\prime}}$ lines are plotted.

## 物理代写|热力学代写thermodynamics代考|MIXTURE OF IDEAL GASES

For a mixture of several constituents or components of gases in a volume $V$ at a given temperature $T$, the pressure that each constituent of gas would exert, if it were alone contained in the volume $V$, is its partial pressure. Let the partial pressure of the $i$ th constituent in the mixture of gases be denoted by $p_i$, while the pressure of the mixture of gases is $p$. When each of the constituent gases in the mixture and the mixture of gases are ideal gases, then from the equation of state for an ideal gas $p V=n R_0 T$, we get
$$\sum_{i=1}^N p_i=p$$
since the sum of the number of moles of each of the constituent gas is the total number of moles in the mixture. Equation $2.30$ is Dalton’s law of partial pressures for an ideal gas mixture.

$$\sum_{i=1}^N V_i=V$$
Dalton’s law of partial pressure at constant volume and temperature and Amagat’s law of partial volume at constant pressure and temperature are valid only when each of the constituent gases in the mixture and the mixture of gases are ideal gases.

# 热力学代写

## 物理代写|热力学代写thermodynamics代考|COMPRESSIBILITY FACTOR AND GENERALIZED

$$\frac{p \tilde{v}}{R_0 T}=Z$$

$Z$ 是针对 $p_R$ 对于各种常数值 $T_R$ 如图 2.2 所示。该图代替了状态方程，我们可以找到 $p, v$ 和 $T$ 任何气体的数据。

## 物理代写|热力学代写thermodynamics代考|MIXTURE OF IDEAL GASES

$$\sum_{i=1}^N p_i=p$$

$$\sum_{i=1}^N V_i=V$$

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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。