Contents 1 Effects of temperature
2
3.1 Kinds of temperature scale 3.1.1 Empirically based scales 3.1.2 Theoretically based scales 3.1.3 Absolute thermodynamic scale 3.2 Definition of the
4 Kinetic theory approach to temperature 5 Basic theory 5.1
6
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 and references 11.1 Bibliography of cited references 12 Further reading 13 External links Effects of temperature[edit] This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2013) (Learn how and when to remove this template message) Many physical processes are affected by temperature, such as physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, electrical conductivity rate and extent to which chemical reactions occur[1] the amount and properties of thermal radiation emitted from the surface of an object speed of sound is a function of the square root of the absolute temperature[2]
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T 1 / T 2 = − Q 1 / Q 2 . ( 1 ) displaystyle T_ 1 /T_ 2 =-Q_ 1 /Q_ 2 ,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(1) Kelvin's original work postulating absolute temperature was published
in 1848. It was based on the work of Carnot, before the formulation of
the first law of thermodynamics.
T = ( ∂ U ∂ S ) V , N . ( 2 ) displaystyle T=left( frac partial U partial S right)_ V,N ,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2) [27][28][29] Likewise, when the body is described by stating its entropy S as a function of its internal energy U, and other state variables V, N, with S = S (U, V, N), then the reciprocal of the temperature is equal to the partial derivative of the entropy with respect to the internal energy: 1 T = ( ∂ S ∂ U ) V , N . ( 3 ) displaystyle frac 1 T =left( frac partial S partial U right)_ V,N ,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(3) [27][29][30] The above definition, equation (1), of the absolute temperature is due
to Kelvin. It refers to systems closed to transfer of matter, and has
special emphasis on directly experimental procedures. A presentation
of thermodynamics by Gibbs starts at a more abstract level and deals
with systems open to the transfer of matter; in this development of
thermodynamics, the equations (2) and (3) above are actually
alternative definitions of temperature.[31]
C V = Δ Q Δ T displaystyle C_ V = frac Delta Q Delta T 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).
A typical
See also: Timeline of temperature and pressure measurement technology,
International
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[edit] The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature as energy in units of electronvolts (eV) or kiloelectronvolts (keV). The energy, which has a different dimension from temperature, is then calculated as the product of the Boltzmann constant and temperature, E = k B T displaystyle E=k_ B T . Then, 1 eV corresponds to 11605K. In the study of
A theoretical understanding of temperature in an ideal gas can be obtained from the Kinetic theory. Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases.[64] This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases.[65][66][67] Plots of pressure vs temperature for three different gas samples extrapolated to absolute zero. The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states:[68] p V = n R T displaystyle pV=nRT,! where n is the number of moles of gas and R = 7000831445980000000♠8.3144598(48) J⋅mol−1⋅K−1[69] is the gas constant. This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvins. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer. The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container of one cubic meter, divided by the gas constant. Although it is not a particularly convenient device, the gas thermometer provides an essential theoretical basis by which all thermometers can be calibrated. As a practical matter it is not possible to use a gas thermometer to measure absolute zero temperature since the gases 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, as shown in the figure. The kinetic theory assumes that pressure is caused by the force associated with individual atoms striking the walls, and that all energy is translational kinetic energy. Using a sophisticated symmetry argument,[70] Boltzmann deduced what is now called the Maxwell–Boltzmann probability distribution function for the velocity of particles in an ideal gas. From that probability distribution function, the average kinetic energy, Ek (per particle), of a monatomic ideal gas is:[66][71] E k = 1 2 m v r m s 2 = 3 2 k T , displaystyle E_ text k = frac 1 2 mv_ mathrm rms ^ 2 = frac 3 2 kT,, where the Boltzmann constant, k, is the ideal gas constant divided by the Avogadro number, and v r m s = < v 2 > displaystyle v_ rms = sqrt <v^ 2 > is the root-mean-square speed. Thus the ideal gas law states that
internal energy is directly proportional to temperature.[72] This
direct proportionality between temperature and internal energy is a
special case of the equipartition theorem, and holds only in the
classical limit of an ideal gas. It does not hold for most substances,
although it is true that temperature is a monotonic (non-decreasing)
function of internal energy.
Zeroth law of thermodynamics[edit]
Main article: Zeroth law of thermodynamics
When two otherwise isolated bodies are connected together by a rigid
physical path impermeable to matter, there is spontaneous transfer of
energy as heat from the hotter to the colder of them. Eventually they
reach a state of mutual thermal equilibrium, in which heat transfer
has ceased, and the bodies' respective state variables have settled to
become unchanging.
One 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 helps to define temperature but it does not, by itself,
complete the definition. An empirical temperature is a numerical scale
for the hotness of a thermodynamic system. Such hotness may be defined
as existing on a one-dimensional manifold, stretching between hot and
cold. Sometimes the zeroth law is stated to include the existence of a
unique universal hotness manifold, and of numerical scales on it, so
as to provide a complete definition of empirical temperature.[56] To
be suitable for empirical thermometry, a material must have a
monotonic relation between hotness and some easily measured state
variable, such as pressure or volume, when all other relevant
coordinates are fixed. An exceptionally suitable system is the ideal
gas, which can provide a temperature scale that matches the absolute
efficiency = w c y q H = q H − q C q H = 1 − q C q H ( 4 ) displaystyle textrm efficiency = frac w_ cy q_ H = frac q_ H -q_ C q_ H =1- frac q_ C q_ H ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(4) where wcy is the work done per cycle. 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: q C q H = f ( T H , T C ) ( 5 ) displaystyle frac q_ C q_ H =f(T_ H ,T_ C ),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(5) 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 13 = q 1 q 2 q 2 q 3 displaystyle q_ 13 = frac q_ 1 q_ 2 q_ 2 q_ 3 which implies: q 13 = f ( T 1 , T 3 ) = f ( T 1 , T 2 ) f ( T 2 , T 3 ) displaystyle q_ 13 =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. A temperature scale can now be chosen with the property that: q C q H = T C T H ( 6 ) displaystyle frac q_ C q_ H = frac T_ C T_ H ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(6) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: efficiency = 1 − q C q H = 1 − T C T H ( 7 ) displaystyle textrm efficiency =1- frac q_ C q_ H =1- frac T_ C T_ H ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(7) 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: q H T H − q C T C = 0 displaystyle frac q_ H T_ H - frac q_ C T_ C =0 where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: d S = d q r e v T ( 8 ) displaystyle dS= frac dq_ mathrm rev T ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(8) 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: T = d q r e v d S ( 9 ) displaystyle T= frac dq_ mathrm rev dS ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(9) For a system, where entropy S(E) is a function of its energy E, the temperature T is given by: T − 1 = d d E S ( E ) ( 10 ) displaystyle T ^ -1 = frac d dE S(E),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(10) , i.e. the reciprocal of the temperature is the rate of increase of
entropy with respect to energy.
Definition from statistical mechanics[edit]
τ 1 displaystyle tau _ 1 and τ 2 displaystyle tau _ 2 of the single/double-occupancy system:[75] T = k − 1 ln 2 τ 2 τ 1 ( E − E F ( 1 + 3 2 N ) ) , displaystyle T=k^ -1 ln 2 frac tau _ mathrm 2 tau _ mathrm 1 left(E-E_ text F left(1+ frac 3 2N right)right), where EF is the Fermi energy. This generalized temperature tends to
the ordinary temperature when N goes to infinity.
Negative temperature[edit]
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 have a temperature smaller
than or equal to 0 K, both of which are forbidden by the third law of
thermodynamics.
Temperature Peak emittance wavelength[77] of black-body radiation Kelvin Celsius Absolute zero (precisely by definition) 0 K −273.15 °C cannot be defined Coldest temperature achieved[78] 100 pK −273.149999999900 °C 29,000 km Coldest Bose–Einstein condensate[79] 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)[80] Cosmic microwave background (2013 measurement) 2.7260 K −270.424 °C 0.00106301 m (millimeter-wavelength microwave) Water triple point (precisely by definition) 273.16 K 0.01 °C 10,608.3 nm (long-wavelength IR) Water boiling point[A] 373.1339 K 99.9839 °C 7,766.03 nm (mid-wavelength IR)
Incandescent lamp[B] 2500 K ≈2,200 °C 1,160 nm (near infrared)[C] Sun's visible surface[D][81] 5,778 K 5,505 °C 501.5 nm (green-blue light)
Sun's core[E] 16 MK 16 million °C 0.18 nm (X-rays) Thermonuclear weapon (peak temperature)[E][82] 350 MK 350 million °C 8.3×10−3 nm (gamma rays) Sandia National Labs' Z machine[E][83] 2 GK 2 billion °C 1.4×10−3 nm (gamma rays)[F] Core of a high-mass star on its last day[E][84] 3 GK 3 billion °C 1×10−3 nm (gamma rays) Merging binary neutron star system[E][85] 350 GK 350 billion °C 8×10−6 nm (gamma rays) Relativistic Heavy
CERN's proton vs nucleus collisions[E][87] 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 1.616×10−27 nm (Planck length)[88] A For
See also[edit] Atmospheric temperature
Body temperature (thermoregulation)
Color temperature
Dry-bulb temperature
Notes and references[edit] ^ Agency, International Atomic Energy (1974). Thermal discharges at
nuclear power stations: their management and environmental
impacts : a report prepared by a group of experts as the result
of a panel meeting held in Vienna, 23–27 October 1972. International
Atomic Energy Agency.
^ Watkinson, John (2001). The Art of Digital Audio. Taylor &
Francis. ISBN 978-0-240-51587-8.
^ Middleton, W.E.K. (1966), pp. 89–105.
^ a b c Truesdell, C.A. (1980), Sections 11 B, 11H, pages 306–310,
320–332.
^ Quinn, T.J. (1983).
^ Quinn, T.J. (1983), pp. 61–83.
^ Schooley, J.F. (1986), pp. 115–138.
^ Adkins, C.J. (1968/1983), pp. 119–120.
^ Buchdahl, H.A. (1966), pp. 137–138.
^ Tschoegl, N.W. (2000), p.88.
^ Quinn, T.J. (1983), pp. 98–107.
^ Schooley, J.F. (1986), pp. 138–143.
^ Germer, L.H. (1925). 'The distribution of initial velocities among
thermionic electrons', Phys. Rev., 25: 795–807. here
^ Turvey, K. (1990). 'Test of validity of Maxwellian statistics for
electrons thermionically emitted from an oxide cathode', European
Journal of Physics, 11(1): 51–59. here
^ Zeppenfeld, M., Englert, B.G.U., Glöckner, R., Prehn, A., Mielenz,
M., Sommer, C., van Buuren, L.D., Motsch, M., Rempe, G. (2012).
^ Miller, J. (2013).
^ Thomson, W. (Lord Kelvin) (1848).
^ Thomson, W. (Lord Kelvin) (1851).
^ Partington, J.R. (1949), pp. 175–177.
^ Roberts, J.K., Miller, A.R. (1928/1960), pp. 321–322.
^ Buchdahl, H.A (1986). On the redundancy of the zeroth law of
thermodynamics, J. Phys. A, Math. Gen., 19: L561–L564.
^ C. Carathéodory (1909). "Untersuchungen über die Grundlagen der
Thermodynamik". Mathematische Annalen. 67 (3): 355–386.
doi:10.1007/BF01450409. A partly reliable translation is to be
found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden,
Hutchinson & Ross, Stroudsburg PA.
^ Maxwell, J.C. (1871). Theory of Heat, Longmans, Green, and Co.,
London, p. 57.
^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of
Bibliography of cited references[edit] Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, (1st edition
1968), third edition 1983, Cambridge University Press, Cambridge UK,
ISBN 0-521-25445-0.
Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics,
Cambridge University Press, Cambridge UK.
Middleton, W.E.K. (1966). A History of the
Further reading[edit] Chang, Hasok (2004). Inventing Temperature:
External links[edit] 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 from Oklahoma State University Average yearly temperature by country A tabular list of countries and Thermal Map displaying the average yearly temperature by country v t e Meteorological data and variables General Adiabatic processes
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Surface solar radiation
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Temperature
Pressure Atmospheric pressure
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v t e Scales of temperature Celsius Delisle Fahrenheit Gas Mark Kelvin Leiden Newton Planck Rankine Réaumur Rømer Wedgwood Conversion formulas and comparison v t e Wastewater Sources Acid mine drainage
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