# 物理代写|统计物理代写Statistical Physics of Matter代考|FY828

#### Doug I. Jones

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couryes-lab™ 为您的留学生涯保驾护航 在代写统计物理Statistical Physics of Matter方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计物理Statistical Physics of Matter代写方面经验极为丰富，各种代写统计物理Statistical Physics of Matter相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 物理代写|统计物理代写Statistical Physics of Matter代考|Fluids of Non-interacting Particles

When $\Phi\left{\boldsymbol{r}{i}\right}=0$, the configuration partition function (4.6) reduces to $$Q{N}=q_{1}^{N},$$
where
$$q_{1}=\frac{1}{V} \int d \boldsymbol{r} e^{-\beta u(r)},$$
so (4.14) becomes
$$n(\boldsymbol{r})=n e^{-\beta u(\boldsymbol{r})} .$$
The non-uniform fluid density follows the Boltzmann distribution. For a gas under uniform gravity directed downward along the $z$ axis, $u(z)=m g z$, we get
$$n(z)=n e^{-\beta m g z}=n e^{-z / z^{}},$$ which is none other than the barometric formula. It means that thermal agitation allows the gas to overcome gravitational sedimentation. It is because the characteristic altitude $z^{}=k_{B} T /(m g)$ of the density decay increases with $T$ and decreases with m. At $T=300 \mathrm{~K}, z^{}$ of $\mathrm{O}{2}\left(m=32 \mathrm{~g} / \mathrm{mol}=5.32 \times 10^{-26} \mathrm{~kg} / \mathrm{molecule}\right)$ is $7.95 \mathrm{~km}$ and the $z^{}$ of $\mathrm{H}{2}\left(m=2 \mathrm{~g} / \mathrm{mol}=3.32 \times 10^{-27} \mathrm{~kg} /\right.$ molecule $)$ is $127 \mathrm{~km}$; this inverse relationship between $z^{*}$ and $m$ means that at high altitude light gases are more abundant than heavy gases. This prediction is not strictly valid because $T$ and $g$ vary with altitude. Also we note that the barometric formula can be applied to sedimentation of colloidal particles suspended in a solvent provided that the mass is modified in such a way to incorporate the buoyancy and hydration.

For thermodynamic properties, the partition function (4.4) is calculated easily using (4.9) and (4.25):
$$Z_{N}=\frac{1}{N !}\left(\frac{V}{\lambda^{3}}\right)^{N} q_{1}^{N} .$$

## 物理代写|统计物理代写Statistical Physics of Matter代考|A gas of Polyatomic Molecules-the Internal Degrees

A polyatomic molecule consists of two or more nuclei and many electrons. In addition to the translational degrees of freedom of the center of the mass, the molecule has the internal degrees of freedom, arising from rotational, vibrational molecular motions, and electronic, other subatomic motions. At room temperature, $T \approx 300 \mathrm{~K}$, two rotational degrees of freedom in diatomic molecule can fully be excited, and therefore contribute $k_{B}$ to heat capacity per molecule. The partition function of an ideal gas of polyatomic molecules, including the internal degrees of the freedom, may be written as
$$Z_{N}=\frac{1}{N !}\left(\frac{V q_{1}}{\lambda^{3} z_{i}}(T)\right)^{N}$$
where $z_{i}(T)$ is the partition function from the internal degrees of the freedom per molecule. In the absence of an external potential, the chemical potential is
\begin{aligned} \mu &=\frac{\partial F}{\partial N}=k_{B} T \ln \left[n \hat{\lambda}^{3} / z_{i}(T)\right] \ &=k_{B} T \ln \left(n \hat{\lambda}^{3}\right)+f_{i}(T) \end{aligned}
where $f_{i}=-k_{B} T \ln \left(z_{i}(T)\right)$ is the free energy from the internal degrees of freedom in a single molecule.
In general, chemical potential can be written as
$$\mu=\mu_{0}(T)+k_{B} T \ln \left{n / n_{0}(T)\right}$$
Here the subscript 0 denotes a standard or reference state at which the density and chemical potential are $n_{0}(T)$ and $\mu_{0}(T)$ respectively. At the standard state, the $2^{\text {nd }}$ term (concentration-dependent entropy) in (4.47) vanishes, so $\mu_{0}(T)$ is the intrinsic free energy of a single polyatomic molecule that includes such an extreme as a long chain polymer. For solutes, the standard density $n_{0}(T)$ is usually taken to be 1 mol concentration $(\mathrm{M})$, which is an Avogadro number $\left(N_{a}\right)$ per $1 \mathrm{~L}$ (liter).

# 统计物理代考

## 物理代写|统计物理代写Statistical Physics of Matter代考|Fluids of Non-interacting Particles

$$Q N=q_{1}^{N}$$

$$q_{1}=\frac{1}{V} \int d r e^{-\beta u(r)}$$

$$n(\boldsymbol{r})=n e^{-\beta u(\boldsymbol{r})} .$$

$$n(z)=n e^{-\beta m g z}=n e^{-z / z},$$

$\mathrm{O} 2\left(m=32 \mathrm{~g} / \mathrm{mol}=5.32 \times 10^{-26} \mathrm{~kg} /\right.$ molecule $)$ 是 $7.95 \mathrm{~km}$ 和 $z$ 的
$\mathrm{H} 2\left(m=2 \mathrm{~g} / \mathrm{mol}=3.32 \times 10^{-27} \mathrm{~kg} /\right.$ 分子 $)$ 是 $127 \mathrm{~km}$; 之间的这种反比关系 $z^{*}$ 和
$m$ 意味着在高海拔地区，轻气体比重气体更丰富。这个预测并不严格有效，因为 $T$ 和 $g$ 随海 拔而妾化。我们还注意到气压公式可以应用于县浮在溶剂中的胶体颗粒的沉降，前提是质 量被改变以结合浮力和水合作用。

$$Z_{N}=\frac{1}{N !}\left(\frac{V}{\lambda^{3}}\right)^{N} q_{1}^{N}$$

## 物理代写|统计物理代写Statistical Physics of Matter代考|A gas of Polyatomic Molecules-the Internal Degrees

$$Z_{N}=\frac{1}{N !}\left(\frac{V q_{1}}{\lambda^{3} z_{i}}(T)\right)^{N}$$

$$\mu=\frac{\partial F}{\partial N}=k_{B} T \ln \left[n \hat{\lambda}^{3} / z_{i}(T)\right] \quad=k_{B} T \ln \left(n \hat{\lambda}^{3}\right)+f_{i}(T)$$

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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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