Joule heating (also known as resistive heating, resistance heating, or Ohmic heating) is the process by which the passage of an electric current through a conductor produces heat.
Joule's first law (also just Joule's law), also known in countries of the former USSR 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 and the square of the current. Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another.
Joule-heating or resistive-heating is used in many devices and industrial processes. The part that converts electricity into heat is called a heating element.
Practical applications of joule heating include, but are not limited to:
Buildings are often heated with electric heaters where grid power is available. Electric stoves and ovens use Joule heating to cook food. Soldering irons generate heat to melt conductive solder and make electrical connections. Cartridge heaters are used in various manufacturing processes. Electric fuses are used as a safety device, breaking a circuit by melting if enough current flows to heat them to the melting point. Electronic cigarettes vaporize liquid by Joule heating. Food processing equipment may make use of Joule heating: running a 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. Joule 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.
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 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.
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).
Resistive heating was independently studied by Heinrich Lenz in 1842.
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.
Microscopic description
Joule heating is caused by interactions between charge carriers (usually electrons) and the body of the conductor.
A potential difference (voltage) 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 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") 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. 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 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:
where is the power (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 across the element.
The explanation of this formula () is:Electric power systems: a conceptual introduction by Alexandra von Meier, p67, Google books link
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, , 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 active power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power. For an ideal resistor, with zero reactance, the average Joule-heating power is
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
If the reactance is nonzero, the formulas are modified. The average Joule-heating power is
where is phase difference between current and voltage, means real part, Z is the complex impedance, and Y* is the complex conjugate of the admittance (equal to 1/Z*). Note that , and
.
For more details in the reactive case, see AC power.
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. 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.
Electricity transmission
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 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
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.
Heat is generated rapidly and uniformly in the liquid matrix as well as in particulates, producing a higher quality sterile product that is suitable for aseptic processing.
Electrical energy is linearly translated to thermal energy as electrical conductivity increases, and this is the key process parameter that affects heating uniformity and heating rate. This heating method is best for foods that contain particulates suspended in a weak salt containing medium due to their high resistance properties. Ohmic heating is beneficial due to its ability to inactivate microorganisms through thermal and non-thermal cellular damage.
This method can also inactivate antinutritional factors thereby maintaining nutritional and sensory properties. However, ohmic heating is limited by viscosity, electrical conductivity, and fouling deposits. Although ohmic heating has not yet been approved by the Food and Drug Administration (FDA) for commercial use, this method has many potential applications, ranging from cooking to fermentation.
There are different configurations for continuous ohmic heating systems, but in the most basic process, a power supply or generator is needed to produce electrical current. Electrodes, in direct contact with food, pass electric current through the matrix. The distance between the electrodes can be adjusted to achieve the optimum electrical field strength.
The generator creates the electrical current which flows to the first electrode and passes through the food product placed in the electrode gap. The food product resists the flow of current causing internal heating. The current continues to flow to the second electrode and back to the power source to close the circuit. The insulator caps around the electrodes controls the environment within the system.
The electrical field strength and the residence time are the key process parameters which affect heat generation.
The ideal foods for ohmic heating are viscous with particulates.
Thick soups Sauces Stews Salsa Fruit in a syrup medium Milk Ice cream mix Egg Whey Heat sensitive liquids Soymilk