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Internal energy
Common symbols
U
SI unit
J
In SI base units
m2⋅kg/s2
Derivations from other quantities
Thermodynamics
The classical Carnot heat engine
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Classical
Statistical
Chemical
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Note: Conjugate variables in italics
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Fundamental relation
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Potentials
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Internal energy
Enthalpy
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History
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An Experimental Enquiry Concerning ... Heat
On the Equilibrium of Heterogeneous Substances
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Nucleation
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Self-organization
Order and disorder
Category
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The 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.[1][2] 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. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. The internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics.
The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of matter, or of energy, as heat, or by thermodynamic work.[3] These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property.
Thermodynamics defines internal energy macroscopically, for the body as a whole. In statistical mechanics, the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energies associated with microscopic forces, including chemical bonds.
The unit of energy in the International System of Units (SI) is the joule (J). The internal energy relative to the mass with unit J/kg is the specific internal energy. The corresponding quantity relative to the amount of substance with unit J/mol is the molar internal energy.[4]
^Crawford, F. H. (1963), pp. 106–107.
^Haase, R. (1971), pp. 24–28.
^Born, M. (1949), Appendix 8, pp. 146–149.
^International Union of Pure and Applied Chemistry. Physical and Biophysical Chemistry Division (2007). Quantities, units, and symbols in physical chemistry(PDF) (3rd ed.). Cambridge, UK: RSC Pub. ISBN 978-1-84755-788-9. OCLC 232639283.
The internalenergy of a thermodynamic system is the energy contained within it, measured as the quantity of energy necessary to bring the system from...
associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internalenergy contained within a thermodynamic system....
The latent internalenergy of a system is the internalenergy a system requires to undergo a phase transition. Its value is specific to the substance or...
considered a thermodynamic system, then the energy flowing within the metal bar is called internalenergy, not heat. The hot metal bar is also transferring...
system's internalenergy be consumed, so that the amount of internalenergy lost by that work must be resupplied as heat by an external energy source or...
concepts. These include the internalenergy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer (as is thermodynamic...
gravitational potential (higher internalenergy thus higher potential for work) to a lower gravitational potential (lower internalenergy). In the same way, as...
have internal structure and therefore have additional internal degrees of freedom (see Fig. 3, below), which makes molecules absorb more heat energy for...
free energy is expressed as G ( p , T ) = U + p V − T S = H − T S {\displaystyle G(p,T)=U+pV-TS=H-TS} where U {\textstyle U} is the internalenergy of the...
thermodynamics states that, when energy passes into or out of a system (as work, heat, or matter), the system's internalenergy changes in accordance with the...
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case...
chemical energy into kinetic energy which is used to propel, move or power whatever the engine is attached to. The first commercially successful internal combustion...
the surroundings by converting internalenergy to work until equilibrium is reached. There are different types of energy stored in materials, and it takes...
Internal pressure is a measure of how the internalenergy of a system changes when it expands or contracts at constant temperature. It has the same dimensions...
thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system (the others being internalenergy, enthalpy, entropy, etc.)....
{\displaystyle \Delta {U_{f}^{\circ }}_{\mathrm {reactants} }} , the internalenergy of formation of the reactant molecules, and Δ U f ∘ p r o d u c t s...
may generate thermal energy, causing the material's temperature to rise. Thermal energy in solids is often carried by internal elastic waves, called...
the internalenergy with respect to the entropy: Likewise, when the body is described by stating its entropy S as a function of its internalenergy U,...
= Q − W, where ΔU denotes the change of the system's internalenergy, Q the quantity of energy added to it as heat, and W the work done by the system...
thermodynamic equilibrium where the entropy is highest at the given internalenergy. An increase in the combined entropy of system and surroundings accounts...
c e {\displaystyle \Delta U_{lattice}} is the lattice energy (i.e., the molar internalenergy change), Δ H l a t t i c e {\displaystyle \Delta H_{lattice}}...
counteract the internal one – no work is generated, and the heat energy that would have gone into it must instead contribute to the internalenergy of the sample...
thermodynamic potential that has a physical interpretation is the internalenergy U. It is the energy of configuration of a given system of conservative forces...
energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels...
substance, n enthalpy, H entropy, S Gibbs energy, G heat capacity, Cp Helmholtz energy, A or F internalenergy, U spring stiffness, K mass, m volume, V...
the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating...
The energy policy of the European Union focuses on energy security, sustainability, and integrating the energy markets of member states. An increasingly...
{\displaystyle \Delta T=0} d T = 0 {\displaystyle dT=0} For ideal gases only, internalenergy Δ U = 0 {\displaystyle \Delta U=0} while in adiabatic processes: Q...
dV} Since both internalenergy and entropy are monotonic functions of temperature T {\displaystyle T} , implying that the internalenergy is fixed when...
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