范德华状态方程

麦克斯韦方程组是一组由四个耦合偏微分方程组成的方程组，构成了经典电磁学的基础。它们描述了电场和磁场如何相互产生，以及它们如何被电荷和电流改变。它们是高斯​​定律、高斯磁定律、法拉第电磁感应定律和安培-麦克斯韦定律。

The Boltzmann distribution describes the probability that a system in thermal equilibrium at temperature T will be in a specific microstate with energy E. This probability is proportional to the Boltzmann factor, [latex]e^{-E / k_B T}[/latex]. It implies that states with lower energy are exponentially more likely to be occupied than states with higher energy, with temperature modulating this preference.

电动势 (EMF) 和电势差（电压）是两个不同的概念，尽管它们的单位都是伏特。电动势是指非保守力（例如化学反应、变化磁场）在源内移动电荷时对单位电荷所做的功。电势差是指两点之间保守静电场对单位电荷所做的功。

This foundational formula connects the macroscopic thermodynamic quantity of entropy (S) with the number of possible microscopic arrangements, or microstates (W), corresponding to the system's macroscopic state. The equation, [latex]S = k_B \ln W[/latex], reveals that entropy is a measure of statistical disorder or randomness. The constant [latex]k_B[/latex] is the Boltzmann constant, linking energy at the particle level with temperature.

升华，即从固态到气态的直接相变，发生在低于物质三相点的温度和压力下。三相点是一种独特的热力学状态，其中固相、液相和气相可以平衡共存。在相图上，升华曲线将固相和气相分开，始于原点，止于三相点。

Mohr's circle is a two-dimensional graphical representation of the Cauchy stress tensor. It visualizes the transformation of normal stress ([latex]\sigma_n[/latex]) and shear stress ([latex]\tau_n[/latex]) on an arbitrarily oriented plane at a point. The abscissa of each point on the circle is the normal stress, and the ordinate is the shear stress, allowing for easy determination of principal stresses.

One of the four Maxwell's equations, Gauss's law for magnetism states that the net magnetic flux out of any closed surface is zero. This is expressed mathematically as [latex]\oint_S \vec{B} \cdot d\vec{A} = 0[/latex]. This law is a statement of the experimental observation that magnetic monopoles (isolated north or south poles) have never been detected. Magnetic field lines always form closed loops.

Electromagnetic waves are disturbances of the electromagnetic field that propagate through space, carrying energy. They are created by accelerating electric charges and consist of synchronized, perpendicular oscillations of electric and magnetic fields. In a vacuum, they travel at the speed of light, [latex]c[/latex]. The electromagnetic spectrum encompasses radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

临界温度是指无论施加何种压力，高于该温度都无法形成明显液相的温度。每种气体都有其独特的临界温度。要使气体液化，必须先将其冷却至该温度以下。这一概念由托马斯·安德鲁斯提出，对于理解任何液化过程所需的条件至关重要。

瑞利散射是指光被远小于光波长的粒子弹性散射的现象。这种现象是白天天空呈现蓝色的原因。与波长较长的红色光相比，波长较短的蓝色阳光更容易被大气中的氮和氧分子散射，从而使天空在观察者看来呈现蓝色。

理想奥托循环是火花点火发动机的热力学模型。它由四个内部可逆过程组成：等熵压缩（1-2）、等容（等容）吸热（2-3）、等熵膨胀（3-4）和等容（等容）放热（4-1）。该循环是分析汽油发动机性能的理论基础，其工作流体假设为理想气体。

这种气体液化工艺由 Raoul Pictet 首创，利用一系列沸点逐渐降低的其他气体来液化一种气体。第一种气体在常温下加压液化。然后，其蒸发部分用于冷却和液化第二种挥发性更强的气体，后者又用于冷却和液化目标气体，从而形成一系列“级联”冷却过程。

爆轰速度（VoD）是指冲击波阵面在爆炸物中传播的速度。它是衡量炸药性能和威力的主要指标，也是区分高能炸药和低能炸药的关键因素。爆轰速度是一种受密度、粒径和密闭性影响的特性，高能炸药的典型爆轰速度可达数千米每秒。

For a general three-dimensional state of stress, the analysis is represented by three Mohr's circles. These circles are drawn in the [latex]\sigma_n - \tau_n[/latex] plane using the three principal stresses ([latex]\sigma_1, \sigma_2, \sigma_3[/latex]) as diameters. The largest circle, defined by [latex]\sigma_1[/latex] and [latex]\sigma_3[/latex], encloses the other two and determines the absolute maximum shear stress, [latex]\tau_{abs max} = (\sigma_1 - \sigma_3)/2[/latex].