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About Temperature


This document was prepared for the middle school math teachers who
are taking part in Project Skymath. It is also hoped that the
general public will find it interesting.

Disponible en espanol, toque aqui.

Contents (click on star)

What is Temperature
The Development of Thermometers and Temperature Scales
Heat and Thermodynamics
The Kinetic Theory
Thermal Radiation
3 K - The Temperature of the Universe

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 objectsof 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 mercury-in-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.

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.

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.

The Development of Thermometers and Temperature Scales

The historical highlights in the development of thermometers and their
scales given here are based on "Temperature" by T. J. Quinn and "Heat"
by James M. Cork.

One of the first attempts to make a standard temperature scale
occurred about AD 170, when Galen, in his medical writings, proposed a
standard "neutral" temperature made up of equal quantities of boiling
water and ice; on either side of this temperature were four degrees of
heat and four degrees of cold, respectively.

The earliest devices used to measure the temperature were called

They consisted of a glass bulb having a long tube extending
downward into a container of colored water, although Galileo in 1610
is supposed to have used wine. Some of the air in the bulb was
expelled before placing it in the liquid, causing the liquid to rise
into the tube. As the remaining air in the bulb was heated or cooled,
the level of the liquid in the tube would vary reflecting the change
in the air temperature. An engraved scale on the tube allowed for a
quantitative measure of the fluctuations.

The air in the bulb is referred to as the thermometric medium, i.e.
the medium whose property changes with temperature.

In 1641, the first sealed thermometer that used liquid rather than air
as the thermometric medium was developed for Ferdinand II, Grand Duke
of Tuscany. His thermometer used a sealed alcohol-in-glass device,
with 50 "degree" marks on its stem but no "fixed point" was used to
zero the scale. These were referred to as "spirit" thermometers.

Robert Hook, Curator of the Royal Society, in 1664 used a red dye in
the alcohol . His scale, for which every degree represented an equal
increment of volume equivalent to about 1/500 part of the volume of
the thermometer liquid, needed only one fixed point. He selected the
freezing point of water. By scaling it in this way, Hook showed that a
standard scale could be established for thermometers of a variety of
sizes. Hook's original thermometer became known as the standard of
Gresham College and was used by the Royal Society until 1709. (The
first intelligible meteorological records used this scale).

In 1702, the astronomer Ole Roemer of Copenhagen based his scale upon
two fixed points: snow (or crushed ice) and the boiling point of
water, and he recorded the daily temperatures at Copenhagen in 1708-
1709 with this thermometer.

It was in 1724 that Gabriel Fahrenheit, an instrument maker of Däanzig
and Amsterdam, used mercury as the thermometric liquid. Mercury's
thermal expansion is large and fairly uniform, it does not adhere to
the glass, and it remains a liquid over a wide range of temperatures.
Its silvery appearance makes it easy to read.

Fahrenheit described how he calibrated the scale of his mercury

"placing the thermometer in a mixture of sal ammoniac or sea salt,
ice, and water a point on the scale will be found which is denoted
as zero. A second point is obtained if the same mixture is used
without salt. Denote this position as 30. A third point,
designated as 96, is obtained if the thermometer is placed in the
mouth so as to acquire the heat of a healthy man." (D. G.
Fahrenheit,Phil. Trans. (London) 33, 78, 1724)

On this scale, Fahrenheit measured the boiling point of water to be
212. Later he adjusted the freezing point of water to 32 so that the
interval between the boiling and freezing points of water could be
represented by the more rational number 180. Temperatures measured on
this scale are designated as degrees Fahrenheit (° F).

In 1745, Carolus Linnaeus of Upsula, Sweden, described a scale in
which the freezing point of water was zero, and the boiling point 100,
making it a centigrade (one hundred steps) scale. Anders Celsius
(1701-1744) used the reverse scale in which 100 represented the
freezing point and zero the boiling point of water, still, of course,
with 100 degrees between the two defining points.

In 1948 use of the Centigrade scale was dropped in favor of a new
scale using degrees Celsius (° C). The Celsius scale is defined by the
following two items that will be discussed later in this essay:

(i) The triple point of water is defined to be 0.01° C.
(ii) A degree Celsius equals the same temperature change as a degree
on the ideal-gas scale.

On the Celsius scale the boiling point of water at standard
atmospheric pressure is 99.975 C in contrast to the 100 degrees
defined by the Centigrade scale.

To convert from Celsius to Fahrenheit: multiply by 1.8 and add 32.

° F = 1.8° C + 32
° K = ° C + 273.

(Or, you can get someone else to do it

for you!)

In 1780, J. A. C. Charles, a French physician, showed that for the
same increase in temperature, all gases exhibited the same increase in
volume. Because the expansion coefficient of gases is so very nearly
the same, it is possible to establish a temperature scale based on a
single fixed point rather than the two fixed- point scales, such as
the Fahrenheit and Celsius scales. This brings us back to a
thermometer that uses a gas as the thermometric medium.

In a constant volume gas thermometer a large bulb B of gas,
hydrogen for example, under a set pressure connects with a
mercury-filled "manometer" by means of a tube of very small volume.
(The Bulb B is the temperature-sensing portion and should contain
almost all of the hydrogen). The level of mercury at C may be adjusted
by raising or lowering the mercury reservoir R. The pressure of the
hydrogen gas, which is the "x" variable in the linear relation with
temperature, is the difference between the levels D and C plus the
pressure above D.

P. Chappuis in 1887 conducted extensive studies of gas thermometers
with constant pressure or with constant volume using hydrogen,
nitrogen, and carbon dioxide as the thermometric medium. Based on his
results, the Comité International des Poids et Mesures adopted the
constant-volume hydrogen scale based on fixed points at the ice point
(0° C) and the steam point (100° C) as the practical scale for
international meteorology.

Experiments with gas thermometers have shown that there is very little
difference in the temperature scale for different gases. Thus, it is
possible to set up a temperature scale that is independent of the
thermometric medium if it is a gas at low pressure. In this case, all
gases behave like an "Ideal Gas" and have a very simple relation
between their pressure, volume, and temperature: pV= (constant)T.

This temperature is called the thermodynamic temperature and is now
accepted as the fundamental measure of temperature. Note that there is
a naturally-defined zero on this scale - it is the point at which the
pressure of an ideal gas is zero, making the temperature also zero. We
will continue a discussion of "absolute zero" in a later section. With
this as one point on the scale, only one other fixed point need be
defined. In 1933, the International Committee of Weights and Measures
adopted this fixed point as the triple point of water , the
temperature at which water, ice, and water vapor coexist in
equilibrium); its value is set as 273.16. The unit of temperature on
this scale is called the kelvin, after Lord Kelvin (William Thompson),
1824-1907, and its symbol is K (no degree symbol used).

To convert from Celsius to Kelvin, add 273.

K = ° C + 273.

Thermodynamic temperature is the fundamental temperature; its unit
is the kelvin which is defined as the fraction 1/273.16 of the
thermodynamic temperature of the triple point of water.

Sir William Siemens, in 1871, proposed a thermometer whose
thermometric medium is a metallic conductor whose resistance changes
with temperature. The element platinum does not oxidize at high
temperatures and has a relatively uniform change in resistance with
temperature over a large range. The Platinum Resistance Thermometer is
now widely used as a thermoelectric thermometer and covers the
temperature range from about -260° C to 1235° C.

Several temperatures were adopted as Primary reference points so as to
define the International Practical Temperature Scale of 1968. The
International Temperature Scale of 1990 was adopted by the
International Committee of Weights and Measures at its meeting in
1989. Between 0.65K and 5.0K, the temperature is defined in terms of
the vapor pressure - temperature relations of the isotopes of helium.
Between 3.0K and the triple point of neon (24.5561K) the temperature
is defined by means of a helium gas thermometer. Between the triple
point of hydrogen (13.8033K) and the freezing point of silver
(961.78°K) the temperature is defined by means of platinum resistance
thermometers. Above the freezing point of silver the temperature is
defined in terms of the Planck radiation law.

T. J. Seebeck, in 1826, discovered that when wires of different metals
are fused at one end and heated, a current flows from one to the
other. The electromotive force generated can be quantitatively related
to the temperature and hence, the system can be used as a thermometer
- known as a thermocouple. The thermocouple is used in industry and
many different metals are used - platinum and platinum/rhodium,
nickel-chromium and nickel-aluminum, for example. The National
Institute of Standards and Technology (NIST) maintains databases for
standardizing thermometers.

For the measurement of very low temperatures, the magnetic
susceptibility of a paramagnetic substance is used as the thermometric
physical quantity. For some substances, the magnetic susceptibility
varies inversely as the temperature. Crystals such as cerrous
magnesium nitrate and chromic potassium alum have been used to measure
temperatures down to 0.05 K; these crystals are calibrated in the
liquid helium range. This diagram and the last illustration in this
text were taken from the Low Temperature Laboratory, Helsinki
University of Technology's picture archive. For these very low, and
even lower, temperatures, the thermometer is also the mechanism for
cooling. Several low-temperature laboratories conduct interesting
applied and theoretical research on how to reach the lowest possible
temperatures and how work at these temperatures may find application.

Heat and Thermodynamics

Prior to the 19th century, it was believed that the sense of how hot
or cold an object felt was determined by how much "heat" it contained.
Heat was envisioned as a liquid that flowed from a hotter to a colder
object; this weightless fluid was called "caloric", and until the
writings of Joseph Black (1728-1799), no distinction was made between
heat and temperature. Black distinguished between the quantity
(caloric) and the intensity (temperature) of heat.

Benjamin Thomson, Count Rumford, published a paper in 1798 entitled
"an Inquiry Concerning the Source of Heat which is Excited by
Friction". Rumford had noticed the large amount of heat generated when
a cannon was drilled. He doubted that a material substance was flowing
into the cannon and concluded "it appears to me to be extremely
difficult if not impossible to form any distinct idea of anything
capable of being excited and communicated in the manner the heat was
excited and communicated in these experiments except motion."

But it was not until J. P. Joule published a definitive paper in 1847
that the the caloric idea was abandoned. Joule conclusively showed
that heat was a form of energy. As a result of the experiments of
Rumford, Joule, and others, it was demonstrated (explicitly stated by
Helmholtz in 1847), that the various forms of energy can be
transformed one into another.

When heat is transformed into any other form of energy, or when
other forms of energy are transformed into heat, the total amount
of energy (heat plus other forms) in the system is constant.

This is the first law of thermodynamics, the conservation of energy.
To express it another way: it is in no way possible either by
mechanical, thermal, chemical, or other means, to obtain a perpetual
motion machine; i.e., one that creates its own energy (except in the
fantasy world of Maurits Escher's "Waterfall"!)

A second statement may also be made about how machines operate. A
steam engine uses a source of heat to produce work. Is it possible to
completely convert the heat energy into work, making it a 100%
efficient machine? The answer is to be found in the second law of

No cyclic machine can convert heat energy wholly into other forms
of energy. It is not possible to construct a cyclic machine that
does nothing but withdraw heat energy and convert it into
mechanical energy.

The second law of thermodynamics implies the irreversibility of
certain processes - that of converting all heat into mechanical
energy, although it is possible to have a cyclic machine that does
nothing but convert mechanical energy into heat!

Sadi Carnot (1796-1832) conducted theoretical studies of the
efficiencies of heat engines (a machine which converts some of its
heat into useful work). He was trying to model the most efficient heat
engine possible. His theoretical work provided the basis for practical
improvements in the steam engine and also laid the foundations of
thermodynamics. He described an ideal engine, called the Carnot
engine, that is the most efficient way an engine can be constructed.
He showed that the efficiency of such an engine is given by

efficiency = 1 - T"/T',

where the temperatures, T' and T" , are the hot and cold "reservoirs"
, respectively, between which the machine operates. On this
temperature scale, a heat engine whose coldest reservoir is zero
degrees would operate with 100% efficiency. This is one definition of
absolute zero, and it can be shown to be identical to the absolute
zero we discussed previously. The temperature scale is called the
absolute, the thermodynamic , or the kelvin scale.

The way that the gas temperature scale and the thermodynamic
temperature scale are shown to be identical is based on the
microscopic interpretation of temperature, which postulates that the
macroscopic measurable quantity called temperature is a result of the
random motions of the microscopic particles that make up a system.

The Kinetic Theory

This brief summary is abridged from a more detailed discussion to be
found in Quinn's "Temperature"

About the same time that thermodynamics was evolving, James Clerk
Maxwell (1831-1879) and Ludwig Boltzmann (1844-1906) developed a
theory describing the way molecules moved - molecular dynamics. The
molecules that make up a perfect gas move about, colliding with each
other like billiard balls and bouncing off the surface of the
container holding the gas. The energy associated with motion is called
Kinetic Energy and this kinetic approach to the behavior of ideal
gases led to an interpretation of the concept of temperature on a
microscopic scale.

The amount of kinetic energy each molecule has is a function of its
velocity; for the large number of molecules in a gas (even at low
pressure), there should be a range of velocities at any instant of
time. The magnitude of the velocities of the various particles should
vary greatly - no two particles should be expected to have the exact
same velocity. Some may be moving very fast; others, quite slowly.
Maxwell found that he could represent the distribution of velocities
statistically by a function known as the Maxwellian distribution. The
collisions of the molecules with their container gives rise to the
pressure of the gas. By considering the average force exerted by the
molecular collisions on the wall, Boltzmann was able to show that the
average kinetic energy of the molecules was directly comparable to the
measured pressure, and the greater the average kinetic energy, the
greater the pressure. From Boyles' Law, we know that the pressure is
directly proportional to the temperature, therefore, it was shown that
the kinetic energy of the molecules related directly to the
temperature of the gas. A simple relation holds for this:

average kinetic energy of molecules=3kT/2,

where k is the Boltzmann constant. Temperature is a measure of the
energy of thermal motion and, at a temperature of zero, the energy
reaches a minimum (quantum mechanically, the zero-point motion remains
at 0 K).

In July, 1995, physicists in Boulder, Colo.achieved a temperature far
lower than has ever been produced before and created an entirely new
state of matter predicted decades ago by Albert Einstein and Satyendra
Nath Bose. The press release describes the nature of this experiment
and a full description of this phenomenon is described by the
University of Colorado's BEC Homepage.

Dealing with a system which contained huge numbers of molecules
requires a statistical approach to the problem. About 1902, J. W.
Gibbs (1839-1903) introduced statistical mechanics with which he
demonstrated how average values of the properties of a system could be
predicted from an analysis of the most probable values of these
properties found from a large number of identical systems (called an
ensemble). Again, in the statistical mechanical interpretation of
thermodynamics, the key parameter is identified with a temperature
which can be directly linked to the thermodynamic temperature, with
the temperature of Maxwell's distribution, and with the perfect gas

Temperature becomes a quantity definable either in terms of
macroscopic thermodynamic quantities such as heat and work, or,
with equal validity and identical results, in terms of a quantity
which characterized the energy distribution among the particles in
a system. (Quinn, "Temperature")

With this understanding of the concept of temperature, it is possible
to explain how heat (thermal energy) flows from one body to another.
Thermal energy is carried by the molecules in the form of their
motions and some of it, through molecular collisions, is transferred
to molecules of a second object when put in contact with it. This
mechanism for transferring thermal energy by contact is called

A second mechanism of heat transport is illustrated by a pot of water
set to boil on a stove - hotter water closest to the flame will rise
to mix with cooler water near the top of the pot. Convection involves
the bodily movement of the more energetic molecules in a liquid or

The third way that heat energy can be transferred from one body to
another is by radiation; this is the way that the sun warms the earth.
The radiation flows from the sun to the earth, where some of it is
absorbed, heating the surface.

A major dilemma in physics since the time of Newton was how to explain
the nature of this radiation.

Thermal Radiation

The nature of radiation has puzzled scientists for centuries. Maxwell
proposed that this form of energy travels as a vibratory electric and
magnetic disturbance through space in a direction perpendicular to
those disturbances.

In the diagram, the electric (red) and magnetic (blue) oscillations
are orthogonal to each other - the electric lying in the xy plane; the
magnetic, in the xz plane. The wave is traveling in the x direction.
An electromagnetic wave can be defined in terms of the frequency of
its oscillation, designated by the Greek letter nu (v). The wave moves
in a straight line with with a constant speed (designated as c if it
is moving through a vacuum); the distance between successive 'peaks'
of the wave is the wavelength,,of the wave and is equal to its
speed divided by its frequency.

The electromagnetic spectrum covers an enormous range in wavelengths,
from very short waves to very long ones.

The only region of the electromagnetic spectrum to which our eye is
sensitive is the "visible" range identified in the diagram by the
rainbow colors.

The sun is not the only object that provides radiant energy; any
object whose temperature is greater than 0 K will emit some radiant
energy. The challenge to scientists was to show how this radiant
energy is related to the temperature of the object.

If an object is placed in a container whose walls are at a uniform
temperature, we expect the object to come into thermal equilibrium
with the walls of the enclosure and the object should emit radiant
energy just like the walls of the container. Such an object absorbs
and radiates the same amount of energy. Now a blackened surface
absorbs all radiation incident upon it and it must radiate in the same
manner if it is in thermal equilibrium. Equilibrium thermal radiation
is therefore called black body radiation.

The first relation between temperature and radiant energy was deduced
by J. Stefan in 1884 and theoretically explained by Boltzmann about
the same time. It states:

where the total energy is per unit area per second emitted by the back
body, T is its absolute (thermodynamic) temperature and is the
Stefan-Boltzmann constant.

The great question at the turn of the century was to explain the way
this total radiant energy emitted by a black body was spread out into
the various frequencies or wavelengths of the radiation. Maxwell's
"classical" theory of electromagnetic oscillators failed to explain
the observed brightness distribution. It was left to Max Planck to
solve the dilemma by showing that the energy of the oscillators must
be quantized, i.e. the energies can not take any value but must change
in steps, the size of each step, or quantum, is proportional to the
frequency of the oscillator and equal to hv, where h is the Planck
constant. With this assumption, Planck derived the brightness
distribution of a black body and showed that it is defined by its
temperature. Once the temperature of a black body is specified, the
Planck law can be used to calculate the intensity of the light emitted
by the body as a function of wavelength. Conversely, if the brightness
distribution of a radiating body is measured, then, by fitting a
Planck curve to it, its temperature can be determined.

The curves illustrated below show that the hotter the body is, the
brighter it is at shorter wavelengths. The surface temperature of the
sun is 6000 K, and its Planck curve peaks in the visible wavelength
range. For bodies cooler than the sun, the peak of the Planck curve
shifts to longer wavelengths, until a temperature is reached such that
very little radiant energy is emitted in the visible range.

This figure (adapted from Adkins' "Thermal Physics") shows
several Planck curves for black bodies. The Intensity is in units of
energy per unit area per unit solid angle per unit time per unit
wavelength interval. The broken line illustrates the variation with
wavelength and temperature of the peaks of the curves.

This is a graphical representation of Wien's law, which states:

(max) ~ 0.29/T,

where (max) is the wavelength of maximum brightness in cm and T
is the absolute temperature of the black body.

The human body has a temperature of about 310 K and radiates primarily
in the far infrared. If a photograph of a human is taken with a camera
sensitive to this wavelength region, we get a "thermal" picture. This
picture is courtesy of the Infrared Processing and Analysis Center,
Jet Propulsion Laboratory, NASA.

A page developed by

3 K - The Temperature of the Universe

The sun and stars emit thermal radiation covering all wavelengths;
other objects in the sky, like the great clouds of gas in the Milky
Way, also emit thermal radiation but are much cooler. These objects
are best detected by infrared and radio telescopes - telescopes whose
detectors are sensitive to the longer wavelengths.

In 1965, Arno Penzias and Robert Wilson were conducting a careful
calibration of their radio telescope at the Bell Laboratory at
Whippany, New Jersey. The found that their receiver showed a "noise"
pattern as if it were inside a container whose temperature was 3K -
i.e. as if it were in equilibrium with a black body at 3 K. This
"noise" seemed to be coming from every direction. Earlier theoretical
predictions by George Gamow and other astrophysicists had predicted
the existence of a cosmic 3 K background. Penzias' and Wilson's
discovery was the observational confirmation of the isotropic
radiation from the Universe, believed to be a relic of the "Big Bang".
The enormous thermal energy released during the creation of the
universe began to cool as the universe expanded. Some 12 billion years
later, we are in a universe that radiates like a black body now cooled
to 3 K. In 1978 Penzias and Wilson were awarded the Nobel prize in
physics for this discovery.

A black body at 3 K emits most of its energy in the microwave
wavelength range. Molecules in the earth's atmosphere absorb this
radiation so that from the ground, astronomers cannot make
observations in this wavelength region. In 1989 the Cosmic Background
Explorer (COBE) satellite, developed by NASA's Goddard Space Flight
Center, was launched to measure the diffuse infrared and microwave
radiation from the early universe. One of its instruments, the Far
Infrared Absolute Spectrophotometer (FIRAS) compared the spectrum of
the cosmic microwave background radiation with a precise blackbody.
The cosmic microwave background spectrum was measured with a precision
of 0.03% and it fit precisely with a black body of temperature 2.726
K. Even though there are billions of stars in the universe, these
precise COBE measurements show that 99.97% of the radiant energy of
the Universe was released within the first year after the Big Bang
itself and now resides in this thermal 3 K radiation field.

A more detailed explanation of the origin of the microwave background
radiation, and its possible anisotropy, may be found here. A new
mission selected by NASA is the Microwave Anisotropy Probe (MAP) will
measure the small fluctuations in the background radiation and will
yield more information on the details of the early universe. The
European Space Agency has a similar mission planned.


The concept of temperature is as fundamental a physical concept as the
three fundamental quantities of mechanics - mass, length, and time.
Through the study of such practical problems as how to make a highly
efficient steam engine, fundamental physical theories emerge,
including the concepts of the quantum theory and the two laws of
thermodynamics. The second law, with its irreversibility requirement,
predicts an inevitable evolution from other forms of energy into heat.
It is the second law alone that provides an "arrow" for the concept of

We can record events (illustration from Low Temperature Laboratory of
Helsinki University of Technology)that cover 18 orders of magnitude in
the temperature range, and we have one clearly defined lower limit to
the temperature, absolute zero. Because of this
10-with-18-zeros-behind-it range in temperatures, there are many
different kinds of thermometers developed to explore it and many
different fields of research.

One of the beauties of "publishing" on the web is the interactive
element it offers. Joachim Reinhardt has written to point out that the
highest temperatures that are accessible on earth (only surpassed by
the early stages of the big bang) occur in high-energy collisions of
particles (in particular of heavy ions), during which one sees a
"fireball" with a temperature of several hundred MeV (which
corresponds to a temperature of 10 to the 12th power k). This fireball
cools down by expanding and by radiating off particles, mostly pions,
quite similar to the thermal black-body radiation.

Thermal physics is a field rich in theoretical and practical


I would like to thank Rick Ebert of IPAC for his help in locating some
of the infrared files used here and Dave Leisawitz of NASA Goddard for
his very careful editing of the article and for his assistance with
the COBE results. Joachim Reinhardt generated the pictures of most of
the scientists. Thanks to Seth Sharpless for scanning Galen's picture.
Carl Mungan provided advice on low-temperature thermodynamics, and
very generously served as an "expert" reviewer.


Adkins, C. J. Thermal Physics 1987 Cambridge University Press ISBN 0
521 33715 1

Brain, Marshall How Thermometers Work

Cork, James M. Heat 1942, John Wiley & Sons

Herzfeld, Charles M. Editor, Temperature: Its Measurement and Control
in Science and Industry, 1962, Reinhold

National Institutes of Science and Technology: The NIST Reference on
Constants, Units, and Uncertainty

Quinn, T. J. Temperature 1990 Academic Press ISBN 0-12-569681-7

Strom, Karen Blackbody Radiation

University of California, Berkeley Properties of Heat and Matter,
Physics Lab Demonstrations

University of Illinois - Thermodynamic Research Laboratory

Weber, Robert L. Heat and Temperature Measurement , 1950,
Prentice-Hall, Inc

Zemansky, Mark W. Heat and Thermodynamics 1968, Mc Graw Hill


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Beverly T. Lynds


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