# User Contributed Dictionary

- Plural of temperature

# Extensive Definition

Temperature is a physical property of a system
that underlies the common notions of hot and cold; something that
is hotter generally has the greater temperature. Specifically,
temperature is a property of matter. Temperature is one of the
principal parameters of thermodynamics. On the
microscopic scale, temperature is defined as the average energy of
microscopic motions of a single particle in the system per
degree of freedom. On the macroscopic scale, temperature is the
unique physical property that determines the direction of heat flow
between two objects placed in thermal contact. If no heat flow
occurs, the two objects have the same temperature; otherwise heat
flows from the hotter object to the colder object. These two basic
principles are stated in the
zeroth law and
second law of thermodynamics, respectively. For a solid, these
microscopic motions are principally the vibrations of its atoms
about their sites in the solid. For an ideal monatomic
gas, the microscopic motions are the translational motions of
the constituent gas particles. For a multiatomic gas, vibrational and rotational motion should be
included too.

Temperature is measured with thermometers that may be
calibrated to a
variety of
temperature scales. In most of the world (except for the
United
States, Jamaica, and a few
other countries), the degree
Celsius scale is used for most temperature measuring purposes.
The entire scientific world (the U.S. included) measures
temperature using the Celsius scale and thermodynamic temperature
using the kelvin scale,
which is just the Celsius scale shifted downwards so that 0 K=
−273.15 °C, or absolute
zero. Many engineering fields in the U.S., especially high-tech
ones, also use the kelvin and degrees Celsius scales. However, the
United States is the last major country in which the degree
Fahrenheit temperature scale is used by most lay people,
industry, popular meteorology, and government.
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.

## Overview

Intuitively, temperature is the measurement of how hot or cold something is, although the most immediate way in which we can measure this, by feeling it, is unreliable, resulting in the phenomenon of felt air temperature, which can differ at varying degrees from actual temperature. On the molecular level, temperature is the result of the motion of particles which make up a substance. Temperature increases as the energy of this motion increases. The motion may be the translational motion of the particle, or the internal energy of the particle due to molecular vibration or the excitation of an electron energy level. Although very specialized laboratory equipment is required to directly detect the translational thermal motions, thermal collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting cold temperature of 700 nK (1 nK = 10−9 K) in 1994, they used optical lattice laser equipment to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature.Molecules, such as
O2, have more degrees
of freedom than single atoms: they can have rotational and
vibrational motions as well as translational motion. An increase in
temperature will cause the average translational energy to
increase. It will also cause the energy associated with vibrational
and rotational modes to increase. Thus a diatomic gas, with extra
degrees of freedom rotation and vibration, will require a higher
energy input to change the temperature by a certain amount, i.e. it
will have a higher heat
capacity than a monatomic gas.

The process of cooling involves removing energy
from a system. When there is no more energy able to be removed, the
system is said to be at absolute
zero, which is the point on the thermodynamic
(absolute) temperature scale where all kinetic motion in the
particles comprising matter ceases and they are at complete rest in
the “classic” (non-quantum
mechanical) sense. By definition, absolute zero is a
temperature of precisely 0 kelvins (−273.15 °C or −459.67
°F).

## Details

The formal properties of temperature follow from its mathematical definition (see below for the zeroth law definition and the second law definition) and are studied in thermodynamics and statistical mechanics.Contrary to other thermodynamic quantities such
as entropy and heat, whose microscopic definitions
are valid even far away from thermodynamic
equilibrium, temperature being an average energy per particle
can only be defined at thermodynamic equilibrium, or at least local
thermodynamic equilibrium (see below).

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

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

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

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

## The role of temperature in nature

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

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

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

## Temperature measurement

Main article: Temperature measurement, see also The International Temperature Scale.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,
alongside the Celsius scale and
the kelvin scale.

### Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (Symbol: K). The kelvin and Celsius (Centigrade) scales are, by international agreement, defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water (water specially prepared with a specified blend of hydrogen and oxygen isotopes). Absolute zero is defined as being precisely 0 K and −273.15 °C. Absolute zero is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. At absolute zero, matter contains no thermal energy. Also, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things: 1) it fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; 2) it establishes that one kelvin has precisely the same magnitude as a one degree increment on the Celsius scale; and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0 K = −273.15 °C and 273.16 K = 0.01 °C). Formulas for converting from these defining units of temperature to other scales can be found at Temperature conversion formulas.In the field of plasma
physics, because of the high temperatures encountered and the
electromagnetic
nature of the phenomena involved, it is customary to express
temperature in electronvolts (eV) or
kiloelectronvolts (keV), where 1 eV = 11,604 K. In the study of
QCD
matter one routinely meets temperatures of the order of a few
hundred MeV,
equivalent to about 1012 K.

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

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

See
temperature conversion formulas for conversions between most
temperature scales.

### Negative temperatures

- See main article: Negative temperature.

For some systems and specific definitions of
temperature, it is possible to obtain a negative
temperature. A system with a negative temperature is not colder
than absolute
zero, but rather it is, in a sense, hotter than infinite temperature.

## Theoretical foundation of temperature

### Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two systems with fixed volumes are brought together in thermal contact, changes most likely will take place in the properties of both systems. These changes are caused by the transfer of heat between the systems. A state must be reached in which no further changes occur, to put the objects into thermal equilibrium.A basis for the definition of temperature can be
obtained from the
zeroth law of thermodynamics which states that if two systems,
A and B, are in thermal equilibrium and a third system C is in
thermal equilibrium with system A then systems B and C will also be
in thermal equilibrium (being in thermal equilibrium is a transitive
relation; moreover, it is an equivalence
relation). This is an empirical fact, based on observation
rather than theory. Since A, B, and C are all in thermal
equilibrium, it is reasonable to say each of these systems shares a
common value of some property. We call this property
temperature.

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

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

- \overline_k = \begin \frac \end kT , where k = R/n (n= Avogadro number, R= ideal gas constant).

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

- E_k = \begin \frac \end mv^2

### Temperature of the vacuum

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

More realistically, no such ideal vacuum exists.
For instance a thermometer in a vacuum chamber which is maintained
at some finite temperature (say, chamber is in the lab at room
temperature) will equilibrate with the thermal radiation it
receives from the chamber and with time reaches the temperature of
the chamber. If a thermometer orbiting the Earth is exposed to a
sunlight, then it
equilibrates at the temperature at which power received by the
thermometer from the Sun is exactly equal to the power radiated
away by thermal radiation of the thermometer. For a black body this
equilibrium temperature is about 281 K (+8 °C). Earth average
temperature (which is maintained by similar balance) is close to
this temperature.

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

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

### Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means that for a perfectly ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which 100% of tosses came up the same.On the other hand, there are multiple
combinations that can result in disordered or mixed systems, where
some fraction are heads and the rest tails. A disordered system can
be 90% heads and 10% tails, or it could be 40% heads and 60% 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 number of
combinations corresponding to ~50% heads and ~50% tails dominates
and obtaining an outcome significantly different from 50/50 becomes
extremely unlikely. Thus the system naturally progresses to a state
of maximum disorder or entropy.

We previously stated that temperature controls
the flow of heat between two systems and we have just shown that
the universe, and we would expect any natural system, tends to
progress so as to maximize entropy. Thus, we would expect there to
be some relationship between temperature and entropy. In order to
find this relationship let's first consider the relationship
between heat, work and temperature. A heat engine
is a device for converting heat into mechanical work and analysis
of the Carnot
heat engine provides the necessary relationships we seek. The
work from a heat engine corresponds to the difference between the
heat put into the system at the high temperature, qH and the heat
ejected at the low temperature, qC. The efficiency is the work
divided by the heat put into the system or: \textrm = \frac = \frac
= 1 - \frac (2)

where wcy is the work done per cycle. We see that
the efficiency depends only on qC/qH. Because qC and qH correspond
to heat transfer at the temperatures TC and TH, respectively, qC/qH
should be some function of these temperatures: \frac = f(T_H,T_C)
(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: q_
= \frac

which implies: q_ = f(T_1,T_3) =
f(T_1,T_2)f(T_2,T_3)

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

\frac = \frac (4)

Substituting Equation 4 back into Equation 2
gives a relationship for the efficiency in terms of temperature:
\textrm = 1 - \frac = 1 - \frac (5)

Notice that for TC = 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: \frac - \frac = 0

where the negative sign indicates heat ejected
from the system. This relationship suggests the existence of a
state function, S, defined by: dS = \frac (6)

where the subscript indicates a reversible
process. The change of this state function around any cycle is
zero, as is necessary for any state function. This function
corresponds to the entropy of the system, which we described
previously. We can rearranging Equation 6 to get a new definition
for temperature in terms of entropy and heat: T = \frac (7)

For a system, where entropy S may be a function
S(E) of its energy E, the temperature T is given by: \frac = \frac
(8)

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

## See also

- Absolute zero
- Body temperature (Thermoregulation)
- Celsius
- Color temperature
- Entropy
- Fahrenheit
- Heat
- Heat conduction
- Heat convection
- ITS-90
- ISO 1
- Kelvin
- Maxwell's demon
- Orders of magnitude (temperature)
- Rankine scale
- Thermal radiation
- Thermodynamic (absolute) temperature
- Thermometer
- Thermography
- Triple point
- Wet Bulb Globe Temperature

## References

- Thermal Physics (2nd ed.)

## External links

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

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