Principal and Maximum Shear Stresses (Mohr’s Circle)

Yield strength, or the yield point, is the stress at which a material begins to deform plastically. Prior to the yield point, the material deforms elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. It marks the limit of elastic behavior.

Concentrated solar power systems use mirrors or lenses to concentrate a large area of sunlight onto a receiver. The concentrated light heats a fluid, which then drives a heat engine (usually a steam turbine) connected to an electrical power generator. This method contrasts with photovoltaics, which convert light directly into electricity. CSP allows for thermal energy storage.

The practical application of the Otto cycle is the four-stroke engine, which completes a thermodynamic cycle in four distinct piston movements (strokes). These are: 1. Intake (suck), where the air-fuel mixture is drawn in; 2. Compression (squeeze), where the mixture is compressed; 3. Power or Combustion (bang), where ignition pushes the piston down; 4. Exhaust (blow), where burnt gases are expelled.

The Hall-Héroult process is the major industrial method for smelting aluminum. It involves dissolving alumina (aluminum oxide, Al₂O₃) in molten cryolite (Na₃AlF₆) and electrolyzing the molten salt bath. Aluminum metal is deposited at the cathode, while oxygen from the alumina reacts with the carbon anode, producing carbon dioxide. This process made aluminum widely available and affordable.

An empirical formula that describes how the available capacity of a battery decreases as the rate of discharge increases. The law is stated as \(C_p = I^k t\), where \(C_p\) is the capacity at a one-ampere discharge rate, \(I\) is the discharge current, \(t\) is the discharge time, and \(k\) is the Peukert constant, specific to the battery type. It quantifies the inefficiency at high loads.

The Coefficient of Performance (COP) is a dimensionless ratio measuring the efficiency of a heat pump. It is the ratio of useful heating or cooling provided to the work required. For heating, \(COP_{heating} = \frac{|Q_H|}{W}\), and for cooling, \(COP_{cooling} = \frac{|Q_C|}{W}\), where Q is heat transferred and W is work input. Higher COP values indicate greater efficiency.

Alfred Nobel discovered that nitroglycerin could be made much safer to handle by absorbing it into an inert, porous material like kieselguhr (diatomaceous earth). This mixture, which he patented as dynamite, transformed the highly sensitive and dangerous liquid into a stable, solid explosive that could be reliably detonated only with a blasting cap, revolutionizing mining, construction, and demolition.

Hydrogen embrittlement (HE) is a process where metals, most notably high-strength steels, become brittle and fracture following exposure to hydrogen. Atomic hydrogen diffuses into the metal lattice and reduces its ductility and load-bearing capacity. Key proposed mechanisms include Hydrogen-Enhanced Decohesion (HEDE), which weakens atomic bonds, and Hydrogen-Enhanced Localized Plasticity (HELP), which facilitates dislocation motion and localized failure.

A peristaltic pump is a positive displacement pump where fluid is contained within a flexible tube fitted inside a circular pump casing. A rotor with several 'rollers' or 'shoes' compresses the tube as it turns. This compression wave moves along the tube, forcing the fluid to move. The fluid only contacts the tube's interior, making it ideal for sterile applications.

The chloralkali process is an industrial method for the electrolysis of sodium chloride (NaCl) solution, known as brine. It is the primary source for producing chlorine (Cl₂), sodium hydroxide (NaOH), and hydrogen (H₂), which are essential commodity chemicals. Modern methods use a membrane cell to separate the anode and cathode products, ensuring high purity and efficiency.

Pumped-storage hydroelectricity (PSH) is a type of hydroelectric energy storage used by electric power systems for load balancing. The method stores energy in the form of gravitational potential energy of water, pumped from a lower elevation reservoir to a higher elevation one. During periods of high electricity demand, the stored water is released to drive turbines and generate electricity.

Exothermic welding, also known as thermite welding, is a technique that uses the superheated molten metal from an aluminothermic reaction to create a strong, permanent molecular bond between metal components. The process is self-contained, requiring no external power source. It is most famously used to join sections of railway track into continuous welded rail, creating a smoother and more durable track.