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Joule heating
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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
through a
conductor
produces
heat
.
Joule’s first law, also known as the Joule–Lenz law,^{}
[1]
states that the
power
of heating generated by an
electrical conductor
is proportional to the product of its
resistance
and the square of the current:
 P∝I2R{displaystyle Ppropto I^{2}R}
Joule heating affects the whole electric conductor, unlike the
Peltier effect
which transfers heat from one electrical junction to another.
History[
edit
]
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
of
water
and measured the
temperature
rise due to a known current flowing through the wire for a 30
minute
period. By varying the current and the length of the wire he deduced that the heat produced was
proportional
to the
square
of the current multiplied by the
electrical resistance
of the immersed wire.^{}
[2]
In 1841 and 1842, subsequent experiments showed that the amount of heat generated was proportional to the
chemical energy
used in the
voltaic pile
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
).^{}
[2]
Resistive heating was independently studied by
Heinrich Lenz
in 1842.^{}
[1]
The
SI unit
of
energy
was subsequently named the
joule
and given the symbol J. The commonly known unit of power, the
watt
, is equivalent to one joule per second.
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Microscopic description[
edit
]
Joule heating is caused by interactions between
charge carriers
(usually
electrons
) and the body of the conductor (usually
atomic
ions
).
A
voltage
difference 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
. When the charged particles collide with ions in the conductor, the particles are
scattered
; their direction of motion becomes random rather than aligned with the electric field, which constitutes
thermal motion
. Thus, energy from the electrical field is converted into
thermal energy
.^{}
[3]
Power loss and noise[
edit
]
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
. However, in applications where heating is an unwanted
byproduct
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
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
fluctuationdissipation theorem
.
Formulas[
edit
]
Direct current[
edit
]
The most fundamental formula for Joule heating is the generalized power equation:
 P=I(VA−VB){displaystyle P=I(V_{A}V_{B})}
where
 P{displaystyle P} is the
power
(energy per unit time) converted from electrical energy to thermal energy,
 I{displaystyle I} is the current travelling through the resistor or other element,
 VA−VB{displaystyle V_{A}V_{B}} is the
voltage drop
across the element.
The explanation of this formula (P=IV{displaystyle P=IV}) is:^{}
[4]
 (Energy dissipated per unit time) = (Charge passing through resistor per unit time) × (Energy dissipated per charge passing through resistor)
Assuming the element behaves as a perfect resistor and that the power is completely converted into heat, the formula can be rewritten by substituting
Ohm’s law
, V=I⋅R{displaystyle V=Icdot R}, into the generalized power equation:
 P=IV=I2R=V2/R{displaystyle P=IV=I^{2}R=V^{2}/R}
where R is the
resistance
.
Alternating current[
edit
]
When current varies, as it does in AC circuits,
 P(t)=U(t)I(t){displaystyle 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:
 Pavg=UrmsIrms=Irms2R=Urms2/R{displaystyle P_{rm {avg}}=U_{text{rms}}I_{text{rms}}=I_{text{rms}}^{2}R=U_{text{rms}}^{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:
 Pavg=UrmsIrmscosϕ=Irms2Re(Z)=Urms2Re(Y∗){displaystyle P_{rm {avg}}=U_{text{rms}}I_{text{rms}}cos phi =I_{text{rms}}^{2}operatorname {Re} (Z)=U_{text{rms}}^{2}operatorname {Re} (Y^{*})}
where ϕ{displaystyle phi } is phase difference between current and voltage, Re{displaystyle operatorname {Re} } means
real part
, Z is the
complex impedance
, and Y* is the
complex conjugate
of the
admittance
(equal to 1/Z*).
For more details in the reactive case, see
AC power
∆0}
Differential form[
edit
]
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.
 dP/dV=J⋅E{displaystyle mathrm {d} P/mathrm {d} V=mathbf {J} cdot mathbf {E} }
Here, J{displaystyle mathbf {J} } is the current density, and E{displaystyle mathbf {E} } is the electric field. For a material with a conductivity σ{displaystyle sigma }, J=σE{displaystyle mathbf {J} =sigma mathbf {E} } and therefore
 dP/dV=J⋅E=J⋅Jρ=J2/σ{displaystyle mathrm {d} P/mathrm {d} V=mathbf {J} cdot mathbf {E} =mathbf {J} cdot mathbf {J} rho =J^{2}/sigma }
where ρ=1/σ{displaystyle rho =1/sigma } is the
resistivity
. This directly resembles the “I2R{displaystyle I^{2}R}” term of the macroscopic form.
In the harmonic case, where all field quantities vary with the angular frequency ω{displaystyle omega } as e−iωt{displaystyle e^{mathrm {i} omega t}}, complex valued
phasors
J^{displaystyle {hat {mathbf {J} }}} and E^{displaystyle {hat {mathbf {E} }}} are usually introduced for the current density and the electric field intensity, respectively. The Joule heating then reads
 dP/dV=12J^⋅E^∗=12J^⋅J^∗ρ=12J2/σ{displaystyle mathrm {d} P/mathrm {d} V={frac {1}{2}}{hat {mathbf {J} }}cdot {hat {mathbf {E} }}^{*}={frac {1}{2}}{hat {mathbf {J} }}cdot {hat {mathbf {J} }}^{*}rho ={frac {1}{2}}J^{2}/sigma },
where ∙∗{displaystyle bullet ^{*}} denotes the
complex conjugate
.
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Highvoltage alternating current transmission of electricity[
edit
]
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
specifications of consumer appliances are fixed.
Usually, a
transformer
is placed between the lines and consumption. When a highvoltage, lowintensity current in the primary circuit (before the transformer) is converted into a lowvoltage, highintensity current in the secondary circuit (after the transformer), the equivalent resistance of the secondary circuit becomes higher^{}
[5]
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[
edit
]
Jouleheating or resistiveheating is used in multiple devices and industrial process. The part which converts electricity into heat by Joule heating is called a
heating element
.

An
incandescent light bulb
‘s filament emitting light

Infrared
–
thermal image
of a light bulb

Bulb filament magnified by
scanning electron microscope

30 kW resistance heating coils

Electric radiative space heater

Small domestic immersion heater, 500 W

Folded tubular heating element from espresso machine

Laboratory water bath
used for reactions at warm temperatures

Electric tabletop hotplate

Laboratory
hot plate
used for reactions at high temperatures

Clothes iron
used to remove wrinkles from clothes

Soldering iron
, used to melt solder in electronic work

Portable
fan heater
, used to heat a room

Hair dryer
, produces hot air flow

Cartridge heater
glowing redhot

Flexible
PTC
heater made of conductive rubber
There are many practical uses of Joule heating:
 An
incandescent light bulb
glows when the filament is heated by Joule heating, due to
thermal radiation
(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
,
soldering irons
,
cartridge heaters
.
 Some
food processing
equipment may make use of Joule heating: running current through food material (which behave as an electrical resistor) causes heat release inside the food.^{}
[6]
The alternating electrical current coupled with the resistance of the food causes the generation of heat.^{}
[7]
A higher resistance increases the heat generated. Ohmic heating allows for fast and uniform heating of food products, which keeps the high quality in foods. Products with particulates heat up faster in Ohmic heating (as compared to conventional heat processing) due to higher resistance.^{}
[8]
Food processing[
edit
]
Joule heating (
Ohmic heating
) is a
flash pasteurization
(also called “hightemperature shorttime” (HTST)) aseptic process that runs an alternating current of 50–60 Hz through food.^{}
[9]
Heat is generated through the electrical resistance of the food.^{}
[9]
As the product heats up, electrical conductivity increases linearly.^{}
[7]
A higher electrical current frequency is best as it reduces oxidation and metallic contamination.^{}
[9]
This heating method is best for foods that contain particulates suspended in a weak saltcontaining medium due to their high resistance properties.^{}
[8]
Ohmic heating allows for a maintained quality of foods due to the uniform heating that decreases deterioration and overprocessing of food.^{}
[9]
Heating efficiency[
edit
]
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.
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Hydraulic equivalent[
edit
]
In the
energy balance of groundwater flow
a hydraulic equivalent of Joule’s law is used:^{}
[10]
 dEdx=vx2K{displaystyle {dE over dx}={v_{x}^{2} over K}}
where:
 dE/dx{displaystyle dE/dx} = loss of hydraulic energy (E{displaystyle E}) due to friction of flow in x{displaystyle x}direction per unit of time (m/day) – comparable to P{displaystyle P}
 vx{displaystyle v_{x}} = flow velocity in x{displaystyle x}direction (m/day) – comparable to I{displaystyle I}
 K{displaystyle K} =
hydraulic conductivity
of the soil (m/day) – the hydraulic conductivity is inversely proportional to the hydraulic resistance which compares to R{displaystyle R}
See also[
edit
]

Resistance wire

Heating element

Nichrome

Tungsten

Molybdenum disilicide

Overheating (electricity)

Thermal management (electronics)

Induction heating
References[
edit
]
 ^
^{a}
^{b}
Джоуля — Ленца закон
Archived
20141230 at the
Wayback Machine
. Большая советская энциклопедия, 3е изд., гл. ред. А. М. Прохоров. Москва: Советская энциклопедия, 1972. Т. 8 (A. M. Prokhorov; et al., eds. (1972). “Joule–Lenz law”.
Great Soviet Encyclopedia
(in Russian). 8. Moscow: Soviet Encyclopedia.)
 ^
^{a}
^{b}
“This Month Physics History: December 1840: Joule’s abstract on converting mechanical power into heat”
. aps.org. American Physical society. Retrieved 16 September 2016.

^
“Drift Velocity, Drift Current and Electron Mobility”
. Electrical4U. Retrieved 26 July 2017.

^
Electric power systems: a conceptual introduction by Alexandra von Meier, p67,
Google books link

^
“Transformer circuits”
. Retrieved 26 July 2017.

^
Ramaswamy, Raghupathy.
“Ohmic Heating of Foods”
. Ohio State University. Archived from
the original
on 20130408. Retrieved 20130422.
 ^
^{a}
^{b}
Fellows, P.J (2009). Food Processing Technology. MA: Elsevier. pp. 813–844.
ISBN
9780081019078
.
 ^
^{a}
^{b}
Varghese, K. Shiby; Pandey, M. C.; Radhakrishna, K.; Bawa, A. S. (October 2014).
“Technology, applications and modelling of ohmic heating: a review”
. Journal of Food Science and Technology. 51 (10): 2304–2317.
doi
:
10.1007/s1319701207103
.
ISSN
00221155
.
PMC
4190208
.
PMID
25328171
.
 ^
^{a}
^{b}
^{c}
^{d}
1953, Fellows, P. (Peter) (2017) [2016]. Food processing technology : principles and practice (4th ed.). Kent: Woodhead Publishing/Elsevier Science.
ISBN
9780081019078
.
OCLC
960758611
.CS1 maint: numeric names: authors list (
link
)

^
R.J.Oosterbaan, J.Boonstra and K.V.G.K.Rao (1996).
The energy balance of groundwater flow
(PDF). In: V.P.Singh and B.Kumar (eds.), SubsurfaceWater Hydrology, Vol.2 of the Proceedings of the International Conference on Hydrology and Water Resources, New Delhi, India. Kluwer Academic Publishers, Dordrecht, The Netherlands. pp. 153–160.
ISBN
9780792336518
.
Categories
:

Electric heating

Electricity

Thermodynamics

James Prescott Joule
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