Riemann surface
matlab
无需担心！我们的统计力学代写专家团队将专业地解决您在统计力学学习中遇到的各种挑战。我们拥有广泛的专业知识和丰富的经验，可以协助您完成高水平的作业和论文，确保您在学习道路上顺利前行！
以下是一些我们可以帮助您解决的问题：
统计力学基础概念：涵盖微观态密度、分布函数、配分函数等各种常用统计力学概念的定义、性质和分类。
统计力学模型：研究和应用于统计力学中的各类模型，如经典统计力学模型、量子统计力学模型等。
热力学与平衡态：常见的热力学定律和平衡态性质的推导与应用，如热力学势函数、热力学过程等。
非平衡态统计力学：研究非平衡态下的统计力学理论和方法，如输运过程、涨落等。
统计力学与量子力学：介绍统计力学在量子系统中的应用，如玻尔兹曼方程、玻色-爱因斯坦凝聚等。
相变与临界现象：研究相变和临界现象的统计力学描述和理论，如相变点、临界指数等。
统计力学在材料科学中的应用：介绍统计力学在材料科学中的应用，如相图计算、材料模拟等。
无论您面临的统计力学问题是什么，我们都会竭尽全力提供专业的帮助，确保您的学习之旅顺利无阻！
Describe briefly three different instruments that can be used for the accurate measurement of temperature and state roughly the temperature range in which they are useful and one important advantage of each instrument. Include at least one instrument that is capable of measuring temperatures down to $1 \mathrm{~K}$.
(Wisconsin)
.
Solution:
Magnetic thermometer: Its principle is Curie’s law $\chi=C / T$, where $\chi$ is the susceptibility of the paramagnetic substance used, $T$ is its absolute temperature and $C$ is a constant. Its advantage is that it can measure temperatures below $1 \mathrm{~K}$.
Optical pyrometer: It is based on the principle that we can find the temperature of a hot body by measuring the energy radiated from it, using the formula of radiation. While taking measurements, it does not come into direct contact with the measured body. Therefore, it is usually used to measure the temperatures of celestial bodies.
Vapor pressure thermometer: It is a kind of thermometer used to measure low temperatures. Its principle is as follows. There exists a definite relation between the saturation vapor pressure of a chemically pure material and its boiling point. If this relation is known, we can determine temperature by measuring vapor pressure. It can measure temperatures greater than $14 \mathrm{~K}$, and is the thermometer usually used to measure low temperatures.
A solid object has a density $\rho$, mass $M$, and coefficient of linear expansion $\alpha$. Show that at pressure $p$ the heat capacities $C_p$ and $C_v$ are related by
$$
C_p-C_v=3 \alpha M p / \rho
$$
Solution:
From the first law of thermodynamics $d Q=d U+p d V$ and $\left(\frac{d U}{d T}\right)p \approx$ $\left(\frac{d U}{d T}\right)_v$ (for solid), we obtain $$ C_p-C_v=\left(\frac{d Q}{d T}\right)_p-\left(\frac{d U}{d T}\right)_v=p \frac{d V}{d T} . $$ From the definition of coefficient of linear expansion $\alpha=\alpha{\mathrm{solid}} / 3=\frac{1}{3 V} \frac{d V}{d T}$, we obtain
$$
\frac{d V}{d T}=3 \alpha V=3 \alpha \frac{M}{\rho} .
$$
Substituting this in (*), we find
$$
C_p-C_v=3 \alpha \frac{M}{\rho} p
$$
E-mail: help-assignment@gmail.com 微信:shuxuejun
help-assignment™是一个服务全球中国留学生的专业代写公司
专注提供稳定可靠的北美、澳洲、英国代写服务
专注于数学，统计，金融，经济，计算机科学，物理的作业代写服务