The Meaning of Temperature

Temperature is the property that gives physical meaning to the concept of heat. If an object is cold, we say it has a low temperature. If it is hot, we say it has a high temperature. It can also be observed that if a hot poker is plunged into cold water, the poker becomes cooler and the water becomes warmer. This means that the hot body gives up some of its heat to the cold body. The exchange of heat will continue until the water and the poker have the same temperature. Thus the temperature of a substance will determine whether heat flows from it or to it when the substance is in contact with another body at a different temperature.

 

For accuracy it is necessary to have a definition of temperature that is based on some value which does not change. There is such a value for temperature. It is called absolute zero. The idea of absolute zero first appeared in 1802. The chemist Joseph L. Gay-Lussac found that all gases, when heated through one degree, expand by 1/273 of the volume that they occupy at the freezing point of water. It was reasoned that if the gas
were cooled, its volume would decrease by the same amount as the temperature decreased.


Therefore if we assume the freezing point of water is 0o and the gas is cooled, its volume will shrink to zero at 273 degrees below 0 degrees. Further study has supported the idea of an absolute zero. It is now defined as the temperature at which all molecular and atomic motion stops completely. In this sense, then, the temperature of a substance is a measure of the intensity of motion of all atoms and molecules in the
substance. Absolute zero is also the temperature below which it is impossible to go.


What is Temperature?

In a qualitative manner, we can describe the temperature of an object as that which determines the sensation of warmth or coldness felt from contact with it.


It is easy to demonstrate that when two objects of the same material are placed together (physicists say when they are put in thermal contact), the object with the higher temperature cools while the cooler object becomes warmer until a point is reached after which no more change occurs, and to our senses, they feel the same. When the thermal changes have stopped, we say that the two objects (physicists define them more rigorously
as systems) are in thermal equilibrium. We can then define the temperature of the system by saying that the temperature is that quantity which is the same for both systems when they are in thermal equilibrium.


If we experiment further with more than two systems, we find that many systems can be brought into thermal equilibrium with each other; thermal equilibrium does not depend on the kind of object used. Put more precisely,

if two systems are separately in thermal equilibrium with a third, then they must also be in thermal equilibrium with each other,

and they all have the same temperature regardless of the kind of systems they are.

The statement in italics, called the zeroth law of thermodynamics may be restated as follows:


If three or more systems are in thermal contact with each other and all in equilibrium together, then any two taken separately are in equilibrium with one another. (quote from T. J. Quinn's monograph "Temperature")

Now one of the three systems could be an instrument calibrated to measure the temperature - i.e. a thermometer. When a calibrated thermometer is put in thermal contact with a system and reaches thermal equilibrium, we then have a quantitative measure of the temperature of the system. For example, a mercuryin- glass clinical thermometer is put under the tongue of a patient and allowed to reach thermal equilibrium in
the patient's mouth - we then see by how much the silvery mercury has expanded in the stem and read the scale of the thermometer to find the patient's temperature.


Effects of Temperature

Temperature plays an important part in determining the conditions in which living matter can exist. Thus, birds and mammals demand a very narrow range of body temperatures for survival and must be protected against extreme heat or cold. Aquatic species can exist only within a narrow temperature range of the water, which differs for various species. Thus, for example, the increase in temperature of river water by only a few
degrees as a result of heat discharged from power plants may kill most of the native fish.


The properties of all materials are also markedly affected by temperature changes. At arctic temperatures, for example, steel becomes very brittle and breaks easily, and liquids either solidify or become very viscous, offering high frictional resistance to flow. At temperatures near absolute zero, many materials exhibit strikingly different characteristics. At high temperatures, solid materials liquefy or become gaseous; chemical compounds may break up into their constituents.


The temperature of the atmosphere is greatly influenced by both the land and the sea areas. In January, for example, the great landmasses of the northern hemisphere are much colder than the oceans at the same latitude, and in July the situation is reversed. At low elevations, the air temperature is also determined largely by the surface temperature of the earth. The periodic temperature changes are due mainly to the sun's
radiant heating of the land areas of the earth, which in turn convect heat to the overlying air. As a result of this phenomenon, the temperature decreases with altitude, from a standard reference value of 15.5°C (60°F) at sea level (in temperate latitudes), to about -55°C (about -67°F) at about 11,000 m (about 36,000 ft). Above this altitude, the temperature remains nearly constant up to about 33,500 m (about 110,000 ft).


The Measurement of Temperature

To measure temperature exactly it is necessary to design and construct a thermometer scale. First, two natural events, each of which always occurs at the same temperature, are selected. The freezing point of water and the boiling point of water are two such fixed points. They can be reproduced easily. Then a number which indicates a temperature is arbitrarily assigned to each of these fixed points (32º and 212º F or 0º and
100º C). Finally, the interval between these points is divided into a fixed number of equal degrees. A temperature below zero is marked negative.


Temperature Scales

Five different temperature scales are in use today: the Celsius scale, known also as the centigrade scale, the Fahrenheit scale, the Kelvin scale, the Rankine scale, and the international thermodynamic temperature scale. The centigrade scale, with a freezing point of O°C and a boiling point of 100°C, is widely used throughout the world, particularly for scientific work, although it was superseded officially in 1950 by the international
temperature scale. In the Fahrenheit scale, used in English-speaking countries for purposes other than scientific work and based on the mercury thermometer, the freezing point of water is defined as 32°F and the boiling point as 212°F. In the Kelvin scale, the most commonly used thermodynamic temperature scale, zero is defined as the absolute zero of temperature, that is, -273.15°C, or - 459.67°F. Another scale employing
absolute zero as its lowest point is the Rankine scale, in which each degree of temperature is equivalent to one degree on the Fahrenheit scale. The freezing point of water on the Rankine scale is 492°R, and the boiling point is 672°R.


In 1933 scientists of 31 nations adopted a new international temperature scale with additional fixed temperature points, based on the Kelvin scale and thermodynamic principles. The international scale is based on the property of electrical resistivity, with platinum wire as the standard for temperature between -190° and 660°C. Above 660°C, to the melting point of gold, 1063°C, a standard thermocouple, which is a device that
measures temperature by the amount of voltage produced between two wires of different metals, is used; beyond this point temperatures are measured by the so - called optical pyrometer, which uses the intensity of light of a wavelength emitted by a hot body for the purpose.


In 1954 the triple point of water—that is, the point at which the three phases of water (vapor, liquid, and ice) are in equilibrium—was adopted by international agreement as 273.16 K. The triple point can be determined with greater precision than the freezing point and thus provides a more satisfactory fixed point for the absolute thermodynamic scale. In cryogenics, or low-temperature research, temperatures as low as 0.003 K
have been produced by the demagnetization of paramagnetic materials. Momentary high temperatures estimated to be greater than 100,000,000 K have been achieved by nuclear explosions.

 

One of the earliest temperature scales was that devised by the German physicist Gabriel Daniel Fahrenheit. According to this scale, at standard atmospheric pressure, the freezing point (and melting point of ice) is 32°F, and the boiling point is 212°F. The centigrade, or Celsius scale, invented by the Swedish astronomer Anders Celsius, and used throughout most of the world, assigns a value of 0°C to the freezing point and
100°C to the boiling point. In scientific work, the absolute or Kelvin scale, invented by the British mathematician and physicist William Thomas, 1st Baron Kelvin, is most widely used. In this scale, absolute zero is at -273.16°C, which is zero K, and the degree intervals are identical to those measured on the centigrade scale. The corresponding "absolute Fahrenheit" or Rankine scale, devised by the British engineer
and physicist William J. M. Rankine (1820-72), places absolute zero at -459.69°F, which is 0°R, and the freezing point at 491.69°R. A more consistent scientific temperature scale, based on the Kelvin scale, was adopted in 1933. It is often necessary to convert a temperature on one scale to a corresponding temperature on another. Some useful conversion relations are:

Fahrenheit to Celsius ºC 5/9 (ºF - 32)
Celsius to Fahrenheit ºF 9/5 ºC + 32
Celsius to Kelvin ºC + 273
Fahrenheit to Rankine ºR ºF + 460


What is a Thermometer?

A thermometer is an instrument that measures the temperature of a system in a quantitative way. The easiest way to do this is to find a substance having a property that changes in a regular way with its temperature. The most direct 'regular' way is a linear one:


t(x) = ax + b,


where t is the temperature of the substance and changes as the property x of the substance changes. The constants a and b depend on the substance used and may be evaluated by specifying two temperature points on the scale, such as 32° for the freezing point of water and 212° for its boiling point.


For example, the element mercury is liquid in the temperature range of -38.9° C to 356.7° C (we'll discuss the Celsius ° C scale later). As a liquid, mercury expands as it gets warmer, its expansion rate is linear and can be accurately calibrated.

thermometer


The mercury-in-glass thermometer, illustrated in the above figure, contains a bulb filled with mercury that is allowed to expand into a capillary. Its rate of expansion is calibrated on the glass scale.