temperature

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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 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.

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.

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.

LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!

1. One of the critical factors in a reaction.
   
2. Also an important influence in usually increasing solubility of solid ingredients.
   
3. Important in reducing harmful microbially contamination. High temperatures can kill or deduce the number of harmful organisms, and refrigeration or freezing is used to hold down their growth.
   
4. Is critical for volatile stability. Volatile chemicals will dissipate at higher temperatures. Introduction of excessive heat will send the flavor profile potentially out of balance. For this reason flavors should be kept stored in a cool and dry area.
   

1. The process of slow cooling so fat crystallization can properly form smaller particles. Tempering allows for a smooth physical/visual finish and mouthfeel. The tempering of chocolate liquor (i.e., cocoa butter plus cocoa powder is called conching).
   
2. Metals can also be tempered. Both cast iron and Teflon-coated pans need a sufficient amount of tempering before they can perform optimally.
   

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).

The degree of sensible heat or cold.

• Forecasting and Meteorology - temperature: degree of hotness or coldness as measured on standardized scale
• Heat - temperature: physical quantity measured by the average kinetic energy of particles in matter
• Physical Properties and Changes - temperature: property of a body or region of space that determines direction of net flow of heat with neighboring objects or regions

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

A map of global long term monthly average surface air temperatures in Mollweide projection.

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot. Heat spontaneously flows from bodies of a higher temperature to bodies of lower temperature, at a rate that increases with the temperature difference and the thermal conductivity. No heat will be exchanged between bodies of the same temperature; such bodies are said to be in "thermal equilibrium".

The temperature of a substance typically varies with the average speed of the particles that it contains, raised to the second power; that is, it is proportional to the mean kinetic energy of its constituent particles. Formally, temperature is defined as the derivative of the internal energy with respect to the entropy.

Quantitatively, temperature is measured with thermometers, which may be calibrated to a variety of temperature scales.

Thermal vibration of a segment of protein alpha helix. The amplitude of the vibrations increases with temperature.

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

Contents 1 Use in science 2 Temperature scales 3 Thermodynamic approach to temperature 4 Statistical mechanics approach to temperature 5 Basic theory 5.1 Temperature for bodies in thermodynamic equilibrium 5.2 Temperature for bodies in a steady state but not in thermodynamic equilibrium 5.3 Temperature for bodies not in a steady state 5.4 Thermodynamic equilibrium axiomatics 6 Heat capacity 7 Temperature measurement 7.1 Units 7.1.1 Conversion 7.1.2 Plasma physics 8 Theoretical foundation 8.1 Kinetic theory of gases 8.2 Zeroth law of thermodynamics 8.3 Second law of thermodynamics 8.4 Definition from statistical mechanics 8.5 Generalized temperature from single particle statistics 8.6 Negative temperature 9 Examples of temperature 10 See also 11 Notes 12 References 13 Further reading 14 External links

Use in science

Annual mean temperature around the world

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 310 K, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also determines the 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 scales

See also: Scale of temperature

Most of the world uses the Celsius scale (°C) for most temperature measurements.^{[citation needed]} It has the same incremental scaling as the Kelvin scale used by scientists, but fixes its null point, at 0°C = 273.15K, approximately the freezing point of water (under one atmosphere of pressure).^{[note 1]} The United States uses the Fahrenheit scale for common purposes, a scale on which water freezes at 32 °F and boils at 212 °F (under one atmosphere of pressure).^{[citation needed]}

For practical purposes of scientific temperature measurement, the International System of Units (SI) defines a scale and unit for the thermodynamic temperature by using the easily reproducible temperature of the triple point of water as a second reference point. The reason for this choice is that, unlike the freezing and boiling point temperatures, the temperature at the triple point is independent of pressure (since the triple point is a fixed point on a two-dimensional plot of pressure vs. temperature). For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, which has been named the kelvin in honor of the Scottish physicist who first defined the scale. The unit symbol of the kelvin is K.

Absolute zero is defined as a temperature of precisely 0 kelvins, which is equal to −273.15 °C or −459.68 °F.

Thermodynamic approach to temperature

Temperature is one of the principal quantities studied in the field of thermodynamics. Thermodynamics investigates the relation between heat and work, using a special scale of temperature called the absolute temperature, and thus relates temperature to work, as considered below. In thermodynamic terms, temperature is a macroscopic intensive variable because it is independent of the bulk amount of elementary entities contained inside, be they atoms, molecules, or electrons. Real world systems are not homogeneous. For study, a body is usually spatially and temporally divided conceptually into imagined 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in each 'cell', then a temperature exists for each 'cell', and local thermodynamic equilibrium is said to prevail in the body.

Statistical mechanics approach to temperature

Statistical mechanics provides a microscopic explanation of temperature, based on macroscopic systems' being composed of many particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena in terms of the mechanics of the molecules and ions, and statistical assessments of their joint adventures. In the statistical thermodynamic approach, degrees of freedom are used instead of particles.

On the molecular level, temperature is the result of the motion of the particles that constitute the material. Moving particles carry kinetic energy. Temperature increases as this motion and the kinetic energy increase. The motion may be the translational motion of particles, or the 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 laser equipment to create an optical lattice to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7mm per second in order to calculate their temperature.

Molecules, such as oxygen (O₂), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase in temperature due to an increase in the average translational energy of the molecules. Heating will also cause, through equipartitioning, the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas will require a higher energy input to increase its temperature by a certain amount, i.e. it will have a higher heat capacity than a monatomic gas.

The process of cooling involves removing thermal energy from a system. When no more energy can be removed, the system is at absolute zero, which cannot be achieved experimentally. Absolute zero is the null point of the thermodynamic temperature scale, also called absolute temperature. If it were possible to cool a system to absolute zero, all motion of the particles comprising matter would cease and they would be at complete rest in this classical sense. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.

Basic theory

As distinct from a quantity of heat, temperature may be viewed as a measure of a quality of a body ^[1] or of heat.^[2][3][4][5] The quality is called hotness by some writers.^[6][7]

When two systems are at the same temperature, no net heat transfer occurs spontanteously, by conduction or radiation, between them. When a temperature difference does exist, and there is a thermally conductive or radiative connection between them, there is spontaneous heat transfer from the warmer system to the colder system, until they are at mutual thermal equilibrium. Heat transfer occurs by conduction or by thermal radiation.^{[8][9][10][11][12][13][14][15]}

Experimental physicists, for example Galileo and Newton,^[16] found that there are indefinitely many empirical temperature scales.

Temperature for bodies in thermodynamic equilibrium

For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.^[17] This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic.^[18][19] A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum; this frequency is always positive, but can have values that tend to zero. Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional manifold. This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium.^{[20][6][21][22][7]}

Except for a system undergoing a first-order phase change such as the melting of ice, as a closed system receives heat, without change in its volume and without change in external force fields acting on it, its temperature rises. For a system undergoing such a phase change so slowly that departure from thermodynamic equilibrium can be neglected, its temperature remains constant as the system is supplied with latent heat. Conversely, a loss of heat from a closed system, without phase change, without change of volume, and without change in external force fields acting on it, decreases its temperature.^[23]

Temperature for bodies in a steady state but not in thermodynamic equilibrium

While for bodies in their own thermodynamic equilibrium states, the notion of temperature safely requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is the hotter, and if this is so, then at least one of the bodies does not have a well defined absolute thermodynamic temperature. Nevertheless, any one given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness and temperature, for a suitable range of processes. This is a matter for study in non-equilibrium thermodynamics.

Temperature for bodies not in a steady state

When a body is not in a steady state, then the notion of temperature becomes even less safe than for a body in a steady state not in thermodynamic equilibrium. This is also a matter for study in non-equilibrium thermodynamics.

Thermodynamic equilibrium axiomatics

For axiomatic treatment of thermodynamic equilibrium, since the 1930's, it has become customary to refer to a zeroth law of thermodynamics. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart on a hotness manifold.^[6][24][22] While the zeroth law permits the definitions of many different empirical scales of temperature, the second law of thermodynamics selects the definition of a single preferred, absolute temperature, unique up to an arbitrary scale factor, whence called the thermodynamic temperature.^{[25][26][6][27][21][28]} If internal energy is considered as a function of the volume and entropy of a homogeneous system in thermodynamic equilibrium, thermodynamic absolute temperature appears as the partial derivative of internal energy with respect the entropy at constant volume. Its natural, intrinsic origin or null point is absolute zero at which the entropy of any system is at a minimum. Although this is the lowest absolute temperature described by the model, the third law of thermodynamics postulates that absolute zero cannot be attained by any physical system.

Heat capacity

See also: Heat capacity and Calorimetry

When a sample is heated, meaning it receives thermal energy from an external source, some of the introduced heat is converted into kinetic energy, the rest to other forms of internal energy, specific to the material. The amount converted into kinetic energy causes the temperature of the material to rise. The introduced heat () divided by the observed temperature change is the heat capacity (C) of the material.

If heat capacity is measured for a well defined amount of substance, the specific heat is the measure of the heat required to increase the temperature of such a unit quantity by one unit of temperature. For example, to raise the temperature of water by one kelvin (equal to one degree Celsius) requires 4186 joules per kilogram (J/kg)..

Temperature measurement

A typical Celsius thermometer measures a winter day temperature of -17°C.

See also: Timeline of temperature and pressure measurement technology, International Temperature Scale of 1990, and Comparison of temperature scales

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 United States for non-scientific applications.

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. Most scientist measures temperature using the Celsius scale and the thermodynamic temperature using the Kelvin scale, which is the Celsius scale offset so that its null point is 0K = −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 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.

Units

The basic unit of temperature in the International System of Units (SI) is the kelvin. It has the symbol K.

For everyday applications, it is often convenient to use the Celsius scale, in which 0°C corresponds very closely to the freezing point of water and 100°C is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, 0°C is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a 1kelvin increment, but the scale is offset by the temperature at which ice melts (273.15 K).

By international agreement^[29] the Kelvin and Celsius scales are defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of hydrogen and oxygen isotopes. Absolute zero is defined as precisely 0K and −273.15°C. It is the temperature at which all classical translational motion of the particles comprising matter ceases and they are at complete rest in the classical model. Quantum-mechanically, however, zero-point motion remains and has an associated energy, the zero-point energy. Matter is in its ground state,^[30] and contains no thermal energy. The triple point of water is defined as 273.16K and 0.01°C. This definition serves the following purposes: it fixes the magnitude of the kelvin as being precisely 1 part in 273.16 parts of the difference between absolute zero and the triple point of water; it establishes that one kelvin has precisely the same magnitude as one degree on the Celsius scale; and it establishes the difference between the null points of these scales as being 273.15K (0K = −273.15°C and 273.16K = 0.01°C).

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 Rankine scale, still used in fields of chemical engineering in the U.S., is an absolute scale based on the Fahrenheit increment.

Conversion

The following table shows the temperature conversion formulas for conversions to and from the Celsius scale.

	from Celsius	to Celsius
Fahrenheit	[°F] = [°C] × 9⁄5 + 32	[°C] = ([°F] − 32) × 5⁄9
Kelvin	[K] = [°C] + 273.15	[°C] = [K] − 273.15
Rankine	[°R] = ([°C] + 273.15) × 9⁄5	[°C] = ([°R] − 491.67) × 5⁄9
Delisle	[°De] = (100 − [°C]) × 3⁄2	[°C] = 100 − [°De] × 2⁄3
Newton	[°N] = [°C] × 33⁄100	[°C] = [°N] × 100⁄33
Réaumur	[°Ré] = [°C] × 4⁄5	[°C] = [°Ré] × 5⁄4
Rømer	[°Rø] = [°C] × 21⁄40 + 7.5	[°C] = ([°Rø] − 7.5) × 40⁄21

Plasma physics

The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11605K. In the study of QCD matter one routinely encounters temperatures of the order of a few hundred MeV, equivalent to about 10¹²K.

Theoretical foundation

Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature.^[31] Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy.

The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. Kinetic energy, a concept of classical mechanics, is one half the product of mass and the square of a particle's velocity. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monoatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model.

In the context of thermodynamics, the kinetic energy is also referred to as thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depend on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom.

Kinetic theory of gases

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

The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average kinetic energy of the atoms in a container of gas. Classical mechanics defines the kinetic energy as follows:

where m is the particle mass and v its velocity. The distribution of energies (and thus speeds) of the particles in any gas are given by the Maxwell-Boltzmann distribution. The temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom E_k via the equation:^[32]

where the Boltzmann constant (n = Avogadro number, R = ideal gas constant). This relation is valid in the classical regime, i.e. when the particle density is much less than , where is the thermal de Broglie wavelength. A monoatomic gas has only the three translational degrees of freedom.

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 masses, the heaviest particles will move slower than lighter particles, but have the same average kinetic energy. A neon atom moves slower relative to a hydrogen molecule of the same kinetic energy; a pollen particle suspended in water moves in a slow Brownian motion among fast moving water molecules.

Zeroth law of thermodynamics

Main article: Zeroth law of thermodynamics

It has long been recognized that if two bodies of different temperatures are brought into thermal connection, conductive or radiative, they exchange heat accompanied by changes of other state variables. Left isolated from other bodies, the two connected bodies eventually reach a state of thermal equilibrium in which no further changes occur. This basic knowledge is relevant to thermodynamics. Some approaches to thermodynamics take this basic knowledge as axiomatic, other approaches select only one narrow aspect of this basic knowledge as axiomatic, and use other axioms to justify and express deductively the remaining aspects of it. The one aspect chosen by the latter approaches is often stated in textbooks as the zeroth law of thermodynamics, but other statements of this basic knowledge are made by various writers.

The usual textbook statement of the zeroth law of thermodynamics is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This statement is taken to justify a statement that all three systems have the same temperature, but, by itself, it does not justify the idea of temperature as a numerical scale for a concept of hotness which exists on a one-dimensional manifold with a sense of greater hotness. Sometimes the zeroth law is stated to provide the latter justification.^[24] For suitable systems, an empirical temperature scale may be defined by the variation of one of the other state variables, such as pressure, when all other coordinates are fixed. The second law of thermodynamics is used to define an absolute thermodynamic temperature scale for systems in thermal equilibrium.

A temperature scale is based on the properties of some reference system to which other thermometers may be calibrated. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure (p) and volume (V) of a gas is directly proportional to the thermodynamic temperature:^[32]

where T is temperature, n is the number of moles of gas and R = 8.314472(15) Jmol^-1K^-1 is the gas constant. Reformulating the pressure-volume term as the sum of classical mechanical particle energies in terms of particle mass, m, and root-mean-square particle speed v, the ideal gas law directly provides the relationship between kinetic energy and temperature:^[33]

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 the gas constant. In practice, such a gas thermometer is not very convenient, but other thermometers 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, however, to extrapolate to absolute zero by using the ideal gas law.

Second law of thermodynamics

Main article: Second law of thermodynamics

In the previous section certain properties of temperature were expressed by the zeroth law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics which deals with entropy. Entropy is often thought of as 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.

For example, in 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 come 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.

It has been previously stated that temperature governs the flow of heat between two systems and it was just shown that the universe tends to progress so as to maximize entropy, which is expected of any natural system. Thus, it is expected that there is some relationship between temperature and entropy. To find this relationship, the relationship between heat, work and temperature is first considered. A heat engine is a device for converting thermal energy into mechanical energy, resulting in the performance of work, and analysis of the Carnot heat engine provides the necessary relationships. 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. 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:

which implies:

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. A temperature scale can now be chosen 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 was described previously. Rearranging Equation 6 gives a new definition for temperature in terms of entropy and heat:

(7)

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

(8),

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

Definition from statistical mechanics

The previous section elaborated the historical derivation relating entropy and heat. A modern definition of temperature is given by statistical mechanics. It is defined in terms of the fundamental degrees of freedom of a system. Eq.(8) of the previous section is taken to be the defining relation of the temperature. Eq. (7) can be derived from first principles.

Generalized temperature from single particle statistics

It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration space ensembles given in statistical mechanics in the case of thermal and particle exchange between a small system of fermions (N even less than 10) with a single/double occupancy system. The finite quantum grand canonical ensemble,^[34] obtained under the hypothesis of ergodicity and orthodicity, allows to express the generalized temperature from the ratio of the average time of occupation ₁ and ₂ of the single/double occupancy system:^[35]

where E_F is the Fermi energy which tends to the ordinary temperature when N goes to infinity.

Negative temperature

Main article: Negative temperature

On the empirical temperature scales, which are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, dry ice has a sublimation temperature of −78.5°C which is equivalent to −109.3°F. On the absolute Kelvin scale, however, this temperature is 194.6 K. On the absolute scale of thermodynamic temperature no material can exhibit a temperature smaller than or equal to 0 K, both of which are forbidden by the third law of thermodynamics.

In the quantum mechanical description of electron and nuclear spin systems that have a limited number of possible states, and therefore a discrete upper limit of energy they can attain, it is possible to obtain a negative temperature, which is numerically indeed less than absolute zero. However, this is not the macroscopic temperature of the material, but instead the temperature of only very specific degrees of freedom, that are isolated from others and do not exchange energy by virtue of the equipartition theorem.

A negative temperature is experimentally achieved with suitable radio frequency techniques that cause a population inversion of spin states from the ground state. As the energy in the system increases upon population of the upper states, the entropy increases as well, as the system becomes less ordered, but attains a maximum value when the spins are evenly distributed among ground and excited states, after which it begins to decrease, once again achieving a state of higher order as the upper states begin to fill exclusively. At the point of maximum entropy, the temperature function shows the behavior of a singularity, because the slope of the entropy function decreases to zero at first and then turns negative. Since temperature is the inverse of the derivative of the entropy, the temperature formally goes to infinity at this point, and switches to negative infinity as the slope turns negative. At energies higher than this point, the spin degree of freedom therefore exhibits formally a negative thermodynamic temperature. As the energy increases further by continued population of the excited state, the negative temperature approaches zero asymptotically.^[36] As the energy of the system increases in the population inversion, a system with a negative temperature is not colder than absolute zero, but rather it has a higher energy than at positive temperature, and may be said to be in fact hotter at negative temperatures. When brought into contact with a system at a positive temperature, energy will be transferred from the negative temperature regime to the positive temperature region.

Examples of temperature

Main article: Orders of magnitude (temperature)

	Temperature		Peak emittance wavelength[37] of black-body radiation
	Kelvin	Degrees Celsius
Absolute zero (precisely by definition)	0 K	−273.15 °C	not defined
Coldest temperature achieved[38]	100 pK	−273.149999999900 °C	29,000 km
Coldest Bose–Einstein condensate[39]	450 pK	−273.14999999955 °C	6,400 km
One millikelvin (precisely by definition)	0.001 K	−273.149 °C	2.89777 m (radio, FM band)[40]
Water's triple point (precisely by definition)	273.16 K	0.01 °C	10,608.3 nm (long wavelength I.R.)
Water's boiling point[A]	373.1339 K	99.9839 °C	7,766.03 nm (mid wavelength I.R.)
Incandescent lamp[B]	2500 K	≈2,200 °C	1,160 nm (near infrared)[C]
Sun's visible surface[D][41]	5,778 K	5,505 °C	501.5 nm (green-blue light)
Lightning bolt's channel[E]	28 kK	28,000 °C	100 nm (far ultraviolet light)
Sun's core[E]	16 MK	16 million °C	0.18 nm (X-rays)
Thermonuclear weapon (peak temperature)[E][42]	350 MK	350 million °C	8.3×10−3 nm (gamma rays)
Sandia National Labs' Z machine[E][43]	2 GK	2 billion °C	1.4×10−3 nm (gamma rays)[F]
Core of a high-mass star on its last day[E][44]	3 GK	3 billion °C	1×10−3 nm (gamma rays)
Merging binary neutron star system[E][45]	350 GK	350 billion °C	8×10−6 nm (gamma rays)
Relativistic Heavy Ion Collider[E][46]	1 TK	1 trillion °C	3×10−6 nm (gamma rays)
CERN's proton vs nucleus collisions[E][47]	10 TK	10 trillion °C	3×10−7 nm (gamma rays)
Universe 5.391×10−44 s after the Big Bang[E]	1.417×1032 K	1.417×1032 °C	1.616×10−26 nm (Planck Length)[48]

• ^A For Vienna Standard Mean Ocean Water at one standard atmosphere (101.325 kPa) when calibrated strictly per the two-point definition of thermodynamic temperature.
• ^B The 2500 K value is approximate. The 273.15 K difference between K and °C is rounded to 300 K to avoid false precision in the Celsius value.
• ^C For a true black-body (which tungsten filaments are not). Tungsten filaments' emissivity is greater at shorter wavelengths, which makes them appear whiter.
• ^D Effective photosphere temperature. The 273.15 K difference between K and °C is rounded to 273 K to avoid false precision in the Celsius value.
• ^E The 273.15 K difference between K and °C is without the precision of these values.
• ^F For a true black-body (which the plasma was not). The Z machine's dominant emission originated from 40 MK electrons (soft x–ray emissions) within the plasma.

See also

• Scale of temperature
• Atmospheric temperature
• Color temperature
• Dry-bulb temperature
• Heat conduction
• Heat convection
• ISO 1
• ITS-90
• Maxwell's demon
• Orders of magnitude (temperature)
• Outside air temperature
• Planck temperature
• Rankine scale
• Relativistic heat conduction
• Stagnation temperature
• Thermal radiation
• Thermoception
• Thermodynamic (absolute) temperature
• Thermography
• Thermometer
• Body temperature (Thermoregulation)
• Virtual temperature
• Wet Bulb Globe Temperature
• Wet-bulb temperature

Notes

1. ^ Historically, the Celsius scale was a purely empirical temperature scale defined only by the freezing and boiling points of water. Since the standardization of the kelvin in the International System of Units, it has subsequently been redefined in terms of the equivalent fixing points on the Kelvin scale.

References

1. ^ Bryan, G.H. (1907). Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications, B.G. Teubner, Leipzig, page 3.[1]
2. ^ Maxwell, J.C. (1872). Theory of Heat, third edition, Longman's, Green & Co, London, page 44.
3. ^ Planck, M. (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green, London, page 31.
4. ^ Gibbs, J.W. (1875). Graphical Methods in the Thermodynamics of Fluids, Collected Works, Vol. 1, page 10, cited by Serrin, J. (1986). Chapter 1, 'An Outline of Thermodynamical Structure', page 7, in New Perspectives in Thermodynamics, edited by J. Serrin, Springer, Berlin, ISBN 3-540-15931-2.
5. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics, New York, ISBN 0-88318-797-3, page 14.
6. ^ ^{a b c d} Mach, E. (1900). Die Principien der Wärmelehre. Historisch-kritisch entwickelt, Johann Ambrosius Barth, Leipzig, section 22, pages 56-57.
7. ^ ^{a b} Serrin, J. (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pages 3-32, especially page 6, in New Perspectives in Thermodynamics, edited by J. Serrin, Springer, Berlin, ISBN 3-540-15931-2.
8. ^ Maxwell, J.C. (1872). Theory of Heat, third edition, Longmans, Green, London, page 32.
9. ^ Tait, P.G. (1884). Heat, Macmillan, London, Chapter VII, pages 39-40.
10. ^ Planck, M. (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green, London, pages 1-2.
11. ^ Planck, M. (1914), The Theory of Heat Radiation, second edition, translated into English by M. Masius, Blakiston's Son & Co., Philadelphia, reprinted by Kessinger.
12. ^ J. S. Dugdale (1996, 1998). Entropy and its Physical Interpretation. Taylor & Francis. p. 13. ISBN 978-0-7484-0569-5. 
13. ^ F. Reif (1965). Fundamentals of Statistical and Thermal Physics. McGraw-Hill. p. 102. 
14. ^ M. J. Moran, H. N. Shapiro (2006). Fundamentals of Engineering Thermodynamics (5 ed.). John Wiley & Sons, Ltd.. p. 14. ISBN 978-0-470-03037-0. 
15. ^ T.W. Leland, Jr.. "Basic Principles of Classical and Statistical Thermodynamics". p. 14. http://www.uic.edu/labs/trl/1.OnlineMaterials/BasicPrinciplesByTWLeland.pdf. "Consequently we identify temperature as a driving force which causes something called heat to be transferred." 
16. ^ Tait, P.G. (1884). Heat, Macmillan, London, Chapter VII, pages 42, 103-117.
17. ^ Beattie, J.A., Oppenheim, I. (1979). Principles of Thermodynamics, Elsevier Scientific Publishing Company, Amsterdam, 0–444–41806–7, page 29.
18. ^ Landsberg, P.T. (1961). Thermodynamics with Quantum Statistical Illustrations, Interscience Publishers, New York, page 17.
19. ^ Thomsen, J.S. (1962). A restatement of the zeroth law of thermodynamics, Am. J. Phys. 30: 294-296.
20. ^ Maxwell, J.C. (1872). Theory of Heat, third edition, Longman's, Green & Co, London, page 45.
21. ^ ^{a b} Truesdell, C.A. (1980). The Tragicomical History of Thermodynamics, 1822-1854, Springer, New York, ISBN 0-387-90403-4, Section 11H, pages 320-332.
22. ^ ^{a b} Pitteri, M. (1984). On the axiomatic foundations of temperature, Appendix G6 on pages 522-544 of Rational Thermodynamics, C. Truesdell, second edition, Springer, New York, ISBN 0-387-90874-9.
23. ^ Truesdell, C., Bharatha, S. (1977). The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines, Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech, Springer, New York, ISBN 0-387-07971-8, page 20.
24. ^ ^{a b} Serrin, J. (1978). The concepts of thermodynamics, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janiero, August 1977, edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, ISBN 0-444-85166-6, pages 411-451.
25. ^ Maxwell, J.C. (1872). Theory of Heat, third edition, Longmans, Green, London, pages 155-158.
26. ^ Tait, P.G. (1884). Heat, Macmillan, London, Chapter VII, Section 95, pages 68-69.
27. ^ H.A. Buchdahl (1966). The Concepts of Classical Thermodynamics. Cambridge University Press. p. 73. 
28. ^ Kondepudi, D. (2008). Introduction to Modern Thermodynamics, Wiley, Chichester, ISBN 978-0-470-01598-8, Section 32., pages 106-108.
29. ^ The kelvin in the SI Brochure
30. ^ "Absolute Zero". Calphad.com. http://www.calphad.com/absolute_zero.html. Retrieved 2010-09-16. 
31. ^ C. Caratheodory (1909). "Untersuchungen über die Grundlagen der Thermodynamik". Mathematische Annalen 67 (3): 355–386. doi:10.1007/BF01450409. 
32. ^ ^{a b} Vu-Quoc, L., Configuration integral (statistical mechanics), 2008
33. ^ Peter Atkins, Julio de Paula (2006). Physical Chemistry (8 ed.). Oxford University Press. p. 9. 
34. ^ Prati, E. (2010). "The finite quantum grand canonical ensemble and temperature from single-electron statistics for a mesoscopic device". J. Stat. Mech. 1: P01003. doi:10.1088/1742-5468/2010/01/P01003. http://www.iop.org/EJ/abstract/1742-5468/2010/01/P01003/.  arxiv.org
35. ^ Prati, E., et al. (2010). "Measuring the temperature of a mesoscopic electron system by means of single electron statistics". Applied Physics Letters 96 (11): 113109. Bibcode 2010ApPhL..96k3109P. doi:10.1063/1.3365204. http://link.aip.org/link/?APL/96/113109.  arxiv.org
36. ^ Kittel, Charles; Kroemer, Herbert (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. pp. Appendix E. ISBN 0-7167-1088-9. 
37. ^ The cited emission wavelengths are for black bodies in equilibrium. CODATA 2006 recommended value of 2.8977685(51)×10⁻³ m K used for Wien displacement law constant b.
38. ^ "World record in low temperatures". http://ltl.tkk.fi/wiki/LTL/World_record_in_low_temperatures. Retrieved 2009-05-05. 
39. ^ A temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium atoms was achieved in 2003 by researchers at MIT. Citation: Cooling Bose–Einstein Condensates Below 500 Picokelvin, A. E. Leanhardt et al., Science 301, 12 Sept. 2003, p. 1515. It's noteworthy that this record's peak emittance black-body wavelength of 6,400 kilometers is roughly the radius of Earth.
40. ^ The peak emittance wavelength of 2.89777 m is a frequency of 103.456 MHz
41. ^ Measurement was made in 2002 and has an uncertainty of ±3 kelvin. A 1989 measurement produced a value of 5,777.0±2.5 K. Citation: Overview of the Sun (Chapter 1 lecture notes on Solar Physics by Division of Theoretical Physics, Dept. of Physical Sciences, University of Helsinki).
42. ^ The 350 MK value is the maximum peak fusion fuel temperature in a thermonuclear weapon of the Teller–Ulam configuration (commonly known as a hydrogen bomb). Peak temperatures in Gadget-style fission bomb cores (commonly known as an atomic bomb) are in the range of 50 to 100 MK. Citation: Nuclear Weapons Frequently Asked Questions, 3.2.5 Matter At High Temperatures. Link to relevant Web page. All referenced data was compiled from publicly available sources.
43. ^ Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term bulk quantity draws a distinction from collisions in particle accelerators wherein high temperature applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during shot Z1137. In fact, the iron and manganese ions in the plasma averaged 3.58±0.41 GK (309±35 keV) for 3 ns (ns 112 through 115). Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2×10⁹ Kelvin, M. G. Haines et al., Physical Review Letters 96 (2006) 075003. Link to Sandia's news release.
44. ^ Core temperature of a high–mass (>8–11 solar masses) star after it leaves the main sequence on the Hertzsprung–Russell diagram and begins the alpha process (which lasts one day) of fusing silicon–28 into heavier elements in the following steps: sulfur–32 → argon–36 → calcium–40 → titanium–44 → chromium–48 → iron–52 → nickel–56. Within minutes of finishing the sequence, the star explodes as a Type II supernova. Citation: Stellar Evolution: The Life and Death of Our Luminous Neighbors (by Arthur Holland and Mark Williams of the University of Michigan). Link to Web site. More informative links can be found here [2], and here [3], and a concise treatise on stars by NASA is here [4].^{[dead link]}
45. ^ Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). It's also noteworthy that at 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass (m) 5% greater than its rest mass (m₀).  Torus Formation in Neutron Star Mergers and Well-Localized Short Gamma-Ray Bursts, R. Oechslin et al. of Max Planck Institute for Astrophysics., arXiv:astro-ph/0507099 v2, 22 Feb. 2006. An html summary.
46. ^ Results of research by Stefan Bathe using the PHENIX detector on the Relativistic Heavy Ion Collider at Brookhaven National Laboratory in Upton, New York, U.S.A.  Bathe has studied gold-gold, deuteron-gold, and proton-proton collisions to test the theory of quantum chromodynamics, the theory of the strong force that holds atomic nuclei together.  Link to news release.
47. ^ How do physicists study particles? by CERN.
48. ^ The Planck frequency equals 1.85487(14)×10⁴³ Hz (which is the reciprocal of one Planck time). Photons at the Planck frequency have a wavelength of one Planck length. The Planck temperature of 1.41679(11)×10³² K equates to a calculated b /T = λ_max wavelength of 2.04531(16)×10⁻²⁶ nm. However, the actual peak emittance wavelength quantizes to the Planck length of 1.61624(12)×10⁻²⁶ nm.

Further reading

• Chang, Hasok (2004). Inventing Temperature: Measurement and Scientific Progress. Oxford: Oxford University Press. ISBN 978-0-19-517127-3.
• Zemansky, Mark Waldo (1964). Temperatures Very Low and Very High. Princeton, N.J.: Van Nostrand.
• T. J. Quinn (1983), Temperature, Academic Press, London.

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.
• from Oklahoma State University

v t 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 Lifted condensation level (LCL) Precipitation Water vapor Convection Convective available potential energy (CAPE) Convective inhibition (CIN) Convective instability Convective temperature (Tc) Equilibrium level (EL) Helicity Level of free convection (LFC) Lifted index (LI) Bulk Richardson number (BRN) Temperature Dew point (Td) Equivalent temperature (Te) Forest fire weather index Haines Index 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 t e Scales of temperature Celsius Delisle Fahrenheit Gas Mark Kelvin Leiden Newton Planck Rankine Réaumur Rømer Wedgwood 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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