Ideal Gas Law (Statistical Form)

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials, like a rubber band, strain when stretched and quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both.

The first commercially successful rechargeable battery. It uses a lead (Pb) anode, a lead dioxide (PbO₂) cathode, and a sulfuric acid (H₂SO₄) electrolyte. During discharge, both electrodes are converted into lead sulfate (PbSO₄), and the sulfuric acid is consumed. This process is chemically reversible by applying an external current, making it a practical and robust energy storage system.

This is the differential form of Faraday's law of induction, one of Maxwell's four equations. It states that a time-varying magnetic field (\(\mathbf{B}\)) always accompanies a spatially varying, non-conservative electric field (\(\mathbf{E}\)). The relationship is expressed as \(\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}\). This equation governs how changing magnetic fields create electric fields at a specific point in space.

Electromotive force (EMF) and electric potential difference (voltage) are distinct concepts, though both are measured in volts. EMF is the work per unit charge done by a non-conservative force (e.g., chemical reaction, changing magnetic field) to move charge within a source. Potential difference is the work per unit charge done by the conservative electrostatic field between two points.

For a Newtonian fluid, viscosity is a function of temperature and pressure but not shear rate. In liquids, viscosity decreases significantly as temperature increases because higher thermal energy allows molecules to overcome cohesive intermolecular forces more easily. Conversely, in gases, viscosity increases with temperature as more frequent molecular collisions at higher speeds lead to greater momentum transfer.

The enthalpy of sublimation, \(\Delta H_{\text{sub}}\), is the heat required to convert one mole of a substance from solid to gas at a given temperature and pressure. According to Hess's Law, since enthalpy is a state function, this energy change is the sum of the enthalpy of fusion (\(\Delta H_{\text{fus}}\)) and the enthalpy of vaporization (\(\Delta H_{\text{vap}}\)).

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, \(e^{-E / k_B T}\). It implies that states with lower energy are exponentially more likely to be occupied than states with higher energy, with temperature modulating this preference.