Temperature
controlled
Temperature
n. 1. Constitution; state; degree of any quality.
The best composition and temperature is, to have openness in fame
and opinion, secrecy in habit, dissimulation in seasonable use,
and a power to feign, if there be no remedy.
- Bacon.
Memory depends upon the consistence and the temperature of the brain.
- I. Watts.
2. Freedom from passion; moderation.
In that proud port, which her so goodly graceth,
Most goodly temperature you may descry.
- Spenser.
3. (Physics) Condition with respect to heat or cold, especially
as indicated by the sensation produced, or by the thermometer or
pyrometer; degree of heat or cold; as, the temperature of the air;
high temperature; low temperature; temperature of freezing or of
boiling.
4. Mixture; compound.
Made a temperature of brass and iron together.
- Holland.
5. (Physiol. & Med.) The degree of heat of the body of a living
being, esp. of the human body; also (Colloq.), loosely, the excess
of this over the normal (of the human body 98°-99.5° F.,
in the mouth of an adult about 98.4°).Absolute temperature
(Physics) See under Absolute.
Animal temperature
(Physiol.) the nearly constant temperature maintained in the bodies
of warm-blooded (homoiothermal) animals during life. The ultimate
source of the heat is to be found in the potential energy of the
food and the oxygen which is absorbed from the air during respiration.
See Homoiothermal.
Temperature sense
(Physiol.) the faculty of perceiving cold and warmth, and so of
perceiving differences of temperature in external objects.
- H. N. Martin.
Noun 1. temperature - the degree of hotness or coldness of a body
or environment (corresponding to its molecular activity)
2. temperature - the somatic sensation of cold or heat
Temperature is the physical property of a system which underlies
the common notions of "hot" and "cold"; the
material with the higher temperature is said to be hotter.
General descriptionThe
formal properties of temperature are studied in thermodynamics.
Formally, temperature is that property which governs the transfer
of thermal energy, or heat, between one system and another. When
two systems are at the same temperature, they are in thermal equilibrium
and no heat transfer will occur. When a temperature difference does
exist, heat will tend to move from the higher temperature system
to the lower temperature system, until thermal equilibrium is again
established. This heat transfer may occur via conduction, convection
or radiation (see heat for additional discussion of the various
mechanisms of heat transfer).
Temperature
is related to the amount of thermal energy or heat in a system.
As more heat is added the temperature rises, similarly a decrease
in temperature corresponds to a loss of heat from the system. On
the microscopic scale this heat corresponds to the random motion
of atoms and molecules in the system. Thus, an increase in temperature
corresponds in an increase in the rate of movement of the atoms
in the system.
Temperature
is an intrinsic property of a system, meaning that it does not depend
on the system size or the amount of material in the system. Other
intrinsic properties include pressure and density. By contrast,
mass and volume are extrinsic properties, and depend on the amount
of material in the system.
ApplicationsTemperature 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 measurementMany methods have been developed for measuring
temperature. Most of these rely on measuring some physical property
of a working material that varies with temperature. One of the most
common devices for measuring temperature is the glass thermometer.
This consists of a glass tube filled with mercury or some other
liquid, which acts as the working fluid. Temperature increases cause
the fluid to expand, so the temperature can be determined by measuring
the volume of the fluid. Such thermometers are usually calibrated,
so that one can read the temperature, simply by observing the level
of the fluid in the thermometer. Another type of thermometer that
is not really used much in practice, but is important from a theoretical
standpoint is the gas thermometer mentioned previously.
Other important
devices for measuring temperature include:
Thermocouples
Thermistors
Resistance Temperature Detector (RTD)
Pyrometers
Other thermometers
One must be careful when measuring temperature to ensure that the
measuring instrument (thermometer, thermocouple, etc) is really
the same temperature as the material that is being measured. Under
some conditions heat from the measuring instrument can cause a temperature
gradient, so the measured temperature is different from the actual
temperature of the system. In such a case the measured temperature
will vary not only with the temperature of the system, but also
with the heat transfer properties of the system. An extreme case
of this effect gives rise to the wind chill factor, where the weather
feels colder under windy conditions than calm conditions even though
the temperature is the same. What is happening is that the wind
increases the rate of heat transfer from the body, resulting in
a larger reduction in body temperature for the same ambient temperature.
See also: color
temperature, Timeline of temperature and pressure measurement technology,
Planck temperature
Units of temperatureThe basic unit of temperature in the International
System of Units (SI) is the kelvin (K). One kelvin is formally defined
as 1/273.16 of the temperature of the triple point of water (the
point at which water, ice and water vapor exist in equilibrium).
The temperature 0 K is called absolute zero and corresponds to the
point at which the molecules and atoms have the least possible thermal
energy. An important unit of temperature in theoretical physics
is the Planck temperature (1.4 × 1032 K).
For everyday
applications, it is 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 Celsius to kelvin.
K = °C
+ 273.15
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:
°C = 5/9
· (°F - 32)
See temperature
conversion formulas for conversions between most temperature scales.
Comparison of
temperature scales Comment kelvin¹ Celsius Fahrenheit Rankine
Delisle Newton Réaumur Rømer
Absolute zero 0 -273.15 -459.67 0 559.725 -90.14² -218.52 -135.90
Fahrenheit's ice/salt mixture 255.37 -17.78 0 459.67 176.67 -5.87
-14.22 -1.83
Water freezes (at standard pressure) 273.15 0 32 491.67 150 0 0
7.5
Human body temperature 310.15 37 98.6 558.27 94.5 12.21 29.6 26.925
Water boils 373.15 100 212 671.67 0 33 80 60
Titanium melts 1941 1668 3034 3494 -2352 550 1334 883
¹ Only the kelvin, Celsius, and Fahrenheit scales are in use
today.
² Some numbers in this table have been rounded off.
Articles about temperature ranges:1 picokelvin
1 nanokelvin
1 microkelvin
1 millikelvin
1 kelvin
10 kelvin
100 kelvin
1,000 kelvin
10,000 kelvin
100,000 kelvin
106 kelvin
109 kelvin
1012 kelvin
1015 kelvin
1018 kelvin
1021 kelvin
1024 kelvin
1027 kelvin
1030 kelvin
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's consider the concept of thermal equilibrium.
If two closed systems with fixed volumes are brought together, so
that they are in thermal contact, changes may take place in the
properties of both systems. These changes are due to the transfer
of heat between the systems. When a state is reached in which no
further changes occur, the systems are in thermal equilibrium.
Now 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:
(1)
where T is temperature,
n is the number of moles of gas and R is the ideal gas constant.
Thus, one can define a scale for temperature based on the corresponding
pressure and volume of the gas. In practice, such a gas thermometer
is not very convenient, but other measuring instruments can be calibrated
to this scale.
Equation 1 indicates
that for a fixed volume of gas, the pressure increases with increasing
temperature. Pressure is just a measure of the force applied by
the gas on the walls of the container and is related to the energy
of the system. Thus, we can see that an increase in temperature
corresponds to an increase in the thermal energy of the system.
When two systems of differing temperature are placed in thermal
contact, the temperature of the hotter system decreases, indicating
that heat is leaving that system, while the cooler system is gaining
heat and increasing in temperature. Thus heat always moves from
a region of high temperature to a region of lower temperature and
it is the temperature difference that drives the heat transfer between
the two systems.
Temperature in gases
As mentioned previously for a monatomic ideal gas the temperature
is related to the translational motion or average speed of the atoms.
The Kinetic theory of gases uses Statistical mechanics to relate
this motion to the average kinetic energy of atoms and molecules
in the system. For this case 11300 degrees Celsius corresponds to
an average kinetic energy of one electronvolt; to take room temperature
(300 kelvin) as an example, the average energy of air molecules
is 300/11300 eV, or 0.0273 electronvolts. This average energy is
independent of particle mass, which seems counterintuitive to many
people. Although the temperature is related to the average kinetic
energy of the particles in a gas, each particle has its own energy
which may or may not correspond to the average. In a gas the distribution
of energy (and thus speeds) of the particles corresponds to the
Boltzmann distribution.
An electronvolt
is a very small unit of energy, on the order of 1.602e-19 joules.
Temperature of the vacuum
A system in a vacuum will radiate its thermal energy, i.e. convert
heat into electromagnetic waves. It will do so until an equilibrium
with the vacuum is found. This equilibrium will not be at 0 K if
the vacuum is filled with electromagnetic waves. Conversely, the
system can absorb energy from the vacuum if it contains intense
electronic waves.
At equilibrium, the radiation's spectrum will be the same as the
radiation of a black body at the equilibrium temperature, so that
one can say that the vacuum has that temperature. Far from equilibrium,
the spectrum usually have very different shapes, and one temperature
cannot be assigned to the vacuum anymore. Sometimes, a part of the
spectrum follows that shape: for example one can say that the cosmic
microwave background radiation, a part of the cosmic radiation,
has a temperature of about 3 K.
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 every coin toss would come
up either heads or tails. For any number of coin tosses, there is
only one combination of outcomes corresponding to this situation.
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. As the number of coin tosses increases, the number
of 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 than 50/50 becomes extremely
unlikely. Thus the system naturally progresses to a state of maximum
disorder or entropy.
Now, we have
stated previously 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:
(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:
(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. We can now choose
a temperature scale with the property that:
(4)
Substituting
Equation 4 back into Equation 2 gives a relationship for the efficiency
in terms of temperature:
(5)
Notice that
for 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:
where the negative
sign indicates heat ejected from the system. This relationship suggests
the existence of a state function, S, defined by:
(6)
where the subscript
indicates a reversible process. The change of this state function
around any cycle is zero, as is necessary for any state function.
This function corresponds to the entropy of the system, which we
described previously. We can rearranging Equation 6 to get a new
definition for temperature in terms of entropy and heat:
(7)
For a system,
where entropy S may be a function S(E) of its energy E, the termperature
T is given by:
(8)
The reciprocal
of the temperature is the rate of increase of entropy with energy.
Negative temperatures
At low temperatures, particles tend to move to their lowest energy
states. As you increase the temperature, particles move into higher
and higher energy states. As the temperature becomes infinite, the
number of particles in the lower energy states and the higher energy
states becomes equal. In some situations, it is possible to create
a system in which there are more particles in the higher energy
states than in the lower ones. This situation can be described with
a negative temperature. A negative temperature is not colder than
absolute zero, but rather it is hotter than infinite temperature.
The previous
section described how heat is stored in the various translational,
vibrational, rotational, electronic, and nuclear modes of a system.
The macroscopic temperature of a system is related to the total
heat stored in all of these modes and in a normal system thermal
energy is constantly being exchanged between the various modes.
However, for some cases it is possible to isolate one or more of
the modes. In practice the isolated modes still exchange energy
with the other modes, but the time scale of this exchange is much
slower than for the exchanges within the isolated mode. One example
is the case of nuclear spins in a strong external magnetic field.
In this case energy flows fairly rapidly among the spin states of
interacting atoms, but energy transfer between the nuclear spins
and other modes is relatively slow. Since the energy flow is predominantly
within the spin system, it makes sense to think of a spin temperature
that is distinct from the temperature due to other modes.
Based on Equation
7, we can say a positive temperature corresponds to the condition
where entropy increases as thermal energy is added to the system.
This is the normal condition in the macroscopic world and is always
the case for the translational, vibrational, rotational, and non-spin
related electronic and nuclear modes. The reason for this is that
there are an infinite number of these types of modes and adding
more heat to the system increases the number of modes that are energetically
accessible, and thus the entropy. However, for the case of electronic
and nuclear spin systems there are only a finite number of modes
available (often just 2, corresponding to spin up and spin down).
In the absence of a magnetic field, these spin states are degenerate,
meaning that they correspond to the same energy. When an external
magnetic field is applied, the energy levels are split, since those
spin states that are aligned with the magnetic field will have a
different energy than those that are anti-parallel to it.
In the absence
of a magnetic field, one would expect such a two-spin system to
have roughly half the atoms in the spin-up state and half in the
spin-down state, since this maximizes entropy. Upon application
of a magnetic field, some of the atoms will tend to align so as
to minimize the energy of the system, thus slightly more atoms should
be in the lower-energy state (for the purposes of this example we'll
assume the spin-down state is the lower-energy state). It is possible
to add energy to the spin system using radio frequency (RF) techniques.
This causes atoms to flip from spin-down to spin-up. Since we started
with over half the atoms in the spin-down state, initially this
drives the system towards a 50/50 mixture, so the entropy is increasing,
corresponding to a positive temperature. However, at some point
more than half of the spins are in the spin-up position. In this
case adding additional energy, reduces the entropy since it moves
the system further from a 50/50 mixture. This reduction in entropy
with the addition of energy corresponds to a negative temperature.
See also Maxwell's demon
External links
Temperature Conversion: Celsius (Centigrade), Fahrenheit, Kelvin,
Réaumur, and Rankine
An elementary introduction to temperature aimed at a middle school
audience
Related Words
cold, coldness, comfort zone, heat, somaesthesia, somatesthesia,
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conversion temperature Adj. 1. controlled - restrained or managed
or kept within certain bounds; "controlled emotions";
"the controlled release of water from reservoirs"
Antonyms:
uncontrolled - not being under control; out of control; "the
greatest uncontrolled health problem is AIDS"; "uncontrolled
growth"
2. controlled - curbed or regulated; "controlled emotions"
Synonyms: restricted
Related Words
limited, restricted |
