Thermocouples

Type of physical science: Condensed matter physics

Field of study: Solids

Thermocouples determine temperature differences, relative to a reference junction, by monitoring electromotive forces in systems consisting of junctions between dissimilar, electrically conducting materials. This useful temperature measurement technique involves low thermal masses and responds quickly to temperature changes.

Overview

Thermoelectricity involves the study of energy transfer by charged particles flowing through electrical conductors as a result of thermal gradients. Different electrically conducting materials promote charge carrier diffusion throughout their volume at rates determined by atomic structure. Consider a pair of thermal reservoirs at temperatures T₁ and T₂ separated physically from each other. The reservoir at temperature T₁ is referred to as the reference reservoir, and the one at temperature T₂ is the test reservoir. These reservoirs are connected by a pair of dissimilar metallic conductors. Both conductors are joined at a junction where they are in thermal contact with each thermal reservoir. At no other point in the space between the two reservoirs are the dissimilar metallic conductors in physical or thermal contact. A number of thermoelectric effects can be observed simultaneously in this system.

Charge carrier density is determined by atomic structure; in other words, the number of free electrons per unit volume and the mobility of those electrons are different in the two metals.

Thus, diffusion of charge carriers in each metal connected between the pair of thermal reservoirs will not be equivalent. As a result, there will be a thermal emf (electromotive force) across the combination of connected dissimilar metals. The production of such a thermal emf is called the Seebeck effect. It is the fundamental operating principle of a practical device called a thermocouple, which is often used for temperature measurement in the laboratory.

The net motion of charge carriers in the dissimilar metals could be described as driven by an electric field of nonelectrostatic origin. Using the relationship defining electric potential in terms of electric field, the thermal emf can be calculated by evaluating the line integral of this nonelectrostatic field around the two dissimilar metals joined at each of the two thermal reservoirs. This Seebeck potential difference is a function of the temperature difference between the two reservoirs. The exact value of the Seebeck effect is determined by the given value of the reference junction temperature and the temperature difference between the two reservoirs. The rate of change of thermal emf with reservoir temperature difference is independent of the value of the reference temperature T₁. This rate is referred to as the thermoelectric power or Seebeck coefficient of the junction of dissimilar metals. For many common pairs of materials used to construct thermocouples, the thermoelectric power is in the range of several microvolts per unit degree Celsius. Thus, for many thermocouples, the Seebeck emf is a small effect, significantly observable only when there is a reservoir temperature difference of more than 100 degrees Celsius.

Because the Seebeck emf is not externally compensated by external sources, it will result in a current, or a flow of free charge carriers, through the thermocouple. When current passes through a normal conductor (possessing resistance to the flow of electrical charge under the influence of an emf ), heat is generated and dissipated within the conductor. The power dissipated in this Joule heating effect is given by I²R, where I represents the current and R is the resistance of the conducting material.

Suppose that the temperatures T₁ and T₂ of the two reservoirs joined by the thermo-couple are identical. If an external emf (not of thermal origin) is established across the thermocouple, a current will flow in a direction determined by the sense of the external emf. This current will alter the temperature of the thermocouple junctions by conduction of heat in excess of that produced by Joule heating alone. The heat conduction is determined by the current flow direction; whereas Joule heating can raise only the temperature of a junction, this effect, known as Peltier heating, can either raise or lower the junction temperature. Peltier heating is reversible, whereas Joule heating is irreversible. The Peltier heat production rate is proportional to the current flow. The constant of proportionality is called the Peltier coefficient or Peltier power. Its value for a given junction of dissimilar materials depends only on the temperature of that junction and the composition of the junction materials.

Along the different materials that make up the thermocouple attached to the two reservoirs, there exists a thermal gradient. The distribution of temperature along the length of each side of the thermocouple is uniform if the material contains no defects or impurities. When a current passes through each side of the thermocouple, excess heat beyond the Joule heating effect will be produced. This effect is known as Thomson heat. The current flow direction determines whether that heat is absorbed or reflected. Thus, like the Peltier effect, the Thomson effect is reversible. The power of Thomson heat transfer is proportional to the product of the current and thermal gradient. The constant of proportionality, called the Thomson coefficient, is determined by the composition of the material and the average temperature. Unlike the Seebeck and Peltier effects, which involve two dissimilar materials, the Thomson effect occurs in a single material. The Seebeck, Peltier, and Thomson coefficients are not independent of one another.

Thermodynamic formalism relates the three coefficients using a pair of equations, one of a differential nature and one of an algebraic form, known as Kelvin relations.

Because the Peltier and Thomson effects are reversible, it is possible to use these effects with a suitably directed current flow to lower temperature. This simple process forms the basis of the process of thermoelectric refrigeration. Thermoelectric effects also can be used to generate electricity directly from thermal gradients.

Applications

The primary application of thermoelectric properties of current-carrying materials is the thermocouple. The basic thermocouple design consists of a pair of dissimilar conductors in the form of wires joined together to construct two junctions of the dissimilar conductors in series.

The two unconnected wires must be made of the same conducting material. The wires of the other conducting material connect the two junctions together in series. The reference junction is inserted into a thermal reservoir of known temperature. The test junction is in good thermal contact with the object whose temperature is being measured via the Seebeck effect.

To be useful, a thermocouple must be calibrated accurately. The thermocouple must be placed in thermal equilibrium with materials at precisely known temperatures. Depending upon the size of the temperature range for which the thermocouple is meant to be useful, the number of calibration points varies, as does the degree of the polynomial fit between measured thermal emf and temperature. Usually, a quartic fit is sufficient over a temperature range of several hundred degrees Celsius. Once calibrated against a sufficient number of known temperatures, the thermocouple can be used to ascertain unknown temperatures by measuring experimentally the thermal emf generated across the two junctions. Thermocouples are particularly useful when determining the temperature of small amounts of a substance. Because the junction has such small thermal mass, thermal equilibrium between the test junction and the sample is rapidly reached. As a result, relatively rapid changes in temperature of the sample can be monitored. One practical difficulty in using a thermocouple involves keeping the wires that are connected to a digital voltmeter or potentiometer at constant temperature and vibration-free. Temperature and vibration changes can alter the emf read by the meter beyond the generated thermal emfs that are indicative of the sample's temperature.

The choice of thermocouple depends on the temperature range for which it will be used. An upper limit of availability is the lower melting point of the two materials used to construct the thermocouple. High-melting-point metals, such as platinum and platinum-rhodium, are used for high-temperature measurement (above 1,000 degrees Celsius). Commonly used thermocouple materials and alloys include iron, copper, constantan, alumel, chromel, platinum-rhodium, and platinum. Such materials are chosen because of their high melting points and (when used in pairs) thermoelectric powers. Some of these materials have thermoelectric powers as large as 40 microvolts per degree Celsius. Occasionally, semiconducting materials with thermoelectric powers as high as about 1 millivolt per degree Celsius will be used to construct a thermocouple. Voltmeter accuracy determines which materials can be used for thermocouples in some applications.

A thermopile is useful in measuring very small temperature differences for which the thermal emf that is produced will be small. It consists of a number of identical thermocouples placed in series with each other. One junction of each thermocouple in the thermopile is in thermal equilibrium with the reference reservoir. The other junctions are in thermal contact with the sample. Each thermocouple generates the same thermal emf; and by being connected in series, the total thermal emf across the entire thermopile is the linear sum of the individual thermal emfs. This larger voltage can be read more easily and be corrected to determine the sample temperature.

Powders of specially heat-treated Y-Ba-Cu-O can be pressed under high pressure into the shape of thin disks to make high-temperature superconductors. Superconductivity is a unique state of electrical conduction without resistance. This property is lost in a phase transition from the superconducting state to normal conductivity at a critical temperature. Measurement of the superconducting property can be accomplished using a technique referred to as a four-point probe. Four wires are connected to the sample disk. Two wires carry applied current and the other two measure the voltage between two points on the disk. Resistance, which is the voltage divided by the current, is monitored as a function of temperature as the sample is either cooled or warmed. Below the critical temperature, the resistance of the superconductor vanishes; above the critical temperature, the sample resistance rises abruptly. A thermocouple can be included in the preparation of the sample disk so that the test junction of the thermocouple is a part of the sample. In such good thermal contact, the test junction of the thermocouple can respond quickly to temperature changes in the sample, which permits an accurate determination of the superconductor's critical temperature.

Context

The history of thermoelectrical understanding is intimately linked to the developments of electromagnetism and thermodynamics. As with most scientific endeavors, practical use of an identified phenomenon occurs well after the initial discovery. Thermocouples remained an experimental curiosity until the thermoelectric properties of many pairs of dissimilar conducting or semiconducting metals were thoroughly investigated and categorized. Measurement of temperature by thermocouple has become a standard experimental technique for temperatures ranging from near absolute zero to the melting points of many common metals and is used in pure physics research laboratories and in the industrial applied research community.

In 1821, Thomas Johann Seebeck demonstrated that an electric current flows between different conductive materials that are kept at different temperatures--the Seebeck effect.

Thermoelectric power, the constant of proportionality between thermal emf and junction temperature difference, is also referred to as the Seebeck coefficient of a thermocouple. This latter designation is perhaps more appropriate, since the dimensionality of thermoelectric power is not energy per unit time as is a normal power rating. Jean-Charles-Athanase Peltier first demonstrated the Peltier effect in 1834. The constant of proportionality between the heat production in excess of Joule heating and the current density flowing through the junction of a thermocouple bears Peltier's name as well. William Thomson, Lord Kelvin, first predicted the Thomson effect in 1854. Lord Kelvin also predicted this phenomenon on theoretical grounds.

Several years later, he experimentally demonstrated excess heat generation in a current-carrying conductor exposed to a thermal gradient. The coefficient relating the excess heat thus generated to the product of current density and thermal gradient bears Thomson's name. Thermodynamic theory eventually related the Seebeck, Peltier, and Thomson coefficients to one another through standard Kelvin relations.

From these basic thermoelectric properties, a host of applications followed, such as the thermocouple, thermopile, thermoelectric power generation, and thermoelectric refrigeration.

Principal terms

CURRENT DENSITY: current flow per unit cross-sectional area in an electrically conducting material

JOULE HEAT: irreversible heat dissipated within an electrical conductor by virtue of current flow

REFERENCE JUNCTION: a connection of dissimilar metals in good thermal contact with a thermal reservoir at a known temperature

THERMAL ELECTROMOTIVE FORCE: a potential difference generated solely by temperature differences

THERMAL GRADIENT: a temperature difference spread over a spatial extent

THERMOCOUPLE: a thermometer that uses thermoelectrical properties of dissimilar metals to monitor temperature differences relative to a selected reference

THERMOELECTRIC POWER: for a junction between dissimilar materials, the ratio of thermoelectric potential difference to the temperature difference between test and reference junctions

THERMOMETER: a device that uses a particular practical temperature scale to measure temperature

THOMSON HEAT: reversible heat given off or absorbed by an electrical conductor that is subjected to a thermal gradient

Bibliography

Besancon, Robert M., ed. THE ENCYCLOPEDIA OF PHYSICS. 2d ed. New York: Van Nostrand Reinhold, 1974. A thorough compendium of all aspects of physics. Graphs and illustrations.

Morse, Philip M. THERMAL PHYSICS. New York: W. A. Benjamin, 1969. Thorough discussion of thermodynamics. Thermoelectric effects are presented from a theoretical standpoint.

Reif, Frederick. FUNDAMENTALS OF STATISTICAL AND THERMAL PHYSICS. New York: McGraw-Hill, 1965. Excellent treatise on all aspects of thermodynamics. Describes thermoelectric effects that are pertinent to the operation of a thermocouple.

Wedlock, Bruce D., and James K. Roberge. ELECTRONIC COMPONENTS AND MEASUREMENTS. Englewood Cliffs, N.J.: Prentice-Hall, 1969. Practical examples of thermocouple use in experimentation. Basic electronics principles presented in a manner accessible to the hobbyist.

Zemansky, Mark W. HEAT AND THERMODYNAMICS. New York: McGraw-Hill, 1968. A classic intermediate textbook for undergraduate instruction in thermodynamics. Excellent treatment of thermoelectric effects. Includes a theoretical description of thermocouple principles.

Thermal Properties of Solids

Thermal Properties of Matter