雷诺平均纳维-斯托克斯 (RANS) 方程

The Nernst equation relates the reduction potential of a half-cell (or the total voltage of an electrochemical cell) to the standard electrode potential, temperature, and the activities (often approximated by concentrations) of the chemical species undergoing redox. The equation is [latex]E = E^{\circ} - \frac{RT}{nF} \ln Q[/latex], where Q is the reaction quotient.

In electrochemical cells like batteries and fuel cells, EMF is generated by chemical reactions. The separation of charge is driven by oxidation and reduction reactions occurring at two different electrodes. The maximum EMF of a cell is related to the change in Gibbs free energy ([latex]\Delta G[/latex]) of the reaction by [latex]\mathcal{E} = -\frac{\Delta G}{nF}[/latex], where [latex]n[/latex] is moles of electrons and [latex]F[/latex] is the Faraday constant.

Chemiluminescence, or chemoluminescence,  is the emission of light (luminescence) as a result of a chemical reaction. An excited state intermediate, denoted as [Product]* (note the asterisk frequently used for that), is formed. This intermediate then decays to a lower energy ground state, releasing energy in the form of a photon. The overall process can be represented as [latex]A + B \rightarrow [Product]* \rightarrow Product + light[/latex].

The Curie temperature ([latex]T_c[/latex]), or Curie point, is the critical temperature above which certain materials lose their permanent magnetic properties. For ferromagnetic materials, they become paramagnetic above [latex]T_c[/latex]. This transition is a phase transition where thermal energy becomes strong enough to overcome the quantum mechanical exchange interactions that cause spontaneous magnetic ordering of atomic moments.

塞曼效应是指在施加外部静磁场时，原子谱线分裂成多个分量的现象。这种分裂的发生是因为磁场与原子轨道和自旋角动量相关的磁偶极矩相互作用，从而改变了电子的能级，这一现象对于探测原子结构至关重要。

In a system at thermodynamic equilibrium, the electrochemical potential, [latex]\bar{\mu}_i[/latex], for any given charged species `i` must be uniform throughout all phases. If a gradient exists ([latex]\nabla \bar{\mu}_i \neq 0[/latex]), ions will spontaneously move from regions of higher potential to lower potential, creating a current or flux, until this gradient is eliminated and equilibrium is re-established.

交流感应电动机的工作原理是定子产生旋转磁场。该磁场是通过向空间分布的定子绕组提供多相交流电流产生的。旋转磁场在转子导体（例如鼠笼式）中感应出电流，从而产生反向磁场。这些磁场之间的相互作用产生了旋转扭矩。

The Nernst equation quantifies the reversible electromotive force (EMF) or open-circuit voltage of a fuel cell under non-standard conditions. It links the cell potential ([latex]E[/latex]) to its standard potential ([latex]E^0[/latex]), temperature, and the activities (approximated by partial pressures) of reactants and products. The equation is [latex]E = E^0 - \frac{RT}{nF} \ln Q[/latex], where Q is the reaction quotient.

Motional EMF is generated when a conductor moves through a magnetic field. The magnetic component of the Lorentz force, [latex]\mathbf{F} = q(\mathbf{v} \times \mathbf{B})[/latex], acts on the charge carriers within the conductor, causing them to move and create a charge separation. This separation establishes an electric field and a potential difference. The resulting EMF is given by the line integral [latex]\mathcal{E} = \oint (\mathbf{v} \times \mathbf{B}) \cdot d\mathbf{l}[/latex].

The distribution ratio (D) is a key equilibrium parameter in Liquid-Liquid Extraction (LLE), defined as the total analytical concentration of a solute in the organic phase divided by its total concentration in the aqueous phase. [latex]D = \frac{[S]_{org,total}}{[S]_{aq,total}}[/latex]. Unlike the partition coefficient (K_D), D accounts for all species of the solute, including dissociated or complexed forms, making it pH-dependent.

汉普森-林德循环利用焦耳-汤姆逊效应和再生冷却技术，将空气等气体液化。高压气体在逆流式热交换器中被从膨胀阀返回的低温低压气体冷却。这逐渐降低阀门处的温度，直至降至临界点以下，开始液化，这构成了现代气体液化工业的基础。

The Lorentz force law describes the total force experienced by a point charge moving through a combined electric and magnetic field. It is the sum of the electrostatic force and the magnetic force. The governing vector equation is [latex]\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})[/latex], where [latex]q[/latex] is the charge, [latex]\mathbf{v}[/latex] is its velocity, [latex]\mathbf{E}[/latex] is the electric field, and [latex]\mathbf{B}[/latex] is the magnetic field.

镍镉电池由瓦尔德马尔·荣格纳（Waldemar Jungner）于1899年发明，以氢氧化镍（NiO(OH)）为正极，以金属镉（Cd）为负极，并使用氢氧化钾（KOH）等碱性电解质。镍镉电池以其较长的循环寿命和良好的低温性能而闻名，但也存在记忆效应和镉的毒性问题。

The absolute electrochemical potential of a single electrode cannot be measured. Instead, potentials are measured relative to a universally accepted reference. The Standard Hydrogen Electrode (SHE) is the primary reference, assigned a potential of exactly 0 volts under standard conditions (1 M [latex]H^+[/latex] concentration, 1 bar [latex]H_2[/latex] gas, 298 K). All other standard electrode potentials are reported relative to this zero point.