Internal energyThe internal energy of a thermodynamic system is the energy contained within it, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields.
Intensive and extensive propertiesPhysical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms "intensive and extensive quantities" were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C.
Legendre transformationIn mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as velocity, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively).
Legendre polynomialsIn mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.
Associated Legendre polynomialsIn mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation or equivalently where the indices l and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on only if l and m are integers with 0 ≤ m ≤ l, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial.
EnergyIn physics, energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).
Internal combustion engineAn internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combustion engine, the expansion of the high-temperature and high-pressure gases produced by combustion applies direct force to some component of the engine. The force is typically applied to pistons (piston engine), turbine blades (gas turbine), a rotor (Wankel engine), or a nozzle (jet engine).
Elementary functionIn mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, including possibly their inverse functions (e.g., arcsin, log, or x1/n). All elementary functions are continuous on their domains. Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Gibbs free energyIn thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.
Thermal energyThe term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer (as is thermodynamic work); and the characteristic energy of a degree of freedom, , in a system that is described in terms of its microscopic particulate constituents (where denotes temperature and denotes the Boltzmann constant).
Thermodynamic equationsThermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot.
Non-equilibrium thermodynamicsNon-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.
