Avogadro’s Law

The electric current in a Voltaic pile is produced by a redox reaction. At the zinc anode, zinc metal is oxidized, releasing two electrons per atom (\(Zn \rightarrow Zn^{2+} + 2e^{-}\)). These electrons travel through the external circuit to the copper cathode. There, hydrogen ions from the aqueous electrolyte are reduced, forming hydrogen gas (\(2H^{+} + 2e^{-} \rightarrow H_2\)).

Electromotive force (\(\mathcal{E}\)) is the work done per unit of electric charge by a non-electrical source, such as a battery or generator. Despite its name, it is not a mechanical force but an electric potential, measured in volts. It represents the energy converted from another form (chemical, mechanical) into electrical energy as a charge traverses the source.

The continuum assumption treats fluids as continuous matter rather than as discrete molecules. This simplification is valid when the length scale of the problem is much larger than the intermolecular distance, allowing properties like density and velocity to be defined at infinitesimally small points. This enables the use of differential equations to describe the macroscopic behavior of fluid flow.

The Cauchy stress tensor, denoted \(\boldsymbol{\sigma}\), is a second-order tensor that completely defines the state of stress at a point inside a material. It relates the traction vector (force per unit area) \(\mathbf{T}\) on any surface passing through that point to the surface's normal vector \(\mathbf{n}\) via the linear relationship \(\mathbf{T} = \boldsymbol{\sigma} \cdot \mathbf{n}\).

The Voltaic pile established the principle of adding voltages by connecting electrochemical cells in series. Each zinc-copper pair, or cell, generates a characteristic electromotive force (EMF) of approximately 0.76 volts. By physically stacking these cells, Volta demonstrated that the total voltage across the pile is the sum of the individual EMFs of each cell, as described by \(V_{total} = n \times V_{cell}\).

The first electric battery, it produces a direct current by stacking pairs of dissimilar metal discs (e.g., zinc and copper) separated by brine-soaked cloth. Each pair forms a galvanic cell, and stacking them in series increases the overall voltage. This arrangement demonstrated the first continuous conversion of chemical energy into electrical energy, paving the way for modern electrochemistry.

A primary flaw of the Voltaic pile is electrode polarization. During operation, hydrogen gas produced at the copper cathode forms an insulating layer of bubbles on its surface. This layer increases the battery's internal resistance and reduces the surface area available for reaction. As a result, the voltage and current output of the pile drop significantly shortly after it begins to be used.

Engineering stress (\(\sigma\)) is the applied load divided by the original cross-sectional area (\(A_0\)), while engineering strain (\(\epsilon\)) is the change in length (\(\Delta L\)) divided by the original length (\(L_0\)). These definitions, \(\sigma = \frac{F}{A_0}\) and \(\epsilon = \frac{\Delta L}{L_0}\), are fundamental for plotting stress-strain curves but assume the specimen's dimensions remain constant during the test.

The Navier–Stokes equations are a set of non-linear partial differential equations describing the motion of viscous fluid substances. They are a statement of Newton's second law, balancing momentum changes with pressure gradients, viscous forces, and external forces. For an incompressible fluid, the equation is \(\rho (\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f}\).

Cathodic protection (CP) is a technique used to control the corrosion of a metal surface by making it the cathode of an electrochemical cell. This is achieved by supplying an external electrical current that suppresses the natural corrosion currents. The protected metal's potential is polarized to a more negative value, shifting it into a region of immunity or passivity.