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

# 物理代写|热力学代写Thermodynamics代考|Can Statistical Mechanics Be Used to Calculate the Properties of Real Fluids?

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|热力学代写Thermodynamics代考|Can Statistical Mechanics Be Used to Calculate the Properties of Real Fluids?

The idealized systems that have been examined in Question $2.4$ are of immense value as limiting cases approached occasionally by real systems. The analysis presented is necessarily simplified in a number of ways compared to that which needs to be applied to real materials. The majority of the differences between real systems and the idealized models we have considered lie in the fact that the non-interacting particles of the idealized system must be replaced by particles that interact. In the case of molecular entities, they interact through intermolecular forces which can affect the total energy of the ensemble of molecules because the total internal energy is not simply the sum of that of individual molecules. It is this difference which is the subject of this question where we illustrate the use of statistical mechanics for the evaluation of the thermodynamic properties of fluids. We are not attempting to be comprehensive in this question, and the reader is referred to specialized texts for greater detail and breadth (e.g. McQuarrie 2000).

## 物理代写|热力学代写Thermodynamics代考|What Is the Canonical Partition Function?

As has been explained previously, the role of statistical mechanics is that of a bridge between the microscopic and macroscopic descriptions of the system. The statistical mechanics of systems at equilibrium, from which the thermodynamic properties may be obtained, is based upon two postulates. The first postulate, concerning the probability distribution of molecules occupying available energy microstates and how this relates to bulk thermodynamic properties, was introduced earlier in Question 2.1, and has enabled us to evaluate some of the properties of some idealized systems. To try to calculate the properties of more complex systems that are less than ideal in some way, in particular where the molecules interact with each other, we need to move away from the single molecular partition function discussed earlier to the canonical partition function, Q. To introduce this concept, we first consider a real system in a thermodynamic state defined by the macroscopic variables of thermodynamics and consisting of $N$ molecules. The individual molecules in this system are in an unknown quantum state, but we know that a very large number of systems must exist in which individual molecules are in different states, but the overall thermodynamic state is the same. The collection of all of these possible systems is consistent with the real system, each of which is a unique quantum state of the system, called the canonical ensemble.

The second postulate of statistical mechanics states that the only dynamic variable upon which the quantum states of the entire canonical ensemble depend is the total ensemble energy. From this postulate, we deduce that all states of the ensemble having the same energy are equally probable. It can then be shown (Sandler 2010; Reed and Gubbins 1973; Hill 1988) that the probability $\Pi_{i}$ that a system selected at random from the ensemble will be found in quantum state $i$ varies exponentially with the energy $E_{i}$ of that state. That is
$$\Pi_{i}\left(E_{i}\right) \propto \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$
Since, however, there is unit probability that the system resides in some state, we have that $\Sigma_{i} \Pi_{i}\left(E_{i}\right)=1$ and
$$\Pi_{i}\left(E_{i}\right)=\frac{\exp \left{-E_{i} /\left(k_{\mathrm{B}} T\right)\right}}{Q},$$
where
$$Q(N, V, T)=\sum_{i} \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$

## 物理代写|热力学代写Thermodynamics代考|What Is the Canonical Partition Function?

$$\Pi_{i}\left(E_{i}\right) \propto \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$

\left 的分隔符缺失或无法识别

$$Q(N, V, T)=\sum_{i} \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right)$$

## 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。