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Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movin ...
through a
conductor Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble, such as an orchestra. * ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of structured free improvisation ...
produces
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
. Joule's first law (also just Joule's law), also known in countries of former
USSR The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...
as the Joule–Lenz law,Джоуля — Ленца закон
. ''Большая советская энциклопедия'', 3-е изд., гл. ред. А. М. Прохоров. Москва: Советская энциклопедия, 1972. Т. 8 ()
states that the power of heating generated by an electrical conductor equals the product of its
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...
and the square of the current: P = I^2 R Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another.


History

James Prescott Joule first published in December 1840, an abstract in the '' Proceedings of the Royal Society'', suggesting that heat could be generated by an electrical current. Joule immersed a length of wire in a fixed
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different element ...
of
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
and measured the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...
rise due to a known current flowing through the wire for a 30
minute The minute is a unit of time usually equal to (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a n ...
period. By varying the current and the length of the wire he deduced that the heat produced was
proportional Proportionality, proportion or proportional may refer to: Mathematics * Proportionality (mathematics), the property of two variables being in a multiplicative relation to a constant * Ratio, of one quantity to another, especially of a part compare ...
to the
square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
of the current multiplied by the
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...
of the immersed wire. In 1841 and 1842, subsequent experiments showed that the amount of heat generated was proportional to the chemical energy used in the
voltaic pile upright=1.2, Schematic diagram of a copper–zinc voltaic pile. The copper and zinc discs were separated by cardboard or felt spacers soaked in salt water (the electrolyte). Volta's original piles contained an additional zinc disk at the bottom, ...
that generated the template. This led Joule to reject the caloric theory (at that time the dominant theory) in favor of the mechanical theory of heat (according to which heat is another form of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) 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 hea ...
). Resistive heating was independently studied by Heinrich Lenz in 1842. The
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) 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 hea ...
was subsequently named the joule and given the symbol ''J''. The commonly known unit of power, the
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
, is equivalent to one joule per second.


Microscopic description

Joule heating is caused by interactions between charge carriers (usually electrons) and the body of the conductor. A potential difference (
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge t ...
) between two points of a conductor creates an electric field that accelerates charge carriers in the direction of the electric field, giving them
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...
. When the charged particles collide with the quasi-particles in the conductor (i.e. the canonically quantized, ionic lattice oscillations in the harmonic approximation of a crystal), energy is being transferred from the electrons to the lattice (by the creation of further lattice oscillations). The oscillations of the ions are the origin of the radiation ("
thermal energy The 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, ...
") that one measures in a typical experiment.


Power loss and noise

Joule heating is referred to as ''ohmic heating'' or ''resistive heating'' because of its relationship to Ohm's Law. It forms the basis for the large number of practical applications involving
electric heating Electric heating is a process in which electrical energy is converted directly to heat energy at around 100% efficiency, using rather cheap devices. Common applications include space heating, cooking, water heating and industrial processes. ...
. However, in applications where heating is an unwanted by-product of current use (e.g., load losses in electrical transformers) the diversion of energy is often referred to as ''resistive loss''. The use of high voltages in
electric power transmission Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This i ...
systems is specifically designed to reduce such losses in cabling by operating with commensurately lower currents. The ring circuits, or ring mains, used in UK homes are another example, where power is delivered to outlets at lower currents (per wire, by using two paths in parallel), thus reducing Joule heating in the wires. Joule heating does not occur in superconducting materials, as these materials have zero electrical resistance in the superconducting state. Resistors create electrical noise, called Johnson–Nyquist noise. There is an intimate relationship between Johnson–Nyquist noise and Joule heating, explained by the fluctuation-dissipation theorem.


Formulas


Direct current

The most fundamental formula for Joule heating is the generalized power equation: P = I (V_ - V_) where * P is the power (energy per unit time) converted from electrical energy to thermal energy, * I is the current travelling through the resistor or other element, * V_-V_ is the voltage drop across the element. The explanation of this formula (P = IV) is:''Electric power systems: a conceptual introduction'' by Alexandra von Meier, p67
Google books link
/ref> Assuming the element behaves as a perfect resistor and that the power is completely converted into heat, the formula can be re-written by substituting Ohm's law, V = I R , into the generalized power equation: P = IV = I^2R = V^2/R where ''R'' is the
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...
.


Alternating current

When current varies, as it does in AC circuits, P(t) = U(t) I(t) where ''t'' is time and ''P'' is the instantaneous power being converted from electrical energy to heat. Far more often, the ''average'' power is of more interest than the instantaneous power: P_ = U_\text I_\text = I_\text^2 R = U_\text^2 / R where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square. These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified: P_ = U_\textI_\text\cos\phi = I_\text^2 \operatorname(Z) = U_\text^2 \operatorname(Y^*) where \phi is phase difference between current and voltage, \operatorname means real part, ''Z'' is the complex impedance, and ''Y*'' is the
complex conjugate In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
of the admittance (equal to 1/''Z*''). For more details in the reactive case, see AC power∆0}


Differential form

Joule heating can also be calculated at a particular location in space. The differential form of the Joule heating equation gives the power per unit volume. \frac = \mathbf \cdot \mathbf Here, \mathbf is the current density, and \mathbf is the electric field. For a material with a conductivity \sigma, \mathbf=\sigma \mathbf and therefore \frac = \mathbf \cdot \mathbf = \mathbf \cdot \mathbf\rho = \frac J^2 where \rho = 1/\sigma is the resistivity. This directly resembles the "I^2R" term of the macroscopic form. In the harmonic case, where all field quantities vary with the angular frequency \omega as e^, complex valued
phasors In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. It is related to a ...
\hat\mathbf and \hat\mathbf are usually introduced for the current density and the electric field intensity, respectively. The Joule heating then reads \frac = \frac\hat\mathbf \cdot \hat\mathbf^* = \frac\hat\mathbf \cdot \hat\mathbf^*\rho = \fracJ^2/\sigma, where \bullet^* denotes the
complex conjugate In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
.


High-voltage alternating current transmission of electricity

Overhead power lines transfer electrical energy from electricity producers to consumers. Those power lines have a nonzero resistance and therefore are subject to Joule heating, which causes transmission losses. The split of power between transmission losses (Joule heating in transmission lines) and load (useful energy delivered to the consumer) can be approximated by a voltage divider. In order to minimize transmission losses, the resistance of the lines has to be as small as possible compared to the load (resistance of consumer appliances). Line resistance is minimized by the use of copper conductors, but the resistance and
power supply A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a ...
specifications of consumer appliances are fixed. Usually, a transformer is placed between the lines and consumption. When a high-voltage, low-intensity current in the primary circuit (before the transformer) is converted into a low-voltage, high-intensity current in the secondary circuit (after the transformer), the equivalent resistance of the secondary circuit becomes higher and transmission losses are reduced in proportion. During the war of currents, AC installations could use transformers to reduce line losses by Joule heating, at the cost of higher voltage in the transmission lines, compared to DC installations.


Applications

Joule-heating or resistive-heating is used in multiple devices and industrial process. The part that converts electricity into heat is called a heating element. Among the many practical uses are: * An incandescent light bulb glows when the filament is heated by Joule heating, due to
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
(also called blackbody radiation). * Electric fuses are used as a safety, breaking the circuit by melting if enough current flows to melt them. * Electronic cigarettes vaporize propylene glycol and vegetable glycerine by Joule heating. * Multiple heating devices use Joule heating, such as electric stoves,
electric heaters Electric heating is a process in which electrical energy is converted directly to heat energy at around 100% efficiency, using rather cheap devices. Common applications include space heating, cooking, water heating and industrial processes. An ...
, soldering irons, cartridge heaters. * Some
food processing Food processing is the transformation of agricultural products into food, or of one form of food into other forms. Food processing includes many forms of processing foods, from grinding grain to make raw flour to home cooking to complex industr ...
equipment may make use of Joule heating: running current through food material (which behave as an electrical resistor) causes heat release inside the food. The alternating electrical current coupled with the resistance of the food causes the generation of heat. A higher resistance increases the heat generated. Ohmic heating allows for fast and uniform heating of food products, which maintains quality. Products with particulates heat up faster (compared to conventional heat processing) due to higher resistance.


Food processing

Joule heating is a flash pasteurization (also called "high-temperature short-time" (HTST)) aseptic process that runs an alternating current of 50–60 Hz through food. Heat is generated through the food's electrical resistance. As the product heats, electrical conductivity increases linearly. A higher electrical current frequency is best as it reduces oxidation and metallic contamination. This heating method is best for foods that contain particulates suspended in a weak salt-containing medium due to their high resistance properties.


Materials synthesis, recovery and processing

Flash joule heating (transient high-temperature electrothermal heating) has been used to synthesize allotropes of carbon, including graphene and diamond. Heating various solid carbon feedstocks (carbon black, coal, coffee grounds, etc.) to temperatures of ~3000 K for 10-150 milliseconds produces turbostratic graphene flakes. FJH has also been used to recover rare-earth elements used in modern electronics from industrial wastes. Beginning from a fluorinated carbon source, fluorinated activated carbon, fluorinated nanodiamond, concentric carbon (carbon shell around a nanodiamond core), and fluorinated flash graphene can be synthesized.


Heating efficiency

Heat is not to be confused with internal energy or synonymously
thermal energy The 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, ...
. While intimately connected to
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
, they are distinct physical quantities. As a heating technology, Joule heating has a coefficient of performance of 1.0, meaning that every joule of electrical energy supplied produces one joule of heat. In contrast, a heat pump can have a coefficient of more than 1.0 since it moves additional thermal energy from the environment to the heated item. The definition of the efficiency of a heating process requires defining the boundaries of the system to be considered. When heating a building, the overall efficiency is different when considering heating effect per unit of electric energy delivered on the customer's side of the meter, compared to the overall efficiency when also considering the losses in the power plant and transmission of power.


Hydraulic equivalent

In the energy balance of groundwater flow a hydraulic equivalent of Joule's law is used: \frac = \frac where: * dE/dx = loss of hydraulic energy (E) due to friction of flow in x-direction per unit of time (m/day) – comparable to P * v_x = flow velocity in x-direction (m/day) – comparable to I * K = hydraulic conductivity of the soil (m/day) – the hydraulic conductivity is inversely proportional to the hydraulic resistance which compares to R


See also

* Resistance wire * Heating element * Nichrome * Tungsten * Molybdenum disilicide *
Overheating (electricity) Overheating is a phenomenon of rising temperatures in an electrical circuit. Overheating causes damage to the circuit components and can cause fire, explosion, and injury. Damage caused by overheating is usually irreversible; the only way to repai ...
* Thermal management (electronics) * Induction heating * Dielectric heating


References

{{DEFAULTSORT:Joule Heating Electric heating Electricity Thermodynamics James Prescott Joule