Posted on Categories:Thermodynamics, 热力学, 物理代写

# 物理代写|热力学代写Thermodynamics代考|ENGRD2210 What Is Exergy Good For?

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## 物理代写|热力学代写Thermodynamics代考|What Is Exergy Good For?

While the Carnot efficiency in Equation $3.15$ poses a fundamental upper limit for the thermal efficiency of a heat engine, practical machines of course exhibit lower efficiencies, and it is the art of the engineer to come as close to the ideal limit as possible with appropriate regard to economic constraints. The resulting actual efficiency is a product of two factors, namely the efficiency determined by the Second Law and, of necessity, a factor that represents the departures of the real machine from perfection. To balance better the actual technical achievement against what is possible in principle and to identify sources within a process where useful energy is destroyed or wasted, it has turned out to be beneficial to introduce a specific term for the useful energy. According to a suggestion of Rant (1956), this property is called exergy $E$. The term exergy does not introduce anything physically new that is different from the Second Law, yet it has proven to be a useful concept for technical purposes.
Thus, exergy is defined as that part of energy that – relative to a given reference state-can, without any restriction, be transformed into any other form of energy. Because the work that can be extracted from a process is the form of energy that is of primary interest, an alternative formulation of the definition is as follows: exergy is that part of energy that – relative to a given reference state – can, without any restriction, be transformed into useful work.
It is important to note that the definition relies on the specification of a reference state, and this is always taken to be the environment when we consider exergy. For example, a cold reservoir with temperature below ambient contains exergy or useful work. However, when a system is brought to the pressure and temperature of the environment, no potential exists for the extraction of useful work. Thus, the environmental state is a dead state and in this context its temperature is designated as $T_0$. An instructive and more detailed discussion of the term’s immediate surroundings and environment is given by Çengel and Boles (2006).
To be complete, the other part of the energy, namely the one that in principle cannot be transformed into useful work, should also have a name: It is termed anergy B. Thus: energy $=$ exergy $E+\operatorname{anergy} B$.

## 物理代写|热力学代写Thermodynamics代考|What Is the Minimum Work Required to Separate Air into Its Constituents?

To tackle the problem, it might seem straightforward to look for one or more processes that promise to separate air – or more generally a mixture of gases – and then seek to find the optimal conditions for each process under which they require the minimum amount of work. In general, it may be difficult to find any such process, and one can never be sure that the result obtained is actually the optimal choice; it may merely be the best from those selected. Thus, it is best to consider the problem from the other end: What is the amount of useful energy that is destroyed by the mixing of gases, or what is the exergy loss $E_{\text {loss }}$ in such a process (See Question 3.8).
To simplify the analysis without losing the major thrust of the argument we consider air in the first instance as a mixture of only nitrogen and oxygen $\left(y_{\mathrm{N}2}=0.79, y{\mathrm{O}_2}=0.21\right)$ and expand the problem to a more general case later. We further restrict the problem to treating dry air and neglect the varying humidity. When nitrogen and oxygen are mixed at standard conditions $\left(T=298.15 \mathrm{~K}, p=10^5 \mathrm{~Pa}\right.$ ), these constituents may be treated as ideal gases. Thus, there is no enthalpy of mixing (nor a change in internal energy), and the mixing at constant pressure and temperature occurs in an adiabatic manner. If we imagine that the two gases are held separately in a single rigid vessel and that we then remove the partition (as shown in Figure 3.6), the system undergoes a diffusion process toward a new equilibrium. This diffusion process is irreversible and accompanied by a rise of entropy (see Equation 2.57)
$$\Delta S_{\text {gen }}=-n R \sum_i y_i \ln y_{i^{\prime}}$$
where $n$ is the total amount of substance and $y$ represents the mole fractions of species in the gas phase. The amount of useful energy destroyed by such a process, or in other words the exergy loss, may be generally described by $E_{\text {loss }}=T_0 \Delta S_{\text {gen, where }} T_0$ is the temperature of the surroundings to give
$$E_{\text {loss }}=-n T_0 R \sum_i y_i \ln y_i .$$

## 物理代写|热力学代写热力学代考|将空气分离成其组分所需的最小功是多少?

$$\Delta S{\text {gen }}=-n R \sum_i y_i \ln y_{i^{\prime}}$$
，其中$n$是物质的总量，$y$表示气相中物种的摩尔分数。这样一个过程所破坏的有用能量的量，或者换句话说火用损失，一般可以用$E_{\text {loss }}=T_0 \Delta S_{\text {gen, where }} T_0$来描述，即周围的温度给
$$E_{\text {loss }}=-n T_0 R \sum_i y_i \ln y_i .$$

## 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。