Kelvin
of these articles is concerned with the temperature unit Kelvin. For other meanings see Kelvin (term clarifying). |
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Unit | |
---|---|
standard | SI fundamental unit |
name | Kelvin |
size of | temperature |
unit symbol | K |
designated after | lord Kelvin |
Kelvin is those SI - fundamental unit of the thermodynamic temperature and its scale, the absolute scale. Kelvin is (apart from the degrees Celsius) in Germany and Austriathe legally prescribed temperature unit.
The absolute scale is no more divided into degrees by definition since 1968. It is called therefore no more „19 degrees Kelvin “(or „19 °K “) separates simply only „19 Kelvin “(19 K).
It became after William Thomson, thatlater lord Kelvin (1824 - 1907) designated, which introduced the thermodynamic thermometric scale with 24 years.
Table of contents |
definition
Kelvin by the CGPM for the first time 1954 were defined again and in the today valid form 1968 and specified as SI - fundamental unit:
- „Kelvin, the unit of the thermodynamic temperature, is that273,16te part of the thermodynamic temperature of the Tripelpunktes of the water. “ (official translation from the English; pure water) this definition
is not meant makes a difference between the application of Kelvin for the indication of an absolute temperature and a temperature difference.
To a simplerUnderstanding of the Kelvins one arrives by feedback at the temperature unit „degrees Celsius “. The zero point of the Kelvin scale is because of the absolute zero with −273,15 °C. This temperature is after the Nernst' heat set not attainable, there particle with 0 Kkinetic energy would not have (the remaining energy - zero-point energy - is a result of the Heisenberg' uncertainty relation).
A temperature difference of a Kelvin is the 273,16te part of the temperature difference between the absolute zero and the thermodynamic temperature of the Tripelpunktes of water (0,01°C). It was reached by this definition that the difference between two temperature levels of a Kelvin and a degree Celsius are exactly alike and
- < math>
\ frac {\ delta \, T} {1 \, \ mathrm {K}} = \ frac {\ delta \, \ vartheta} {\ delta 1 \, ^ {\ circ} \ mathrm {C}}< /math>, because <math> \ delta 1 left \, \ mathrm {{} ^ {\ circ} C} \ ({} = 1 \, \ mathrm {primer}\ right) = 1 \, \ mathrm {K} </math> results in.
Here it applies to note that the unit is no longer valid degree (primer) and was replaced by Kelvin. The degree was in former times needed, there it due to the definition of the degrees Celsiuswith an non-absolute zero point is not possible to use this directly for the indication from temperature differences to.
Since it is unmanageable to use the definition of the Kelvins for calibrating measuring instruments for temperatures removed far from the Tripelpunkt of the water exists „Internationally Temperature Scale OF 1990 “(ITS-90). There temperatures of events are specified, which distribute themselves over a large temperature range.
application
Kelvin becomes particularly in thermodynamics, heat transfer and generally the natural sciences the indication thatTemperature, as well as to the indication of temperature differences uses. With the absolute scale the middle kinetic energy of the particles (atoms or molecules) is proportional to the temperature, i.e. a double kinetic energy corresponds to a double temperature (in Kelvin). A further connection leads itselffrom the Maxwell Boltzmann distribution off: a doubling of the temperature on the absolute scale leads 2 with ideal gases to an increase of the particle speed in the square means around <the factor> math \ sqrt \ approx 1 {,} 4142< /math>.
directly
those follows characteristics from the definitionaccurate definition of the temperature of the Tripelpunktes of water (not turned around). The freezing point of the water with standard conditions is on the absolute scale not accurately 273.1 6 K, but amounts to 273.16 K - 0.010000 K = 273.1 5 K (momentary measuring accuracy).
The temperatureby this definition with the energy and is called therefore thermodynamic temperature is linked. The thermodynamic temperature of a body (or system) stands in connection with its energy content. If it does not contain energy, then it has the temperature 0 K and findsitself thus at the absolute zero. If the numerical value of a temperature is _{x times} larger T 1 on the absolute scale than the one other temperature T_{ 2}, then the energy content is x times as_{ high} with T 1 asT_{ 2} (in contrast to it see the centigrade temperature scale). For this proportionality mentioned however the straight line would have to go through the zero point. That cannot be done it however.
The kind of the definition was selected in such a way that it easily into the practice convertedwill can. Because the Tripelpunkt of a substance (everywhere and always) a continuous material property actual that is, if water at its Tripelpunkt is, it has always the same temperature (and the same pressure) - today among other things Tripelpunktzellen become the calibrationof temperature gauges assigned.
history
the divisions of the Kelvin scale suggested by William Thomson carried first the name °A (for absolute). In SI applied from 1948 to 1968 °K (degrees of Kelvin, until 1954 also degree of absolute)as temperature unit. In addition in the period mentioned temperature differences - deviating from temperature specifications - were indicated in deg (degrees). The use of these old units is today in Germany no longer permissible.
Already 1948 became by the CGPM an absolute thermodynamic scalewith the Tripelpunkt of the water as only fundamental fixed point fixed, but not yet with the temperature links.
future developments
the current definition of Kelvin in SI does not correspond any longer to the accuracies attainable with today's precision measurements; because upOne knows reason of such precision measurements today (2005) that the temperature of the Tripelpunktes of the water is dependent on its isotope composition. Therefore on a redefinition of Kelvin one works. Instead of specifying the isotope composition of the water, thereby a feedback on fundamental constants is tried.
in addition
color temperature in Kelvin is measured the color temperature, which is important particularly in the photography.
temperature and energy
in accordance with the kinetic gas theory the middle kinetic energy of the particles is math \ overline { <E_> {\ mathrm {kin}}} /math in an ideal< gas>proportionally to the absolute temperature T. The proportionality constant contains the Boltzmannkonstante k_{ B}. The relationship reads:
- <math> \ overline {E_ {\ mathrm {kin}}} = \ frac {3} {2} \, k_ \ mathrm {B} \, \ mathrm {T}< /math>
The numeric relationship between the middle energy <math> \ overline {E_ {\ mathrm {kin}}}< /math> in electronvolts and the temperature T inKelvin reads then as follows:
- <math>
\ overline {E_ {\ mathrm {kin}}} = \ mathrm {T} \ cdot \ frac {3} {2} \ cdot \ frac {1} {11605} \ \ frac {\ mathrm {eV}} {\ mathrm {K}} </math> and/or
- < math>
\ mathrm {T} = {\ overline {E_ {\ mathrm {kin}}}} \ cdot \ frac {2} {3} \ cdot 11605 \ \ frac {\ mathrm {K}} {\ mathrm {eV}} </math>
tables
scale | Kelvin | Celsius | Fahrenheit | Rankine | Delisle | Newton | Réaumur | Rømer |
---|---|---|---|---|---|---|---|---|
unit | Kelvin | degrees Celsius | degree of Fahrenheit | degree of Rankine | degrees of Delisle | degree Newton | degree of Réaumur | degrees of Rømer |
unit symbol | K | °C | °F | °Ra, °R | °De, °D | °N | °Ré, °Re | °Rø |
first fixed point F_{ 1} | T_{ 0} = 0 K | T_{ Schm} (H_{ 2} O) = 0 °C | winters in Danzig* = 0 °F | T_{ 0} = 0 °Ra | T_{ simmer} (H_{ 2} O) = 0 °De | T_{ Schm} (H_{ 2} O) = 0 °N | T_{ Schm} (H_{2} O) = 0 °Ré | T_{ Schm} (H_{ 2} O) = 7.5 °Rø |
second fixed point F_{ 2} | T_{ t} (H_{ 2} O) = 273.16 K | T_{ simmer} (H_{ 2} O) = 100 °C | T_{ humans} * = 100 °F | - | T_{ Schm} (H_{ 2} O) = 150 °De | T_{ simmer} (H_{ 2} O) = 33 °N | T_{ simmer} (H_{ 2} O) = 80 °Ré | T_{ simmer} (H_{ 2} O) = 60 °Rø |
Skalenintervall | (F_{ 2} −F_{ 1})/273,16 | (F_{ 2} −F_{ 1})/to 100 | (F_{ 2} −F_{ 1})/96 | see Fahrenheit | (F_{ 2} −F_{ 1})/150 | (F_{ 2} −F_{ 1})/33 | (F_{ 2} −F_{ 1})/80 | (F_{ 2} −F_{1})/100 |
inventors | William Thomson („lord Kelvin “) | differently Celsius | Daniel Fahrenheit | William Rankine | Joseph Delisle | Isaac Newton | René Réaumur | of oils Rømer |
developing year | 1848 | 1742 | 1724 | 1859 | 1732 | ~ 1700 | 1730 | 1701 |
circulation area | world-wide (SI-UNIT) | world-wide | the USA, Jamaica | the USA | Russia (19.Jhd.) | - | Western Europe to 19. Jhd. | - |
* the measured lowest temperature of the winter 1708/1709 was used in Danzig (−17,8 °C) and the Körpertemperatur, which actually measured Fahrenheit (37.8 °C).
after \of | absolute scale (C) | centigrade temperature scale (°C) | Réaumur scale (°Ré) | Fahrenheit scale (°F) |
---|---|---|---|---|
T_{ Kelvin} | = T_{ K} | = T_{ C} + 273.15 | = T_{ Ré} · 1,25 + 273.15 | = (T_{ F} + 459.67) ÷ 1.8 |
T_{ Celsius} | = T_{ K} − 273,15 | = T_{ C} | = T_{ Ré} · 1,25 | = (T_{ F} − 32) ÷ 1.8 |
T_{ Réaumur} | = (T_{ K} − 273,15) · 0,8 | = T_{ C} · 0,8 | = T_{ Ré} | = (T_{ F} − 32) ÷ 2.25 |
T_{Fahrenheit} | = T_{ K} · 1,8 − 459.67 | = T_{ C} · 1,8 + 32 | = T_{ Ré} · 2,25 + 32 | = T_{ F} |
T_{ Rankine} | = T_{ K} · 1,8 | = T_{ C} · 1,8 + 491,67 | = T_{ Ré} · 2,25 + 491.67 | = T_{ F} + 459.67 |
T_{ Rømer} | = (T_{ K} − 273,15) · 21/40 + 7.5 | = T_{ C} · 21/40 + 7.5 | = T_{ Ré} · 21/32 + 7.5 | = T_{ F}− 32) · 7/24 + 7.5 |
T_{ Delisle} | = (373.15 − T_{ K}) · 1,5 | = (100 − T_{ C}) · 1,5 | = (80 − T_{ Ré}) · 1,875 | = (212 − T_{ F}) · 5/6 |
T_{ Newton} | = (T_{ K} − 273,15) · 0,33 | = T_{ C} · 0,33 | = T_{ Ré} · 0,4125 | = (T_{ F} − 32) · 11/60 |
after \ of | Rankine scale (°Ra) | Rømer scale (°Rø) | Delisle scale (°De) | Newton scale (°N) |
---|---|---|---|---|
T_{ Kelvin} | = T_{ RA} ÷ 1.8 | = (T_{ Rø} − 7,5) · 40/21 + 273.15 | = 373.15 − T_{ De} · 2/3 | = T_{ N} · 100/33 + 273.15 |
T_{ Celsius} | = T_{ RA} ÷ 1.8 − 273.15 | = (T_{ Rø}− 7,5) · 40/21 | = 100 − T_{ De} · 2/3 | = T_{ N} · 100/33 |
T_{ Réaumur} | = T_{ RA} ÷ 2.25 - 218.52 | = (T_{ Rø} − 7,5) · 32/21 | = 80 − T_{ De} · 8/15 | = T_{ N} · 80/33 |
T_{ Fahrenheit} | = T_{ RA} − 459.67 | = (T_{ Rø} − 7,5) · 24/7 + 32 | = 212 − T_{ De} · 1,2 | = T_{ N} · 60/11 + 32 |
T_{ Rankine} | = T_{ RA} | = (T_{ Rø} − 7,5) · 24/7 + 491.67 | = 671.67 − T_{ De} · 1,2 | = T_{ N} · 60/11 + 491.67 |
T_{ Rømer} | = (T_{ RA} − 491,67) · 7/24 + 7.5 | = T_{ Rø} | = 60 −T_{ De} · 0,35 | = T_{ N} · 35/22 + 7.5 |
T_{ Delisle} | = (671.67 − T_{ RA}) · 5/6 | = (60 − T_{ Rø}) · 20/7 | = T_{ De} | = (33 − T_{ N}) ÷ 0,22 |
T_{ Newton} | = (T_{ RA} − 491,67) · 11/60 | = (T_{ Rø} − 7,5) · 22/35 | = 33 − T_{ De} · 0,22 | = T_{ N} |
measured value \ scale | Fahrenheit | Rankine | Réaumur | Celsius | Kelvin |
---|---|---|---|---|---|
middle surface temperature of the sun | 10,430 °F | 10,890 °Ra | 4,622 °R | 5,777 °C | 6,050 K |
melting point of iron | 2,795 °F | 3,255 °Ra | 1,228 °R | 1,535 °C | 1,808 K |
melting point of lead | 621,43 °F | 1081.10 °Ra | 261.97 °R | 327.46 °C | 600.61 K |
boiling point of water | 212 °F | 671.67 °Ra | 80 °R | 100 °C | 373.15 K |
highest air temperature 136.04 °F 595.71 | °Ra 46.24 | °R 57.80 | °C 330.95 | K Körpertemperatur | measured in |
the free one of theHumans after Fahrenheit | 100 °F | 559.67 °Ra | 30.22 °R | 37.78 °C | 310.93 K |
freezing point of water | 32 °F | 491.67 °Ra | 0 °R | 0 °C | 273.15 K |
lowest temperature in Danzig, winter 1708/09 | 0 °F | 459.67 °Ra | −14,22 °R | −17,78 °C | 255.37 K |
melting point of mercury | −37,89 °F | 421.78 °Ra | −31,06 °R | −38,83 °C | 234.32 K |
deepest air temperature −130,90 measured in | the free one °F | 328.77 °Ra | −72,40 °R | −90,50 °C | 182.65 K |
freezing point of alcohol | −173,92 °F | 285.75 °Ra | −91,52 °R | to −114,40 °C | 158.75 K |
boiling point of nitrogen | −320,44 °F | 139.23 °Ra | −156,64 °R | −195,80 °C | 77.35 K |
absolute zero | −459,67 °F | 0 °Ra | −218,52 °R | −273,15 °C | 0 K |