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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 moving pa ...
through a
conductor 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 al ...
.
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 nationa ...
as the Joule–Lenz law,
[Джоуля — Ленца закон](_blank)
. ''Большая советская энциклопедия'', 3-е изд., гл. ред. А. М. Прохоров. Москва: Советская энциклопедия, 1972. Т. 8 () states that the
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
of heating generated by an
electrical conductor
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gener ...
equals the product of its
resistance and the square of the current:
Joule heating affects the whole electric conductor, unlike the
Peltier effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when ...
which transfers heat from one electrical junction to another.
History
James Prescott Joule
James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). Th ...
first published in December 1840, an abstract in the ''
Proceedings of the Royal Society
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905:
* Series A: for papers in physical sciences and mathematics.
* Series B: for papers in life s ...
'', 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 elementar ...
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 a ...
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 o ...
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 nega ...
period. By varying the current and the length of the wire he deduced that the heat produced was
proportional 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 adj ...
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 parallels ...
of the immersed wire.
In 1841 and 1842, subsequent experiments showed that the amount of heat generated was proportional to the
chemical energy
Chemical energy is the energy of chemical substances that is released when they undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, Schmidt-Rohr, K. (2018). "How ...
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
The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores i ...
(at that time the dominant theory) in favor of the
mechanical theory of heat
The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Owing to the relevance of thermodynamics in much of science and technology, its history is finely w ...
(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 heat a ...
).
Resistive heating was independently studied by
Heinrich Lenz
Heinrich Friedrich Emil Lenz (; ; also Emil Khristianovich Lenz, russian: Эмилий Христианович Ленц; 12 February 1804 – 10 February 1865), usually cited as Emil Lenz or Heinrich Lenz in some countries, was a Russian physic ...
in 1842.
The
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
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 heat a ...
was subsequently named the
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
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
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
) and the body of the conductor.
A
potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
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 to m ...
) between two points of a conductor creates an
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
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 accele ...
. 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, d ...
") 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
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
. 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
A by-product or byproduct is a secondary product derived from a production process, manufacturing process or chemical reaction; it is not the primary product or service being produced.
A by-product can be useful and marketable or it can be consid ...
of current use (e.g.,
load losses in
electrical transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's c ...
s) the diversion of energy is often referred to as ''resistive loss''. The use of
high voltage
High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and conductors that carry high voltage warrant spec ...
s 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 is ...
systems is specifically designed to reduce such losses in cabling by operating with commensurately lower currents. The
ring circuit
In electricity supply design, a ring circuit is an electrical wiring technique in which sockets and the distribution point are connected in a ring. It is contrasted with the usual radial circuit, in which sockets and the distribution point a ...
s, 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
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
materials, as these materials have zero electrical resistance in the superconducting state.
Resistors create electrical noise, called
Johnson–Nyquist noise
Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens rega ...
. There is an intimate relationship between Johnson–Nyquist noise and Joule heating, explained by the
fluctuation-dissipation theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the th ...
.
Formulas
Direct current
The most fundamental formula for Joule heating is the generalized power equation:
where
*
is the
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
(energy per unit time) converted from electrical energy to thermal energy,
*
is the current travelling through the resistor or other element,
*
is the
voltage drop
Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirab ...
across the element.
The explanation of this formula (
) 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
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
, , into the generalized power equation:
where ''R'' is the resistance.
Alternating current
When current varies, as it does in AC circuits,
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:
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...
.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:
where is phase difference between current and voltage, means real part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
, ''Z'' is the complex impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.
Quantitatively, the impedance of a two-terminal circuit element is the ratio of the compl ...
, 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
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of 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.
Here, is the current density, and is the electric field. For a material with a conductivity , and therefore
where is the resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
. This directly resembles the "" term of the macroscopic form.
In the harmonic case, where all field quantities vary with the angular frequency as , complex valued phasors and are usually introduced for the current density and the electric field intensity, respectively. The Joule heating then reads
where 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 line
An overhead power line is a structure used in electric power transmission and distribution to transmit electrical energy across large distances. It consists of one or more uninsulated electrical cables (commonly multiples of three for three-p ...
s 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 electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distributing the in ...
. 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 conductor
Copper has been used in electrical wiring since the invention of the electromagnet and the telegraph in the 1820s. The invention of the telephone in 1876 created further demand for copper wire as an electrical conductor.
Copper is the electr ...
s, 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 r ...
specifications of consumer appliances are fixed.
Usually, a transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the 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
The war of the currents was a series of events surrounding the introduction of competing electric power transmission systems in the late 1880s and early 1890s. It grew out of two lighting systems developed in the late 1870s and early 1880s; arc ...
, 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
A heating element converts electrical energy into heat through the process of Joule heating. Electric current through the element encounters resistance, resulting in heating of the element. Unlike the Peltier effect, this process is independe ...
.
Among the many practical uses are:
* An incandescent light bulb
An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from oxida ...
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
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spe ...
).
* Electric fuses are used as a safety, breaking the circuit by melting if enough current flows to melt them.
* Electronic cigarette
An electronic cigarette is an electronic device that simulates tobacco smoking. It consists of an atomizer, a power source such as a battery, and a container such as a cartridge or tank. Instead of smoke, the user inhales vapor. As such ...
s vaporize propylene glycol and vegetable glycerine by Joule heating.
* Multiple heating devices use Joule heating, such as electric stove
An electric stove or electric range is a stove with an integrated electrical heating device to cook and bake. Electric stoves became popular as replacements for solid-fuel (wood or coal) stoves which required more labor to operate and maintain. ...
s, electric heaters, soldering iron
A soldering iron is a hand tool used in soldering. It supplies heat to melt solder so that it can flow into the joint between two workpieces.
A soldering iron is composed of a heated metal tip (the ''bit'') and an insulated handle. Heating i ...
s, cartridge heater
A cartridge heater is a tube-shaped, heavy-duty, industrial Joule heating element used in the process heating industry, usually custom manufactured to a specific watt density, based on its intended application. Compact designs are capable of r ...
s.
* 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
Flash pasteurization, also called "high-temperature short-time" (HTST) processing, is a method of heat pasteurization of perishable beverages like fruit and vegetable juices, beer, wine, and some dairy products such as milk. Compared with other ...
(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
Nanodiamonds, or diamond nanoparticles, are diamonds with a size below 100 nanometers. They can be produced by impact events such as an explosion or meteoritic impacts. Because of their inexpensive, large-scale synthesis, potential for surfa ...
, 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
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
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, d ...
. 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 al ...
, they are distinct physical quantities.
As a heating technology, Joule heating has a coefficient of performance
The coefficient of performance or COP (sometimes CP or CoP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work (energy) required. Higher COPs equate to higher efficiency, lower energy ( ...
of 1.0, meaning that every joule of electrical energy supplied produces one joule of heat. In contrast, a heat pump
A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing h ...
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:
where:
* = loss of hydraulic energy () due to friction of flow in -direction per unit of time (m/day) – comparable to
* = flow velocity in -direction (m/day) – comparable to
* = hydraulic conductivity
Hydraulic conductivity, symbolically represented as (unit: m/s), is a property of porous materials, soils and rocks, that describes the ease with which a fluid (usually water) can move through the pore space, or fractures network. It depends on th ...
of the soil (m/day) – the hydraulic conductivity is inversely proportional to the hydraulic resistance which compares to
See also
* Resistance wire
Resistance wire is wire intended for making electrical resistors (which are used to control the amount of current in a circuit). It is better if the alloy used has a high resistivity, since a shorter wire can then be used. In many situations, the ...
* Heating element
A heating element converts electrical energy into heat through the process of Joule heating. Electric current through the element encounters resistance, resulting in heating of the element. Unlike the Peltier effect, this process is independe ...
* Nichrome
* Tungsten
Tungsten, or wolfram, is a chemical element with the symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isolat ...
* Molybdenum disilicide
Molybdenum disilicide (MoSi2, or molybdenum silicide), an intermetallic compound, a silicide of molybdenum, is a refractory ceramic with primary use in heating elements. It has moderate density, melting point 2030 °C, and is electrically co ...
* 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)
All electronic devices and circuitry generate excess heat and thus require thermal management to improve reliability and prevent premature failure. The amount of heat output is equal to the power input, if there are no other energy int ...
* Induction heating
Induction heating is the process of heating electrically conductive materials, namely metals or semi-conductors, by electromagnetic induction, through heat transfer passing through an induction coil that creates an electromagnetic field within th ...
* Dielectric heating
Dielectric heating, also known as electronic heating, radio frequency heating, and high-frequency heating, is the process in which a radio frequency (RF) alternating electric field, or radio wave or microwave electromagnetic radiation heats a die ...
References
{{DEFAULTSORT:Joule Heating
Electric heating
Electricity
Thermodynamics
James Prescott Joule