Ideal Gas Law (Molar Form)

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 Clausius-Clapeyron relation describes the relationship between pressure and temperature for a substance at a phase transition, such as liquid and vapor. For water vapor, it shows that saturation vapor pressure increases exponentially with temperature. The approximate form is \(\frac{dp}{dT} = \frac{L}{T(V_v - V_l)} \approx \frac{L p}{R_v T^2}\), where L is latent heat.

Eddy currents are loops of electrical current induced within bulk conductors by a changing magnetic field, in accordance with Faraday's law. They flow in closed loops in planes perpendicular to the magnetic field. Following Lenz's law, these currents create their own magnetic field that opposes the change in the external flux, causing a repulsive or drag force and resistive heating.

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 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 Joule-Thomson (or Joule-Kelvin) effect describes the temperature change of a real gas when it is forced through a valve or porous plug while kept insulated (an isenthalpic process). At a given pressure, a gas has an inversion temperature. If expanded below this temperature, it cools; if expanded above it, it heats up. This cooling effect is a cornerstone of modern refrigeration and liquefaction.

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.