temperature

1. 1. The degree of hotness or coldness of a body or environment.
   2. A measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale.
2. 1. The degree of heat in the body of a living organism, usually about 37.0°C (98.6°F) in humans.
   2. An abnormally high condition of body heat caused by illness; a fever.

[Middle English, temperate weather, Latin temperātūra, due measure, from temperātus, past participle of temperāre, to mix. See temper.]

Concept

Temperature is one of those aspects of the everyday world that seems rather abstract when viewed from the standpoint of physics. In scientific terms, it is not simply a measure of hot and cold, but an indicator of molecular motion and energy flow. Thermometers measure temperature by a number of means, including the expansion that takes place in a medium such as mercury or alcohol. These measuring devices are gauged in several different ways, with scales based on the freezing and boiling points of water—as well as, in the case of the absolute temperature scale, the point at which all molecular motion virtually ceases.

How It Works

Heat

Energy appears in many forms, including thermal energy, or the energy associated with heat. Heat is internal thermal energy that flows from one body of matter to another—or, more specifically, from a system at a higher temperature to one at a lower temperature.

Two systems at the same temperature are said to be in a state of thermal equilibrium. When this occurs, there is no exchange of heat. Though people ordinarily speak of "heat" as an expression of relative warmth or coldness, in physical terms, heat only exists in transfer between two systems. It is never something inherently part of a system; thus, unless there is a transfer of internal energy, there is no heat, scientifically speaking.

Heat: Energy in Transit

Thus, heat cannot be said to exist unless there is one system in contact with another system of differing temperature. This can be illustrated by way of the old philosophical question: "If a tree falls in the woods when there is no one to hear it, does it make a sound?" From a physicist's point of view, of course, sound waves are emitted whether or not there is an ear to receive their vibrations; but, consider this same scenario in terms of heat. First, replace the falling tree with a hypothetical object possessing a certain amount of internal energy; then replace sound waves with heat. In this case, if this object is not in contact with something else that has a different temperature, it "does not make a sound"—in other words, it transfers no internal energy, and, thus, there is no heat from the standpoint of physics.

This could even be true of two incredibly "hot" objects placed next to one another inside a vacuum—an area devoid of matter, including air. If both have the same temperature, there is no heat, only two objects with high levels of internal energy. Note that a vacuum was specified: assuming there was air around them, and that the air was of a lower temperature, both objects would then be transferring heat to the air.

Relative Motion Between Molecules

If heat is internal thermal energy in transfer, from whence does this energy originate? From the movement of molecules. Every type of matter is composed of molecules, and those molecules are in motion relative to one another. The greater the amount of relative motion between molecules, the greater the kinetic energy, or the energy of movement, which is manifested as thermal energy. Thus, "heat"—to use the everyday term for what physicists describe as thermal energy—is really nothing more than the result of relative molecular motion. Thus, thermal energy is sometimes identified as molecular translational energy.

Note that the molecules are in relative motion, meaning that if one were "standing" on a molecule, one would see the other molecules moving. This is not the same as movement on the part of a large object composed of molecules; in this case, molecules themselves are not directly involved in relative motion.

Put another way, the movement of Earth through space is an entirely different type of movement from the relative motion of objects on Earth—people, animals, natural forms such as clouds, manmade forms of transportation, and so forth. In this example, Earth is analogous to a "large" item of matter, such as a baseball, a stream of water, or a cloud of gas.

The smaller objects on Earth are analogous to molecules, and, in both cases, the motion of the larger object has little direct impact on the motion of smaller objects. Hence, as discussed in the Frame of Reference essay, it is impossible to perceive with one's senses the fact that Earth is actually hurling through space at incredible speeds.

Molecular Motion and Phases of Matter

The relative motion of molecules determines phase of matter—that is, whether something is a solid, liquid, or gas. When molecules move quickly in relation to one another, they exert a small electromagnetic attraction toward one another, and the larger material of which they are a part is called a gas. A liquid, on the other hand, is a type of matter in which molecules move at moderate speeds in relation to one another, and therefore exert a moderate intermolecular attraction.

The kinetic theory of gases relates molecular motion to energy in gaseous substances. It does not work as well in relation to liquids and solids; nonetheless, it is safe to say that—generally speaking—a gas has more energy than a liquid, and a liquid more energy than a solid. In a solid, the molecules undergo very little relative motion: instead of bumping into each other, like gas molecules and (to a lesser extent) liquid molecules, solid molecules merely vibrate in place.

Understanding Temperature

As with heat, temperature requires a scientific definition quite different from its common meaning. Temperature may be defined as a measure of the average molecular translational energy in a system—that is, in any material body.

Because it is an average, the mass or other characteristics of the body do not matter. A large quantity of one substance, because it has more molecules, possesses more thermal energy than a smaller quantity of that same substance. Since it has more thermal energy, it transfers more heat to any body or system with which it is in contact. Yet, assuming that the substance is exactly the same, the temperature, as a measure of average energy, will be the same as well.

Temperature determines the direction of internal energy flow between two systems when heat is being transferred. This can be illustrated through an experience familiar to everyone: having one's temperature taken with a thermometer. If one has a fever, one's mouth will be warmer than the thermometer, and therefore heat will be transferred to the thermometer from the mouth until the two objects have the same temperature. At that point of thermal equilibrium, a temperature reading can be taken from the thermometer.

Temperature and Heat Flow

The principles of thermodynamics—the study of the relationships between heat, work, and energy, show that heat always flows from an area of higher temperature to an area of lower temperature. The opposite simply cannot happen, because coldness, though it is very real in terms of sensory experience, is not an independent phenomenon. There is not, strictly speaking, such a thing as "cold"—only the absence of heat, which produces the sensation of coldness.

One might pour a kettle of boiling water into a cold bathtub to heat it up; or put an ice cube in a hot cup of coffee "to cool it down." These seem like two very different events, but from the standpoint of thermodynamics, they are exactly the same. In both cases, a body of high temperature is placed in contact with a body of low temperature, and in both cases, heat passes from the high-temperature body to the low-temperature one.

The boiling water warms the tub of cool water, and due to the high ratio of cool water to boiling water in the bathtub, the boiling water expends all its energy raising the temperature in the bathtub as a whole. The greater the ratio of very hot water to cool water, on the other hand, the warmer the bathtub will be in the end. But even after the bath water is heated, it will continue to lose heat, assuming the air in the room is not warmer than the water in the tub. If the water in the tub is warmer than the air, it immediately begins transferring thermal energy to the low-temperature air until their temperatures are equalized.

As for the coffee and the ice cube, what happens is quite different from, indeed, opposite to, the common understanding of the process. In other words, the ice does not "cool down" the coffee: the coffee warms up the ice and presumably melts it. Once again, however, it expends at least some of its thermal energy in doing so, and as a result, the coffee becomes cooler than it was.

If the coffee is placed inside a freezer, there is a large temperature difference between it and the surrounding environment—so much so that if it is left for hours, the once-hot coffee will freeze. But again, the freezer does not cool down the coffee; the molecules in the coffee respond to the temperature difference by working to warm up the freezer. In this case, they have to "work overtime," and since the freezer has a constant supply of electrical energy, the heated molecules of the coffee continue to expend themselves in a futile effort to warm the freezer. Eventually, the coffee loses so much energy that it is frozen solid; meanwhile, the heat from the coffee has been transferred outside the freezer to the atmosphere in the surrounding room.

Thermal Expansion and Equilibrium

Temperature is related to the concept of thermal equilibrium, and has an effect on thermal expansion. As discussed below, as well as within the context of thermal expansion, a thermometer provides a gauge of temperature by measuring the level of thermal expansion experienced by a material (for example, mercury) within the thermometer.

In the examples used earlier—the thermometer in the mouth, the hot water in the cool bathtub, and the ice cube in the cup of coffee—the systems in question eventually reach thermal equilibrium. This is rather like averaging their temperatures, though, in fact, the equation involved is more complicated than a simple arithmetic average.

In the case of an ordinary mercury thermometer, the need to achieve thermal equilibrium explains why one cannot get an instantaneous temperature reading: first, the mouth transfers heat to the thermometer, and once both mouth and thermometer reach the same temperature, they are in thermal equilibrium. At that point, it is possible to gauge the temperature of the mouth by reading the thermometer.

Real-Life Applications

Development of the Thermometer

A thermometer can be defined scientifically as a device that gauges temperature by measuring a temperature-dependent property, such as the expansion of a liquid in a sealed tube. As with many aspects of scientific or technological knowledge, the idea of the thermometer appeared in ancient times, but was never developed. Again, like so many other intellectual phenomena, it lay dormant during the medieval period, only to be resurrected at the beginning of the modern era.

The Greco-Roman physician Galen (c. 129-216) was among the first thinkers to envision a scale for measuring temperature. Of course, what he conceived of as "temperature" was closer to the everyday meaning of that term, not its more precise scientific definition: the ideas of molecular motion, heat, and temperature discussed in this essay emerged only in the period beginning about 1750. In any case, Galen proposed that equal amounts of boiling water and ice be combined to establish a "neutral" temperature, with four units of warmth above it and four degrees of cold below.

The Thermoscope

The great physicist Galileo Galilei (1564-1642) is sometimes credited with creating the first practical temperature measuring device, called a thermoscope. Certainly Galileo—whether or not he was the first—did build a thermoscope, which consisted of a long glass tube planted in a container of liquid. Prior to inserting the tube into the liquid—which was usually colored water, though Galileo's thermoscope used wine—as much air as possible was removed from the tube. This created a vacuum, and as a result of pressure differences between the liquid and the interior of the thermoscope tube, some of the liquid went into the tube.

But the liquid was not the thermometric medium—that is, the substance whose temperature-dependent property changes the thermoscope measured. (Mercury, for instance, is the thermometric medium in most thermometers today.) Instead, the air was the medium whose changes the thermoscope measured: when it was warm, the air expanded, pushing down on the liquid; and when the air cooled, it contracted, allowing the liquid to rise.

It is interesting to note the similarity in design between the thermoscope and the barometer, a device for measuring atmospheric pressure invented by Italian physicist Evangelista Torricelli (1608-1647) around the same time. Neither were sealed, but by the mid-seventeenth century, scientists had begun using sealed tubes containing liquid instead of air. These were the first true thermometers.

Early Thermometers

Ferdinand II, Grand Duke of Tuscany (1610-1670), is credited with developing the first thermometer in 1641. Ferdinand's thermometer used alcohol sealed in glass, which was marked with a temperature scale containing 50 units. It did not, however, designate a value for zero.

English physicist Robert Hooke (1635-1703) created a thermometer using alcohol dyed red. Hooke's scale was divided into units equal to about 1/500 of the volume of the thermometric medium, and for the zero point, he chose the temperature at which water freezes. Thus, Hooke established a standard still used today; likewise, his thermometer itself set a standard. Built in 1664, it remained in use by the Royal Society—the foremost organization for the advancement of science in England during the early modern period—until 1709.

Olaus Roemer (1644-1710), a Danish astronomer, introduced another important standard. In 1702, he built a thermometer based not on one but two fixed points, which he designated as the temperature of snow or crushed ice, and the boiling point of water. As with Hooke's use of the freezing point, Roemer's idea of the freezing and boiling points of water as the two parameters for temperature measurements has remained in use ever since.

Temperature Scales

Fahrenheit

Not only did he develop the Fahrenheit scale, oldest of the temperature scales still used in Western nations today, but German physicist Daniel Fahrenheit (1686-1736) also built the first thermometer to contain mercury as a thermometric medium. Alcohol has a low boiling point, whereas mercury remains fluid at a wide range of temperatures. In addition, it expands and contracts at a very constant rate, and tends not to stick to glass. Furthermore, its silvery color makes a mercury thermometer easy to read.

Fahrenheit also conceived the idea of using "degrees" to measure temperature in his thermometer, which he introduced in 1714. It is no mistake that the same word refers to portions of a circle, or that exactly 180 degrees—half the number in a circle—separate the freezing and boiling points for water on Fahrenheit's thermometer. Ancient astronomers attempting to denote movement in the skies used a circle with 360 degrees as a close approximation of the ratio between days and years. The number 360 is also useful for computations, because it has a large quantity of divisors, as does 180—a total of 16 whole-number divisors other than 1 and itself.

Though it might seem obvious that 0 should denote the freezing point and 180 the boiling point on Fahrenheit's scale, such an idea was far from obvious in the early eighteenth century. Fahrenheit considered the idea not only of a 0-to-180 scale, but also of a 180-to-360 scale. In the end, he chose neither—or rather, he chose not to equate the freezing point of water with zero on his scale. For zero, he chose the coldest possible temperature he could create in his laboratory, using what he described as "a mixture of sal ammoniac or sea salt, ice, and water." Salt lowers the melting point of ice (which is why it is used in the northern United States to melt snow and ice from the streets on cold winter days), and, thus, the mixture of salt and ice produced an extremely cold liquid water whose temperature he equated to zero.

With Fahrenheit's scale, the ordinary freezing point of water was established at 32°, and the boiling point exactly 180° above it, at 212°. Just a few years after he introduced his scale, in 1730, a French naturalist and physicist named Rene Antoine Ferchault de Reaumur (1683-1757) presented a scale for which 0° represented the freezing point of water and 80° the boiling point. Although the Reaumur scale never caught on to the same extent as Fahrenheit's, it did include one valuable addition: the specification that temperature values be determined at standard sea-level atmospheric pressure.

Celsius

With its 32-degree freezing point and its 212-degree boiling point, the Fahrenheit system is rather ungainly, lacking the neat orderliness of a decimal or base-10 scale. The latter quality became particularly important when, 10 years after the French Revolution of 1789, France adopted the metric system for measuring length, mass, and other physical phenomena. The metric system eventually spread to virtually the entire world, with the exception of English-speaking countries, where the more cumbersome British system still prevails. But even in the United States and Great Britain, scientists use the metric system. The metric temperature measure is the Celsius scale, created in 1742 by Swedish astronomer Anders Celsius (1701-1744).

Like Fahrenheit, Celsius chose the freezing and boiling points of water as his two reference points, but he determined to set them 100, rather than 180, degrees apart. Interestingly, he planned to equate 0° with the boiling point, and 100° with the freezing point—proving that even the most apparently obvious aspects of a temperature scale were once open to question. Only in 1750 did fellow Swedish physicist Martin Strömer change the orientation of the Celsius scale.

Celsius's scale was based not simply on the boiling and freezing points of water, but, specifically, those points at normal sea-level atmospheric pressure. The latter, itself a unit of measure known as an atmosphere (atm), is equal to 14.7 lb/in², or 101,325 pascals in the metric system. A Celsius degree is equal to 1/100 of the difference between the freezing and boiling temperatures of water at 1 atm.

The Celsius scale is sometimes called the centigrade scale, because it is divided into 100 degrees, cent being a Latin root meaning "hundred." By international convention, its values were refined in 1948, when the scale was redefined in terms of temperature change for an ideal gas, as well as the triple point of water. (Triple point is the temperature and pressure at which a substance is at once a solid, liquid, and vapor.) As a result of these refinements, the boiling point of water on the Celsius scale is actually 99.975°. This represents a difference equal to about 1 part in 4,000—hardly significant in daily life, though a significant change from the standpoint of the precise measurements made in scientific laboratories.

Kelvin

In about 1787, French physicist and chemist J. A. C. Charles (1746-1823) made an interesting discovery: that at 0°C, the volume of gas at constant pressure drops by 1/273 for every Celsius degree drop in temperature. This seemed to suggest that the gas would simply disappear if cooled to −273°C, which, of course, made no sense. In any case, the gas would most likely become first a liquid, and then a solid, long before it reached that temperature.

The man who solved the quandary raised by Charles's discovery was born a year after Charles—who also formulated Charles's law—died. He was William Thomson, Lord Kelvin (1824-1907), and in 1848, he put forward the suggestion that it was molecular translational energy, and not volume, that would become zero at −273°C. He went on to establish what came to be known as the Kelvin scale.

Sometimes known as the absolute temperature scale, the Kelvin scale is based not on the freezing point of water, but on absolute zero—the temperature at which molecular motion comes to a virtual stop. This is −273.15°C (−459.67°F), which in the Kelvin scale is designated as 0K. (Kelvin measures do not use the term or symbol for "degree.")

Though scientists normally use metric or SI measures, they prefer the Kelvin scale to Celsius, because the absolute temperature scale is directly related to average molecular translational energy. Thus, if the Kelvin temperature of an object is doubled, this means that its average molecular translational energy has doubled as well. The same cannot be said if the temperature were doubled from, say, 10°C to 20°C, or from 40°C to 80°F, since neither the Celsius nor the Fahrenheit scale is based on absolute zero.

Conversions

The Kelvin scale is, however, closely related to the Celsius scale, in that a difference of 1 degree measures the same amount of temperature in both. Therefore, Celsius temperatures can be converted to Kelvins by adding 273.15. There is also an absolute temperature scale that uses Fahrenheit degrees. This is the Rankine scale, created by Scottish engineer William Rankine (1820-1872), but it is seldom used today: scientists and others who desire absolute temperature measures prefer the precision and simplicity of the Celsius-based Kelvin scale.

Conversion between Celsius and Fahrenheit figures is a bit more challenging. To convert a temperature from Celsius to Fahrenheit, multiply by 9/5 and add 32. It is important to perform the steps in that order, because reversing them will produce a wrong answer. Thus, 100°C multiplied by 9/5 or 1.8 equals 180, which, when added to 32 equals 212°F. Obviously, this is correct, since 100°C and 212°F each represent the boiling point of water. But, if one adds 32 to 100°, then multiplies it by 9/5, the result is 237.6°F—an incorrect answer.

For converting Fahrenheit temperatures to Celsius, there are also two steps, involving multiplication and subtraction, but the order is reversed. Here, the subtraction step is performed before the multiplication step: thus, 32 is subtracted from the Fahrenheit temperature, then the result is multiplied by 5/9. Beginning with 212°F, if 32 is subtracted, this equals 180. Multiplied by 5/9, the result is 100°C—the correct answer.

One reason the conversion formulae use fractions instead of decimal fractions (what most people simply call "decimals") is that 5/9 is a repeating decimal fraction (0.55555….) Further more, the symmetry of 5/9 and 9/5 makes memorization easy. One way to remember the formula is that F ahrenheit is multiplied by a f raction—since 5/9 is a real fraction, whereas 9/5 is actually a whole number plus a fraction.

Thermometers

As discussed earlier, with regard to the early history of the thermometer, it is important that the glass tube be kept sealed; otherwise, atmospheric pressure contributes to inaccurate readings, because it influences the movement of the thermometric medium. Also important is the choice of the thermometric medium itself.

Water quickly proved unreliable, due to its unusual properties: it does not expand uniformly with a rise in temperature, or contract uniformly with a lowered temperature. Rather, it reaches its maximum density at 39.2°F (4°C), and is less dense both above and below that temperature. Therefore, alcohol, which responds in a much more uniform fashion to changes in temperature, took its place.

Mercury Thermometers

Alcohol is still used in thermometers today, but the preferred thermometric medium is mercury. As noted earlier, its advantages include a much higher boiling point, a tendency not to stick to glass, and a silvery color that makes its levels easy to gauge visually. Like alcohol, mercury expands at a uniform rate with an increase in temperature: hence, the higher the temperature, the higher the mercury stands in the thermometer.

In a typical mercury thermometer, mercury is placed in a long, narrow sealed tube called a capillary. The capillary is inscribed with figures for a calibrated scale, usually in such a way as to allow easy conversions between Fahrenheit and Celsius. A thermometer is calibrated by measuring the difference in height between mercury at the freezing point of water, and mercury at the boiling point of water. The interval between these two points is then divided into equal increments—180, as we have seen, for the Fahrenheit scale, and 100 for the Celsius scale.

Electric Thermometers

Faster temperature measures can be obtained by thermometers using electricity. All matter displays a certain resistance to electrical current, a resistance that changes with temperature. Therefore, a resistance thermometer uses a fine wire wrapped around an insulator, and when a change in temperature occurs, the resistance in the wire changes as well. This makes possible much quicker temperature readings than those offered by a thermometer containing a traditional thermometric medium.

Resistance thermometers are highly reliable, but expensive, and are used primarily for very precise measurements. More practical for everyday use is a thermistor, which also uses the principle of electric resistance, but is much simpler and less expensive. Thermistors are used for providing measurements of the internal temperature of food, for instance, and for measuring human body temperature.

Another electric temperature-measurement device is a thermocouple. When wires of two different materials are connected, this creates a small level of voltage that varies as a function of temperature. A typical thermocouple uses two junctions: a reference junction, kept at some constant temperature, and a measurement junction. The measurement junction is applied to the item whose temperature is to be measured, and any temperature difference between it and the reference junction registers as a voltage change, which is measured with a meter connected to the system.

Other Types of Thermometer

A pyrometer also uses electromagnetic properties, but of a very different kind. Rather than responding to changes in current or voltage, the pyrometer is a gauge that responds to visible and infrared radiation. Temperature and color are closely related: thus, it is no accident that greens, blues, and purples, at one end of the visible light spectrum, are associated with coolness, while reds, oranges, and yellows at the other end are associated with heat. As with the thermocouple, a pyrometer has both a reference element and a measurement element, which compares light readings between the reference filament and the object whose temperature is being measured.

Still other thermometers, such as those in an oven that tell the user its internal temperature, are based on the expansion of metals with heat. In fact, there are a wide variety of thermometers, each suited to a specific purpose. A pyrometer, for instance, is good for measuring the temperature of an object that the thermometer itself does not touch.

Where to Learn More

About Temperature (Web site). <http://www.unidata.ucar.edu/staff/blynds/tmp.html> (April 18, 2001).

About Temperature Sensors (Web site). <http://www.temperatures.com> (April 18, 2001).

Gardner, Robert. Science Projects About Methods of Measuring. Berkeley Heights, N.J.: Enslow Publishers, 2000.

Maestro, Betsy and Giulio Maestro. Temperature and You. New York: Macmillan/McGraw-Hill School Publishing, 1990.

Megaconverter (Web site). <http://www.megaconverter.com> (April 18, 2001).

NPL: National Physics Laboratory: Thermal Stuff: Beginners' Guides (Web site). <http://www.npl.co.uk/npl/cbtm/thermal/stuff/guides.html> (April 18, 2001).

Royston, Angela. Hot and Cold. Chicago: Heinemann Library, 2001.

Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, N.J.: Troll Associates, 1985.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

Walpole, Brenda. Temperature. Illustrated by Chris Fairclough and Dennis Tinkler. Milwaukee, WI: Gareth Stevens Publishing, 1995.

A concept related to the flow of heat from one object or region of space to another. The term refers not only to the senses of hot and cold but to numerical scales and thermometers as well. Fundamental to the concept are the absolute scale and absolute zero and the relation of absolute temperatures to atomic and molecular motions.

Thermometers do not measure a special physical quantity. They measure length (as of a mercury column) or pressure or volume (with the gas thermometer at the National Institute of Standards and Technology) or electrical voltage (with a thermocouple). The basic fact is that if a mercury column has the same length when touching two different, separated objects when the objects are placed in contact, no heat will flow from one to the other. See also Thermometer.

The numbers on the thermometer scales are merely historical choices; they are not scientifically fundamental. The most widely used scales are the Fahrenheit (°F) and the Celsius (°C). The centigrade scale with 0° assigned to ice water (ice point) and 100° assigned to water boiling under one atmosphere pressure (steam point) was formerly used, but it has been succeeded by the Celsius scale, defined in a different way than the centigrade scale. However, on the Celsius scale the temperatures of the ice and steam points differ by only a few hundredths of a degree from 0° and 100°, respectively.See also Ice point.

In 1848 William Thomson (Lord Kelvin), following ideas of Sadi Carnot, stated the concept of an absolute scale of temperature in terms of measuring amounts of heat flowing between objects. Most important, Kelvin conceived of a body which would not give up any heat and which was at an absolute zero of temperature. Experiments have shown that absolute zero corresponds to −273.15°C or −459.7°F.

In practice, absolute temperatures are measured by using low-density helium gas and dilute paramagnetic crystals, the most nearly ideal of real materials. The measurement of a single temperature with a gas or magnetic thermometer is a major scientific event done at a national standards laboratory. Only a few temperatures have been measured, including the freezing point of gold (1337.91 K or 1948.57°F), and the boiling points of sulfur (717.85 K or 832.46°F), oxygen (90.18 K or −297.35°F), and helium (4.22 K or −452.07°F). Various types of thermometers (platinum, carbon, and doped germanium resistors; thermocouples) are calibrated at these temperatures and used to measure intermediate temperatures. See also Temperature measurement; Thermodynamic principles.

The degree of sensible heat or cold.

The standard temperature scale of science and most of the world is Celsius, with its zero at the freezing point of water; the absolute thermodynamic or kelvin scale has its unit the kelvin (K) of identical size but its zero at the thermodynamic null. For scientific accuracy over a vast range, the thermodynamic scale exists in a ‘practical’ form as the international temperature scale. The Fahrenheit scale and its ‘absolute’ version, the Rankine, are of comparable vintage to the Celsius and kelvin, and have enjoyed major use, but are now little used outside the USA. Their degree is only ⁵/₉ K or degree C, while the Fahrenheit zero is well below the freezing point of water, which is 32°F. The Réaumur scale is the next most common of the many scales that have been introduced, but sees no significant use in modern times; it has zero at freezing point but a degree equal to ⁵/₄ K. Notable comparative points are shown in Table 54.

For more information on temperature, visit Britannica.com.

A measure of hotness; a property that determines the rate at which heat will be transferred between bodies that are in direct contact: heat flows from regions of high temperature to regions of low temperature. In science, temperature is expressed in terms of degrees kelvin or degrees Celsius.

The degree of sensible heat or cold, expressed in terms of a specific scale. See also hypothermia, hyperthermia.

• absolute t. — that reckoned from absolute zero (−459.67°F or −273.15°C).
• air t. — the temperature of the surrounding air as measured by a dry-bulb thermometer.
• ambient t. — temperature of the immediate environment.
• body t. — a prime technique for assessing health status of a patient. Always a rectal temperature. Average temperatures above which hyperthermia, pyrexia or fever can be said to occur are listed under pyrexia.
• critical t. — 1. that below which a gas may be converted to a liquid by pressure.
— 2. the environmental temperature at which the body is unable to maintain a constant body temperature and at which heat production must be increased (cold temperatures) or at which heat loss must be increased (high temperatures).
• effective t. — the combination of air temperature, humidity and wind speed. See also temperateness index.
• environmental t. — air temperature.
• nonpermissive t. — one at which a conditional gene mutation is nonfunctional. See also temperature-sensitive mutation.
• normal body t. — that usually registered by a healthy animal. See pyrexia.
• permissive t. — one at which a conditional gene mutation can express its normal function. See also temperature-sensitive mutation.
• premortal t. fall — the sudden fall in body temperature of a previously fevered animal just before death.
• rectal t. — the body temperature as measured by a rectal thermometer which has been in situ and in contact with the mucosa of the rectum with the anal sphincter tightly closed for at least 30 seconds. Alternative equipment is a dipolar electrode in a rectal probe.
• t. stress — exposure to excessively high or low environmental temperature.
• windchill t. — a combination of wind velocity and air temperature. See also effective temperature (above).

Some of the measurements we take for granted were not known in the ancient world. Among them is temperature. Certainly, ancient people knew that it was cold sometimes and hot sometimes, but no one had a way of putting a number to it. It was Galileo who made the first steps toward a quantitative means of measuring temperature. He noted that gases expand when heated. Using this principle, he developed a thermoscope, an inaccurate gas thermometer. Although Galileo did not know it, the gas he used -- air -- changed in volume according to outside air pressure as well as heating.

A really good thermometer was not made until 1714, when Gabriel Fahrenheit made the first mercury thermometer. Instead of air Fahrenheit used changes in the expansion of mercury to measure temperature. He set 0° as the lowest temperature he could reach by freezing salted water, hoping to avoid negative temperatures.

Anders Celsius did not create a new type of thermometer, but he did create the scale that is most commonly used around the world today. In one of the great mistakes of science, Celsius first set his scale with 0° as the temperature of boiling water and 100° as the temperature of freezing water. Wiser heads prevailed, however, and the scale was reversed. Until 1948 the scale Celsius devised was known in the United States as centigrade, but that year scientists agreed to rename it after its inventor. Gradually the world has gotten used to the idea that 37°C means 37 degrees Celsius, not 37 degrees centigrade.

More accurate thermometers have been developed over the years. Instead of using the simple expansion of materials upon heating, other thermometers use differences in the coefficient of expansion of two metals, the amount of energy emitted at different temperatures by certain substances, or the changes in electrical resistance at different temperatures.

Fahrenheit's idea of a temperature scale with no negative numbers was achieved with the introduction of the Kelvin scale (sometimes called the absolute scale). Lord Kelvin observed in 1848 that Charles's law, which states that gases lose 1/273 of their volume for every degree below 0°C, implies that at -273° the volume becomes zero. He proposed that -273° must be the lowest temperature obtainable, since nothing has a negative volume. This concept has since been verified. Today absolute zero is set more accurately at -273.15°C (-459.7°F). On the Kelvin scale, then, the freezing point of water is 273.15 K (no degree sign is used) and the boiling point is 373.15 K.

This article is about the thermodynamic property. For other uses, see Temperature (disambiguation).

It has been suggested that Cold be merged into this article or section. (Discuss)

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The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold).

In physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics. If no heat flow occurs between two objects, the objects have the same temperature; otherwise heat flows from the hotter object to the colder object. This is the content of the zeroth law of thermodynamics. On the microscopic scale, temperature can be defined as the average energy in each degree of freedom in the particles in a system. Because temperature is a statistical property, a system must contain a few particles for the question as to its temperature to make any sense. For a solid, this energy is found in the vibrations of its atoms about their equilibrium positions. In an ideal monatomic gas, energy is found in the translational motions of the particles; with molecular gases, vibrational and rotational motions also provide thermodynamic degrees of freedom.

Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. The entire scientific world (these countries included) measures temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is just the Celsius scale shifted downwards so that 0 K^[1]= −273.15 °C, or absolute zero. Many engineering fields in the U.S., notably high-tech and US federal specifications (civil and military), also use the kelvin and degrees Celsius scales. Other engineering fields in the U.S. also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion.

Contents 1 Overview 2 Details 3 The role of temperature in nature 4 Temperature measurement 4.1 Units of temperature 4.2 Negative temperatures 5 Comparison of temperature scales 6 Theoretical foundation 6.1 Definition Based on Zeroth Law of Thermodynamics 6.2 Temperature in gases 6.3 Temperature in plasmas 6.4 Temperature of the vacuum 6.5 Definition based on second law of thermodynamics 7 Importance of temperature 8 See also 9 Notes 10 References 11 External links

Overview

Heating a body, such as a segment of protein alpha helix (above), tends to cause its atoms to vibrate more, and to cause it to expand or change phase.

Intuitively, temperature is the measurement of how hot or cold something is, although the most immediate way in which we can measure this, by feeling it, is unreliable, resulting in the phenomenon of felt air temperature, which can differ at varying degrees from actual temperature. On the molecular level, temperature is the result of the motion of particles which make up a substance. Temperature increases as the energy of this motion increases. The motion may be the translational motion of the particle, or the internal energy of the particle due to molecular vibration or the excitation of an electron energy level. Although very specialized laboratory equipment is required to directly detect the translational thermal motions, thermal collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting low temperature of 700 nK (1 nK = 10⁻⁹ K) in 1994, they used optical lattice laser equipment to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature.

Molecules, such as O₂, have more degrees of freedom than single atoms: they can have rotational and vibrational motions as well as translational motion. An increase in temperature will cause the average translational energy to increase. It will also cause the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas, with extra degrees of freedom rotation and vibration, will require a higher energy input to change the temperature by a certain amount, i.e. it will have a higher heat capacity than a monatomic gas.

The process of cooling involves removing energy from a system. When there is no more energy able to be removed, the system is said to be at absolute zero, which is the point on the thermodynamic (absolute) temperature scale where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. By definition, absolute zero is a temperature of precisely 0 kelvins (−273.15 °C or −459.68 °F).

Details

Conjugate variables of thermodynamics
Pressure	Volume
(Stress)	(Strain)
Temperature	Entropy
Chem. potential	Particle no.

The formal properties of temperature follow from its mathematical definition (see below for the zeroth law definition and the second law definition) and are studied in thermodynamics and statistical mechanics.

Contrary to other thermodynamic quantities such as entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium, temperature being an average energy per particle can only be defined at thermodynamic equilibrium, or at least local thermodynamic equilibrium (see below).

As a system receives heat, its temperature rises; similarly, a loss of heat from the system tends to decrease its temperature (at the—uncommon—exception of negative temperature; see below).

When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation or combinations of them (see heat for additional discussion of the various mechanisms of heat transfer) and some ions may vary.

Temperature is also related to the amount of internal energy and enthalpy of a system: the higher the temperature of a system, the higher its internal energy and enthalpy.

Temperature is an intensive property of a system, meaning that it does not depend on the system size, the amount or type of material in the system, the same as for the pressure and density. By contrast, mass, volume, and entropy are extensive properties, and depend on the amount of material in the system.

The role of temperature in nature

A map of monthly mean temperatures

Water freezes at 0 °C. The frost shown here is at -17 °C.

Temperature plays an important role in almost all fields of science, including physics, geology, chemistry, and biology.

Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted.

Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Impact of temperature on speed of sound, air density and acoustic impedance at sea level
T in °C	c in m/s	ρ in kg/m³	Z in N·s/m³
−10	325.4	1.341	436.5
−5	328.5	1.316	432.4
0	331.5	1.293	428.3
5	334.5	1.269	424.5
10	337.5	1.247	420.7
15	340.5	1.225	417.0
20	343.4	1.204	413.5
25	346.3	1.184	410.0
30	349.2	1.164	406.6

Temperature measurement

Main article: Temperature measurement

See also: Timeline of temperature and pressure measurement technology

See also: International Temperature Scale of 1990

Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use in the USA, with the Celsius scale in use in the rest of the world and the kelvin scale.

Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (Symbol: K). The kelvin and Celsius scales are, by international agreement, defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water (water specially prepared with a specified blend of hydrogen and oxygen isotopes). Absolute zero is defined as being precisely 0 K and −273.15 °C. Absolute zero is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. At absolute zero, matter contains no thermal energy. Also, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things: 1) it fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; 2) it establishes that one kelvin has precisely the same magnitude as a one degree increment on the Celsius scale; and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0 K = −273.15 °C and 273.16 K = 0.01 °C). Formulas for converting from these defining units of temperature to other scales can be found at Temperature conversion formulas.

In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,604 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K.

For everyday applications, it's very often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins.

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following formula can be used to convert from Fahrenheit to Celsius:

See temperature conversion formulas for conversions between most temperature scales.

Negative temperatures

Main article: Negative temperature

In the macroscopic sense relevant to most people, a negative temperature is one below the zero-point of the measurement system used. For example, a temperature of 100 K is equivalent to −173.15 °C. Temperatures of macroscopic systems may have negative values in the Celsius and Fahrenheit, but not in the Kelvin or Rankine scales.

However, for some systems and specific definitions of temperature, it is possible to obtain a negative temperature, which is numerically less than absolute zero. However, a system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature.^[2]

Comparison of temperature scales

Comparison of temperature scales

Comment	Kelvin K	Celsius °C	Fahrenheit °F	Rankine °Ra (°R)	Delisle °D ¹	Newton °N ¹	Réaumur °R (°Ré, °Re) ¹	Rømer °Rø (°R) ¹
Absolute zero	0	−273.15	−459.67	0	559.725	−90.14	−218.52	−135.90
Lowest recorded natural temperature on Earth (Vostok, Antarctica - 21 July 1983)	184	−89	−128	331	284	−29	−71	−39
Celsius / Fahrenheit's "cross-over" temperature	233.15	−40	–40	419.67	210	–13.2	–32	–13.5
Fahrenheit's ice/salt mixture	255.37	−17.78	0	459.67	176.67	−5.87	−14.22	−1.83
Water freezes (at standard pressure)	273.15	0	32	491.67	150	0	0	7.5
Average surface temperature on Earth	288	15	59	519	128	5	12	15
Average human body temperature ²	310.0 ±0.7	36.8 ±0.7	98.2 ±1.3	557.9 ±1.3	94.8 ±1.1	12.1 ±0.2	29.4 ±0.6	26.8 ±0.4
Highest recorded surface temperature on Earth (Al 'Aziziyah, Libya - 13 September 1922)	331	58	136	596	63	19	46	38
Water boils (at standard pressure)	373.1339	99.9839	211.97102	671.64102	0	33	80	60
Gas Flame	1773 ~	1500 ~	2732 ~
Titanium melts	1941	1668	3034	3494	−2352	550	1334	883
The surface of the Sun	5800	5526	9980	10440	−8140	1823	4421	2909

¹ The temperature scale is in disuse, and of mere historical interest.
² Normal human body temperature is 36.8 ±0.7 °C, or 98.2 ±1.3 °F. The commonly given value 98.6 °F is simply the exact conversion of the nineteenth-century German standard of 37 °C. Since it does not list an acceptable range, it could therefore be said to have excess (invalid) precision. See Temperature of a Healthy Human (Body Temperature) for more information.
Some numbers in this table have been rounded off.

Theoretical foundation

This section uses first-person ("I"; "we") or second-person ("you") inappropriately. Please rewrite it to use a more formal, encyclopedic tone. (May 2009)

Definition Based on Zeroth Law of Thermodynamics

If two systems with fixed volumes are brought together in thermal contact, changes will most likely take place in the properties of both systems. These changes are caused by the transfer of heat between the systems. A state must be reached in which no further changes occur, to put the objects into thermal equilibrium.

A basis for the definition of temperature can therefore be obtained from the Zeroth Law of Thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. This property is called temperature.

Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale.

Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature^[3]:

(1)

where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale.

The pressure, volume, and the number of moles of a substance are all inherently greater than or equal to zero, suggesting that temperature must also be greater than or equal to zero. As a practical matter it is not possible to use a gas thermometer to measure absolute zero temperature since the gasses tend to condense into a liquid long before the temperature reaches zero. It is possible to extrapolate how many degrees below the present temperature the absolute zero is from the temperature range where Equation 1 works.

Temperature in gases

For an ideal gas the kinetic theory of gases uses statistical mechanics to relate the temperature to the average kinetic energy of the atoms in the system. This average energy is independent of particle mass, which seems counter-intuitive. Temperature is related only to the average kinetic energy of the particles in a gas - each particle has its own energy which may or may not correspond to the average; the distribution of energies (and thus speeds) of the particles in any gas are given by the Maxwell-Boltzmann distribution. The temperature of an ideal gas is related to its average kinetic energy via the equation^[3]:

, where k = R / n (n= Avogadro number, R= ideal gas constant).

In the case of a monoatomic gas, the kinetic energy is:

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy per particle (and hence the same temperature). In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy. A neon atom moves slower relative to a hydrogen molecule of the same kinetic energy; a pollen particle moves in a slow Brownian motion among fast moving water molecules, etc. A visual illustration of this from Oklahoma State University makes the point more clear. Particles with different mass have different velocity distributions, but the average kinetic energy is the same because of the ideal gas law.

Temperature in plasmas

Temperature of the vacuum

It is possible to use the zeroth law definition of temperature to assign a temperature to something we don't normally associate temperatures with, like a perfect vacuum. Because all objects emit black body radiation, a thermometer in a vacuum away from thermally radiating sources will radiate away its own thermal energy; decreasing in temperature indefinitely until it reaches the zero-point energy limit. At that point it can be said to be in equilibrium with the vacuum and by definition at the same temperature. If we could find a gas that behaved ideally all the way down to absolute zero the kinetic theory of gases tells us that it would achieve zero kinetic energy per particle, and thereby achieve absolute zero temperature. Thus, by the zeroth law a perfect, isolated vacuum is at absolute zero temperature. Note that in order to behave ideally in this context it is necessary for the atoms of the gas to have no zero point energy. It will turn out not to matter that this is not possible because the second law definition of temperature will yield the same result for any unique vacuum state.

More realistically, no such ideal vacuum exists. For instance a thermometer in a vacuum chamber which is maintained at some finite temperature (say, chamber is in the lab at room temperature) will equilibrate with the thermal radiation it receives from the chamber and with time reaches the temperature of the chamber. If a thermometer orbiting the Earth is exposed to a sunlight, then it equilibrates at the temperature at which power received by the thermometer from the Sun is exactly equal to the power radiated away by thermal radiation of the thermometer. For a black body this equilibrium temperature is about 281 K (+8 °C). Since Earth has an albedo of 30%, average temperature as seen from space is lower than for a black body, 254 K, while the surface temperature is considerably higher due to the greenhouse effect.

A thermometer isolated from solar radiation (in the shade of the Earth, for example) is still exposed to thermal radiation of Earth - thus will show some equilibrium temperature at which it receives and radiates equal amount of energy. If this thermometer is close to Earth then its equilibrium temperature is about 236 K (-37 °C) provided that Earth surface is at 281 K.

A thermometer far away from the Solar system still receives Cosmic microwave background radiation. Equilibrium temperature of such thermometer is about 2.725 K, which is the temperature of a photon gas constituting black body microwave background radiation at present state of expansion of Universe. This temperature is sometimes referred to as the temperature of space. This temperature is thus like a test charge in that it facilitates a measure of the system even though temperature is not strictly defined there.

Definition based on second law of thermodynamics

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means that for a perfectly ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which 100% of tosses came up the same.

On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. A disordered system can be 90% heads and 10% tails, or it could be 98% heads and 2% tails, et cetera. As the number of coin tosses increases, the number of possible combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the combinations to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.

We previously stated that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or:

(2)

where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures:

(3)

Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and T₂, and the second between T₂ and T₃. This can only be the case if:

Since the first function is independent of T₂, this temperature must cancel on the right side, meaning f(T₁,T₃) is of the form g(T₁)/g(T₃) (i.e. f(T₁,T₃) = f(T₁,T₂)f(T₂,T₃) = g(T₁)/g(T₂)· g(T₂)/g(T₃) = g(T₁)/g(T₃)), where g is a function of a single temperature. We can now choose a temperature scale with the property that:

(4)

Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature:

(5)

Notice that for T_C = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives:

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by:

(6)

where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat:

(7)

For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by:

(8)

ie. the reciprocal of the temperature is the rate of increase of entropy with respect to energy.

Importance of temperature

The below table demonstrates that the properties of air change significantly with temperature.

Table — speed of sound in air c, density of air ρ, acoustic impedance Z vs. temperature

Effect of temperature
Temperature	Speed of sound	Density of air	Acoustic impedance
in °C	c in m·s−1	ρ in kg·m−3	Z in N·s·m−3
−25	315.8	1.423	449.4
−20	318.9	1.395	444.9
−15	322.1	1.368	440.6
−10	325.2	1.342	436.1
−5	328.3	1.317	432.0
0	331.3	1.292	428.4
+5	334.3	1.269	424.3
+10	337.3	1.247	420.6
+15	340.3	1.225	416.8
+20	343.2	1.204	413.2
+25	346.1	1.184	409.8
+30	349.0	1.164	406.2
+35	351.9	1.146	403.3

See also

Absolute zero Body temperature (Thermoregulation) Celsius Color temperature Dry-bulb temperature Entropy Fahrenheit Heat Heat conduction Heat convection

ISO 1 ITS-90 Kelvin Maxwell's demon Orders of magnitude (temperature) Planck temperature Rankine scale Relativistic heat conduction

Stagnation temperature Thermal radiation Thermodynamic (absolute) temperature Thermography Thermometer Triple point Virtual temperature Wet Bulb Globe Temperature Wet-bulb temperature

Notes

1. ^ This means "zero kelvin"; the unit kelvin is not used with a degree symbol because it is an absolute scale, i.e. the notation 0 °K is not correct according to international standards
2. ^ Kittel and Kroemer, pp. 462
3. ^ ^{a b} Vu-Quoc, L., Configuration integral (statistical mechanics), 2008

References

• Chang, Hasok (2004). Inventing Temperature: Measurement and Scientific Progress. Oxford: Oxford University Press. ISBN 9780195171273.
• Kittel, Charles; Kroemer, Herbert (1980). Thermal Physics (2nd ed. ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
• Zemansky, Mark Waldo (1964). Temperatures Very Low and Very High. Princeton, N.J.: Van Nostrand.

External links

Wikimedia Commons has media related to: Temperature

Look up temperature in Wiktionary, the free dictionary.

• An elementary introduction to temperature aimed at a middle school audience
• What is Temperature? An introductory discussion of temperature as a manifestation of kinetic theory.
• Why do we have so many temperature scales?

v • d • e Meteorological data and variables General Adiabatic processes · Lapse rate · Lightning · Surface solar radiation · Surface weather analysis · Visibility · Vorticity · Wind Condensation Cloud · Cloud condensation nuclei · Fog · Precipitation · Water vapor Convection Convective available potential energy (CAPE) · Convective inhibition (CIN) · Convective instability · Convective temperature (Tc) · Helicity · Lifted index (LI) · Bulk Richardson number (BRN) Temperature Dew point (Td) · Equivalent temperature (Te) · Heat index · Humidex · Humidity · Potential temperature (θ) · Equivalent potential temperature (θe) · Sea surface temperature (SST) · Wet-bulb temperature · Wet-bulb potential temperature  · Wind chill Pressure Atmospheric pressure · Baroclinity  · Barotropicity

v • d • e Temperature scales Celsius · Fahrenheit · Kelvin · Rankine · Delisle · Leiden · Newton · Réaumur · Rømer Conversion formulas

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Common misspelling(s) of temperature

• temperture

Dansk (Danish)
n. - temperatur

idioms:

• have a temperature    have feber
• room temperature    rumtemperatur
• run a temperature    have feber

Nederlands (Dutch)
temperatuur, verhoging, stemming verhoging hebben

Français (French)
n. - température, fièvre, (Météo, Phys) température, (Méd) température, (fig) température

idioms:

• have a temperature    avoir de la fièvre
• room temperature    température ambiante
• run a temperature    avoir de la fièvre

Deutsch (German)
n. - Temperatur, erhöhte Temperatur, Fieber

idioms:

• have a temperature    erhöhte Temperatur haben, fiebern
• room temperature    Raumtemperatur
• run a temperature    erhöhte Temperatur haben, fiebern

Ελληνική (Greek)
n. - θερμοκρασία, (μτφ.) πυρετός, δέκατα

idioms:

• have a temperature    έχω πυρετό
• room temperature    θερμοκρασία περιβάλλοντος
• run a temperature    έχω πυρετό

Italiano (Italian)
temperatura, febbre

idioms:

• have/run a temperature    avere la febbre
• room temperature    temperatura ambiente

Português (Portuguese)
n. - temperatura (f)

idioms:

• have/run a temperature    ter febre
• room temperature    temperatura ambiente

Русский (Russian)
температура, жар

idioms:

• have/run a temperature    (о больном) повышение температуры
• room temperature    комнатное тепло

Español (Spanish)
n. - temperatura, fiebre, calentura

idioms:

• have a temperature    tener fiebre o calentura o temperatura
• room temperature    temperatura ambiente
• run a temperature    tener fiebre o calentura o temperatura

Svenska (Swedish)
n. - temperatur, feber

中文（简体）(Chinese (Simplified))
温度, 热度, 发烧

idioms:

• have a temperature    发烧
• room temperature    室温, 常温
• run a temperature    发烧

中文（繁體）(Chinese (Traditional))
n. - 溫度, 熱度, 發燒

idioms:

• have a temperature    發燒
• room temperature    室溫, 常溫
• run a temperature    發燒

한국어 (Korean)
n. - 온도, 체온, 고열

idioms:

• have a temperature    열이 있다
• run a temperature    열을 내다, 열이 있다

日本語 (Japanese)
n. - 温度, 体温, 高熱

idioms:

• have/run a temperature    熱がある
• temperature inversion    気温の逆転

العربيه (Arabic)
‏(الاسم) درجه الحرارة‏

עברית (Hebrew)
n. - ‮חום, טמפרטורה‬

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