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Kelvin

Kelvin

The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. It is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. A temperature given in kelvins, without further qualification, is measured with respect to absolute zero, where molecular motion stops. It is also common to give a temperature relative to the reference temperature of 273.15 K, approximately the melting point of water under ordinary conditions; this convention is the Celsius temperature scale. The kelvin is named after the British physicist and engineer William Thomson, 1st Baron Kelvin; his barony was in turn named after the River Kelvin, which runs through the grounds of the University of Glasgow.

SI multiples

Typographical conventions

The word kelvin as an SI unit is correctly written with a lowercase k (unless at the beginning of a sentence), and is never preceded by the words degree or degrees, or the symbol °, unlike degrees Fahrenheit, or degrees Celsius. This is because the latter are adjectives, whereas kelvin is a noun. It takes the normal plural form by adding an s in English: kelvins. When the kelvin was introduced in 1954 (10th General Conference on Weights and Measures (CGPM), Resolution 3, CR 79), it was the "degree Kelvin", and written °K; the "degree" was dropped in 1967 (13th CGPM, Resolution 3, CR 104). Note that the symbol for the kelvin unit is always a capital K and never italicised. There is a space between the number and the K, as with all other SI units. Unicode includes the "kelvin sign" at U+212A (in your browser it looks like K). However, the "kelvin sign" is canonically decomposed into U+004B, thereby seen as a (preexisting) encoding mistake, and it is better to use U+004B (K) directly.

Conversion factors

Kelvins and Celsius

The Celsius temperature scale is now defined in terms of the kelvin, with 0 °C corresponding to 273.15 kelvins.
- kelvins to degrees Celsius
- :

\mathrm = \mathrm - 273.15

Temperature and energy

In a thermodynamic system, the energy of the particles of a perfect gas is proportional to the absolute temperature, where the constant of proportionality is the Boltzmann constant. As a result, it is possible to determine the average kinetic energy

\overline

of the gas particles at the temperature T or to calculate the temperature of the gas from the average kinetic energy of the particles: :

\overline = \frac \cdot k_B \cdot \mathrm

External link

- [http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html BIPM brochure on the kelvin] Category:SI base units Category:Units of temperature ko:켈빈 ja:ケルビン simple:Kelvin th:เคลวิน

SI

The International System of Units (abbreviated SI from the French language name Système International d'Unités) is the modern form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. The older metric system included several groupings of units. The SI was developed in 1960 from one of these, the metre-kilogram-second (MKS) system, rather than the centimetre-gram-second (CGS) system, which, in turn, had many variants. The SI introduced several newly named units. The SI is not static; it is a living set of standards where units are created and definitions are modified with international agreement as measurement technology progresses. With few exceptions (such as draught beer sales in the United Kingdom), the system is legally being used in every country in the world, and many countries do not maintain official definitions of other units. In the United States, industrial use of SI is increasing, but popular use is still limited. In the United Kingdom, conversion to metric units is official policy but not yet complete. Those countries that still recognize non-SI units (e.g. the US and UK) have redefined most of their traditional, non-SI units in terms of SI units.

History

:See main articles: metre, kilogram, second, ampere, Kelvin, and candela. The metric system was officially adopted in France after the French Revolution. During the history of the metric system a number of variations have evolved and their use spread around the world replacing many traditional measurement systems. By the end of World War II a number of different systems of measurement were still in use throughout the world. Some of these systems were metric system variations whilst others were based on the Imperial and American systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities. Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the metre, kilogram, second, ampere, Kelvin degree (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name: Le Système International d'Unités. The seventh base unit, the mole, was added in 1970 by the 14th CGPM. The International System is now either obligatory or permissible throughout the world. It is administered by the standards organisation: the Bureau International des Poids et Mesures (International Bureau of Weights and Measures).
Units
:Main articles: SI base unit, SI derived unit, SI prefix The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are the seven base units. Each of these base units are dimensionally independent. From these seven base units several other units are derived. In addition to the SI units there are also a set of non-SI units accepted for use with SI. A prefix may be added to units to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.
SI writing style

- Symbols are written in lower case, except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa" whereas the unit itself is written "pascal". The one exception is the litre, whose original abbreviation "l" is dangerously similar to "1". The NIST recommends that "L" be used instead, a usage which is common in the U.S., Canada and Australia, and has been accepted as an alternative by the CGPM. The cursive "ℓ" is occasionally seen, especially in Japan, but this is not currently recommended by any standards body. For more information, see Litre.
- Symbols are written without grammatical markers when used with singular numerals: i.e. "25 kg", not "25 kgs". Pluralization would be language dependent; "s" plurals (as in French and English) are particularly undesirable since "s" is the symbol of the second. Other cases may be marked in a language-dependent manner, e.g. Finnish 25 kg:lla = 25 kilogrammalla "with 25 kg".
- Symbols do not have an appended period (.).
- It is preferable to write symbols in upright Roman type (m for metres, L for litres), so as to differentiate from the italic type used for mathematical variables (m for mass, l for length).
- A space should separate the number and the symbol, e.g. "2.21 kg", "7.3×10² m²", "22 °C" [http://physics.nist.gov/Pubs/SP811/sec07.html]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
- Spaces should be used to group decimal digits in threes, e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000).
- The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". In practice, the full stop is used in English, and the comma in most other European languages.
- Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (·), e.g. N m or N·m.
- Symbols formed by division of two units are joined with a solidus (/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s^-1", "m·s^-1" or $\frac$ . A solidus should not be used if the result is ambiguous, i.e. "kg·m^-1·s^-2" is preferable to "kg/m/s²".
Spelling variations

- Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre' in keeping with standard American English spelling. In addition, the official US spelling for the SI prefix 'deca' is 'deka'.
- The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and its use is declining.
Cultural issues
The swift worldwide adoption of the metric system as a tool of economy and everyday commerce was based mainly on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal numeral system. Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former USSR. In some countries, the informal cup measurement has become 250 mL, and prices for items are sometimes given per 100 g rather than per kilogram. A profound cultural difference between physicists and engineers, especially radio engineers, existed prior to the adoption of the metre-kilogram-second (MKS) system and hence its descendent, SI. Engineers work with volts, amperes, ohms, farads, and coulombs, which are of great practical utility, while the centimetre-gram-second (CGS) units, which, though appropriate for theoretical physics, can be inconvenient for electrical engineering usage and are largely unfamiliar to householders using appliances rated in volts and watts. People with diabetes test their plasma glucose level regularly. In the U.S., measurement are recorded in milligrams per deciliter (mg/dL); in Europe, the standard is millimole/liter (mmol/L). The fine-tuning that has happened to the metric base units over the past 200 years, as experts have tried periodically to refine the metric system to fit the best scientific research do not affect the everyday use of metric units. Since most non-SI units, such as the U.S. customary units, are nowadays defined in terms of SI units, any change in the definition of the SI units results in a change of the definition of the older units as well.
See also

- Units of measurement
- Weights and measures
- Mesures usuelles
- Metrified English unit
- History of measurement
- Other systems of measurement:
- Imperial units
- U.S. customary units
- Metre-tonne-second system of units
- Chinese system of units
- Planck units
- Atomic units
- Geometrized units
- CODATA
- Metrication
- Metric system in the United States
- Metrology
- UTC (Coordinated Universal Time)
- Binary prefixes - used to quantify large amounts of computer data
- Orders of magnitude
- ISO 31
External links
Official
- [http://www.bipm.fr/en/si/ BIPM (SI maintenance agency)] (home page)
- [http://www.bipm.org/en/si/si_brochure/ BIPM brochure] (SI reference)
- [http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=5448&ICS1=1 ISO 1000:1992 SI units and recommendations for the use of their multiples and of certain other units], with its price tag of 99 Swiss francs for a 22 page, coverless pamphlet showing why the public is sometimes a little slow to pick up on their recommendations. Information
- [http://physics.nist.gov/cuu/Units/index.html US NIST reference on SI]
- [http://ts.nist.gov/ts/htdocs/200/202/pub814.htm#chart chart]
- [http://www.aticourses.com/international_system_units.htm SI - Its history and use in science and industry]
- [http://www.unc.edu/~rowlett/units/ A Dictionary of Units of Measurement]
- [http://www.unics.uni-hannover.de/ntr/russisch/si-einheiten.html5 Cyrillic transcription of SI symbols]
- Judson, Lewis B., Weights and Measures Standards of the United States: A brief history, NBS Special Publication 447, orig. iss. October 1963, updated March 1976 ([http://ts.nist.gov/ts/htdocs/200/202/SP%20447.pdf 46 page PDF file])
- [http://www.france-property-and-information.com/metric_conversion_table.htm Metric system and conversion tables (courtesy French property advice)]
- [http://www.metre.info metre-info - an encyclopaedia of all metric units] Pro-metric pressure groups
- [http://www.ukma.org.uk/ The UK Metric Association]
- [http://www.metric.org/ The US Metric Association] Pro-customary measures pressure groups
- [http://www.bwmaonline.com/ The British Weights and Measures Association]
Further reading

- I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd ed., Blackwell Science Inc 1993, ISBN 0632035838. Category:SI units Category:Systems of units Category:International standards Category:Dimensional analysis ko:SI 단위계 ja:国際単位系 simple:SI th:หน่วยเอสไอ

Temperature

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. Physically, temperature is a measure of the random agitation of matter and ambiant photons, under the effect of thermal fluctuations. It is a fundamental parameter in thermodynamics and it is conjugate to entropy. More quantitatively, the order of magnitude of the fluctuations of the energy associated with an atom, molecule or another elementary constituant of a physical system is

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

The formal properties of temperature are studied in thermodynamics and statistical mechanics. The temperature of a system at thermodynamic equilibrium is defined by a relation between the amount of heat

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Contrarly to entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium temperature can only be defined at thermodynamic equilibrium, or 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 (see heat for additional discussion of the various mechanisms of heat transfer). 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 are. Temperature is an intensive property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intensive properties include pressure and density. By contrast, mass and volume are extensive properties, and depend on the amount of material in the system.

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 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 (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). 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 = 11,605 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 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 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. ¹ Only the kelvin, Celsius, Fahrenheit, and Rankine scales are in use today.
² Some numbers in this table have been rounded off.
³ Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F.

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 (sic).

Articles about temperature ranges:

- 10⁻¹² K = 1 picokelvin (pK)
- 10⁻⁹ K = 1 nanokelvin (nK)
- 10⁻⁶ K = 1 microkelvin (µK)
- 10⁻³ K = 1 millikelvin (mK)
- 10⁰ K = 1 kelvin
- 10¹ K = 10 kelvins
- 10² K = 100 kelvins
- 10³ K = 1,000 kelvin = 1 kilokelvin (kK)
- 10⁴ K = 10,000 kelvins = 10 kK
- 10⁵ K = 100,000 kelvins = 100 kK
- 10⁶ K = 1 megakelvin (MK)
- 10⁹ K = 1 gigakelvin (GK)
- 10¹² K = 1 terakelvin (TK) See Orders of magnitude (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 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 so-called 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: :

P \cdot V = n \cdot R \cdot T

(1) where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... 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 7736 K = 7463 degrees Celsius corresponds to an average kinetic energy of one electronvolt; to take room temperature (300 K) as an example, the average energy of air molecules is 300/7736 eV, or 0.0388 electronvolt. 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. However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an atom is:
:

K_t = \begin \frac \end mv^2

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

Thus, particles of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than lighter counterparts, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Not all the particles in the container have different velocities, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. 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, approximately 1.602×10^-19 joule.

Temperature of the vacuum

When a satellite in empty space is heated by sunshine and cooled by radiating energy away it is not in thermodynamic equilibrium and has no well-defined temperature. A system in a vacuum will radiate its thermal energy, i.e. convert heat into electromagnetic waves. If vacuum is filled with electromagnetic waves (say, radiation from walls of vacuum chamber, or relic microwave radiation in space) then the system will exchange by energy with these waves and thermally equilibrates at some finite (non zero) temperature. Cosmic microwave background radiation being remnant of radiation of hot early universe when radiation was in thermal equilibrium with matter has Planck spectrum (black body spectrum) with the temperature (at present) of about 2.7 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 from 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, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or: :

\textrm = \frac  = \frac = 1 - \frac

(2) where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H 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_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. 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 T_C = 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) The reciprocal of the temperature is the rate of increase of entropy with energy.

References

External links

- [http://www.unitconversion.org/unit_converter/temperature.html Online Temperature Converter] - convert between various units of temperature, such as kelvin, Celsius, Fahrenheit, Rankine, Reaumur, and even Triple point of water
- [http://www.unitconversion.org/unit_converter/temperature-v.html Interactive Temperature Conversion Table] - convert selected unit to all other units of temperature
- [http://www.indiana.edu/~animal/fun/conversions/temperature.html Temperature Conversions: Celsius, Fahrenheit, Kelvin, Réaumur and Rankine]
- [http://www.unidata.ucar.edu/staff/blynds/tmp.html An elementary introduction to temperature aimed at a middle school audience]
- [http://www.straightdope.com/mailbag/mtempscales.html Why do we have so many temperature scales?]
- [http://thermodynamics-information.net A Brief History of Temperature Measurement] Category:Meteorology Category:Physical quantity Category:Thermodynamics Category:Heat ko:온도 ja:温度 th:อุณหภูมิ

Thermodynamic temperature

To convert celsius into absolute temperature in kelvins, add 273.16 to the original celsius measure. Thermodynamic temperature (formerly called absolute temperature) is a measure, in kelvins (K), of temperature for thermodynamics. A temperature of 0 K is called "absolute zero", and coincides with the minimum molecular activity (i.e., thermal energy) of matter. In practice, the International Temperature Scale of 1990 (ITS-90) serves as an operational definition and the basis for high-accuracy temperature measurements in science and technology.

Derivation of thermodynamic temperature

There are many possible scales of temperature, derived from a variety of observations of physical phenomena. The thermodynamic temperature can be shown to have special properties, and in particular can be seen to be uniquely defined (up to some constant multiplicative factor) by considering the efficiency of idealized heat engines. Loosely stated, temperature controls the flow of heat between two systems and the universe, as 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, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or: :

\textrm = \frac  = \frac = 1 - \frac

(1) where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures: :

\frac = f(T_H,T_C)

(2) 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_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. We can now choose a temperature scale with the property that: :

\frac = \frac

(3) Substituting Equation 3 back into Equation 1 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

(4) Notice that for T_C=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 so far obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 4 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

(5) 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 5 to get a new definition for temperature in terms of entropy and heat: :

T = \frac

For a system, where entropy S may be a function S(E) of its energy E, the thermodynamic termperature T is given by: :

\frac = \frac

The reciprocal of the thermodynamic termperature is the rate of increase of entropy with energy. Category:Temperature ja:熱力学温度

Triple point

In physics, the triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium. thermodynamic). Note that this is not the phase diagram for water.]] For example, the triple point temperature of mercury is -38.8344 °C at a pressure of 0.2 mPa. The triple point of water is used to define the kelvin, the SI unit of thermodynamic temperature. The number given for the temperature of the triple point of water is an exact definition rather than a measured quantity.

Triple point of water

The single combination of pressure and temperature at which water, ice, and water vapour can coexist in a stable equilibrium occurs at exactly 273.16 kelvins (0.01 °C) and a pressure of 611.73 pascals (ca. 6 millibars). At that point, it is possible to change all of the substance to ice, water, or steam by making infinitesimally small changes in pressure and temperature. (Note that the pressure referred to here is the vapor pressure of the substance, not the total pressure of the entire system.) Water has an unusual and complex phase diagram, although this does not affect general comments about the triple point. At high temperatures, increasing pressure results in first liquid, and then solid water (above around

10^9

Pa a crystalline form of ice which is denser than water forms). At lower temperatures the liquid state ceases to appear with compression causing the state to pass directly from gas to solid. It is, however, possible to melt ice by increasing pressure under specific conditions. At a constant pressure higher than the triple point, heating ice necessarily passes from ice to liquid then to steam. In pressures below the triple point, such as in outer space where the pressure is low, liquid water cannot exist: Ice skips the liquid stage and becomes steam on heating, in a process known as sublimation.

External links

- [http://www1.bipm.org/en/si/base_units/ Definition of the kelvin] at BIPM
- [http://www.lsbu.ac.uk/water/phase.html Phase diagram of water] Category:Chemical properties Category:Thermodynamics ja:三重点

Water

:This article focuses on water as it is experienced in everyday life. See water (molecule) for information on the chemical and physical properties of pure water (H₂O, hydrogen oxide). Water (from the Old English word wæter; c.f German "Wasser", from PIE
- wod-or, "water") is a tasteless, odorless, and nearly colorless (it has a slight hint of blue) substance in its pure form that is essential to all known forms of life and is known also as the most universal solvent. Water is an abundant substance on Earth. It exists in many places and forms. It appears mostly in the oceans and polar ice caps, but also as clouds, rain water, rivers, freshwater aquifers, and sea ice. On the planet, water is continuously moving through the cycle involving evaporation, precipitation, and runoff to the sea. Water fit for human consumption is called potable water. This natural resource is becoming more scarce in certain places as human population in those places increases, and its availability is a major social and economic concern.

Molecular properties

Forms of water

potable water] Water takes many different shapes on earth: water vapor and clouds in the sky, waves and icebergs in the sea, glaciers in the mountain, aquifers in the ground, to name but a few. Through evaporation, precipitation, and runoff, water is continuously flowing from one form to another, in what is called the water cycle. Because of the importance of precipitation to agriculture, and to mankind in general, different names are given to its various forms: while rain is common in most countries, other phenomena are quite surprising when seen for the first time. Hail, snow, fog or dew are examples. When appropriately lit, water drops in the air can refract sunlight to produce rainbows. Similarly, water runoffs have played major roles in human history as rivers and irrigation brought the water needed for agriculture. Rivers and seas offered opportunity for travel and commerce. Through erosion, runoffs played a major part in shaping the environment providing river valleys and deltas which provide rich soil and level ground for the establishment of population centers. Water also infiltrates the ground and goes into aquifers. This groundwater later flows back to the surface in springs, or more spectacularly in hot springs and geysers. Groundwater is also extracted artificially in wells. Because water can contain many different substances, it can taste or smell very differently. In fact, humans and other animals have developed their senses to be able to evaluate the drinkability of water: animals generally dislike the taste of salty sea water and the putrid swamps and favor the purer water of a mountain spring or aquifer.

Water in biology

From a biological standpoint, water has many distinct properties that are critical for the proliferation of life that set it apart from other substances. Water carries out this role by allowing organic compounds to react in ways that ultimately allows replication. It is a good solvent and has a high surface tension, and thus allows organic compounds and living things to be transported in it. Fresh water has its greatest density at 4°C, then becoming less dense as it freezes or heats up from this point. As a stable, polar molecule prevalent in the atmosphere, it plays an important atmospheric role as an absorber of infrared radiation, crucial in the atmospheric greenhouse effect without of which, the average surface temperature would be −18° Celsius. Water also has an unusually high specific heat, which plays many roles in regulating global and regional climate, such as the Gulf Stream climate, allowing life to survive. Water is a very good solvent, chemically not unlike ammonia, and dissolves many types of substances, such as various salts and sugar, and facilitates their chemical interaction, which aids complex metabolisms. Some substances, however, do not mix well with water, including oils and other hydrophobic substances. Cell membranes, composed of lipids and proteins, take advantage of this property to carefully control interactions between their contents and external chemicals. This is facilitated somewhat by the surface tension of water. Water drops are stable due to the high surface tension of water caused by the strong intermolecular forces called cohesive forces. This can be seen when small quantities of water are put onto a nonsoluble surface such as polythene: the water stays together as drops. On extremely clean glass the water may form a thin film because the molecular forces between glass and water molecules (adhesive forces) are stronger than the cohesive forces. This property plays a key role in plant transpiration. A simple but environmentally important and unique property of water is that its common solid form, ice, floats on the liquid. This solid phase is less dense than liquid water, due to the geometry of the strong hydrogen bonds which are formed only at lower temperatures. For almost all other substances and for all other 11 uncommon phases of water ice except ice-XI, the solid form is more dense than the liquid form. Fresh water is most dense at 4°C, and will sink by convection as it cools to that temperature, and if it becomes colder it will rise instead. This reversal will cause deep water to remain warmer than shallower freezing water, so that ice in a body of water will form first at the surface and progress downward, while the majority of the water underneath will hold a constant 4°C. This effectively insulates a lake floor from the cold. While this behavior may seem obvious, even intuitive, it should be noted that almost all other chemicals are denser as solids than they are as liquids, and freeze from the bottom up. Life on earth has evolved with and adapted itself to the important features of water. The existence of abundant liquid, vapor and solid forms of water on Earth has been an important factor in the abundant colonization of Earth's various environments by life-forms adapted to those varying and often extreme conditions. Civilizations have historically flourished around rivers and major waterways; Mesopotamia, the so-called cradle of civilization, is situated between two major rivers. Large metropolises like London, Paris, New York, and Tokyo owe their success in part to their easy accessibility via water and the resultant expansion of trade. Islands with safe water ports, like Singapore and Hong Kong, have flourished for precisely this reason. In places such as North Africa and the Middle East, where water is scarcer, access to clean drinking water was and is a major factor in human development.

Astronomical position of Earth and impact on its water

Mesopotamia The coexistence of the solid, liquid, and gaseous phases of water on Earth is vital to the origin, evolution, and continued existence of life on Earth. However, if the Earth's location in the solar system were even marginally closer or further from the Sun (ie, a million miles or so), the conditions which allow the three forms to be present simultaneously would be far less likely to exist. Earth's mass allows gravity to hold an atmosphere. Water vapor and carbon dioxide in the atmosphere provides a greenhouse effect which helps maintain a relatively steady surface temperature. If Earth were less massive, a thinner atmosphere would cause temperature extremes preventing the accumulation of water except in polar ice caps (as on Mars). According to the solar nebula model of the solar system's formation, Earth's mass may be largely due to its distance from the Sun. The distance between Earth and the Sun and the combination of solar radiation received and the greenhouse effect of the atmosphere ensures that its surface is neither too cold nor too hot for liquid water. If Earth were more distant, most water would be frozen. If Earth were nearer to the Sun, its higher surface temperature would limit the formation of ice caps, or cause water to exist only as vapor. In the former case, the low albedo of oceans would cause Earth to absorb more solar energy. In the second case, a runaway greenhouse effect and inhospitable conditions similar to Venus would result. It has been proposed that life itself may maintain the conditions that have allowed its continued existence. The surface temperature of Earth has been relatively constant through geologic time despite varying solar flux, indicating that a dynamic process governs Earth's temperature via a combination of greenhouse gases and surface or atmospheric albedo. This proposal is known as the Gaia hypothesis.

Human uses of water

Gaia hypothesis All known forms of life depend on water. Water is a vital part of many metabolic processes within the body. Significant quantities of water are used during the digestion of food. (Note however that some bacteria and plant seeds can enter a cryptobiotic state for an indefinite period when dehydrated, and come back to life when returned to a wet environment) About 72% of the fat free mass of the human body is made of water. To function properly the body requires between one and seven litres of water per day to avoid dehydration, the precise amount depending on the level of activity, temperature, humidity, and other factors. It is not clear how much water intake is needed by healthy people. However, for those who do not have kidney problems, it is rather difficult to drink too much water, but (especially in warm humid weather and while exercising) dangerous to drink too little. People do often drink far more water than necessary while exercising, however, putting them at risk of water intoxication, which is frequently fatal. The "fact" that a person should consume eight glasses of water per day cannot be traced back to a scientific source. However, leading dieticians and nutritionists will tell you that this is the RDI (Recommended Daily Intake) of water. [http://ajpregu.physiology.org/cgi/content/full/283/5/R993]. The latest dietary reference intake report by the National Research Council recommended 2.7 liters of water total (including food sources) for women and 3.7 liters for men[http://www.iom.edu/report.asp?id=18495]. Water is lost from the body in urine and feces, through sweating, and by exhalation of water vapor in the breath. Humans require water that does not contain too much salt or other impurities. Common impurities include chemicals and/or harmful bacteria, such as crypto sporidium. Some solutes are acceptable and even desirable for perceived taste enhancement and to provide needed electrolytes.

Water as a precious resource

:See water resources for information about fresh water supplies. fresh water Because of the growth of world population and other factors, the availability of drinking water per capita is shrinking. The issue of water shortage can be solved through more production, better distribution and less waste of it. For this reason, water is a strategic resource for many countries. Many battles and wars, such as the Six-Day War in the Middle East, have been fought to gain access to it. Experts predict more trouble ahead because of the world's growing population, increasing contamination through pollution, and global warming. UNESCO's World Water Development Report (WWDR, 2003) from its World Water Assessment Program indicates that, in the next 20 years, the quantity of water available to everyone is predicted to decrease by 30%. 40% of the world's inhabitants currently have insufficient fresh water for minimal hygiene. More than 2.2 million people died in 2000 from diseases related to the consumption of contaminated water or drought. In 2004, the UK charity WaterAid reported that a child dies every 15 seconds due to easily preventable water-related diseases. Some have predicted that clean water will become the "next oil", making Canada, with this resource in abundance, possibly the richest country in the world.

Regulating water distribution

Drinking water is often collected at springs or extracted from artificial borings in the ground, or wells. Building more wells in adequate places is thus a possible way to produce more water assuming the aquifers can supply an adequate flow. Other water sources are the rainwater and river or lake water. This surface water, however, must be purified for human consumption. This may involve removal of undissolved substances, dissolved substances and harmful microbes. Popular methods are filtering with sand which only removes undissolved material while chlorination and boiling kill harmful microbes. Distillation does all three functions. More advanced techniques exist, such as reverse osmosis. Desalination of abundant ocean or seawater is a more expensive solution used in coastal arid climates. The distribution of drinking water is done through municipal water systems or as bottled water. Governments in many countries have programs to distribute water to the needy at no charge. Others argue that the market mechanism and free enterprise are best to manage this rare resource, and to finance the boring of wells or the construction of dams and reservoirs. Reducing waste, that is using drinking water only for human consumption, is another option. In some cities, such as Hong Kong, sea water is extensively used for flushing toilets citywide in order to conserve fresh water resources. Polluting water may be the biggest single misuse of water; to the extent that a pollutant limits other uses of the water, it becomes a waste of the resource, regardless of benefits to the pollutor. Pharmaceuticals consumed by humans often end up in the waterways and can have detrimental effects on aquatic life if they bioaccumulate and if they are not biodegradable.

The impact of water on human culture

Water is considered a purifier in most religions, including Christianity, Islam, Judaism, and Shinto. For instance, baptism in Christian churches is done with water. In addition, a ritual bath in pure water is performed for the dead in many religions including Judaism and Islam. In Islam, the daily Salah can only be done after ablution (Wodoo), that is, washing parts of the body in clean water. In Shinto, water is used in almost all rituals to cleanse a person or an area. Water is often believed to have spiritual powers. In Celtic mythology, Sulis is the local goddess of thermal springs; in Hinduism, the Ganga is also personified as a goddess. Alternatively, gods can be patrons of particular springs, river or lakes: for example in Greek and Roman mythology, Peneus was a river god, one of the three thousand Oceanids. The Greek philosopher Empedocles held that water is one of the four classical elements along with fire, earth and air, and was regarded as the ylem, or basic stuff of the universe. Water was considered cold and moist. In the theory of the four bodily humours, water was associated with phlegm. Water was also one of the Five Elements in traditional Chinese philosophy, along with earth, fire, wood, and metal. A common misconception about water is that it is a powerful conductor of electricity. Any electrical properties observable in water are due to the ions of mineral salts and carbon dioxide dissolved in it. Water does self-ionize (two water molecules become one hydroxide anion and one hydronium cation), but only at a very slight, almost immeasurable level. Pure water can also be electrolized into oxygen and hydrogen gases but without any dissolved ions, this is a very slow process and thus very little current is conducted. Many bottled water companies exploit another common misconception, advertising both purity and taste, even though pure water is tasteless.

External links

- [http://www.lsbu.ac.uk/water/phase.html Phase diagrams of water]
- [http://www.publicforuminstitute.org/issues/oceans/index.htm Oceans and Water Issues Page]
- [http://www.greenfacts.org/water-disinfectants/index.htm Scientific Facts on Water disinfectants] A faithful summary by GreenFacts of a leading scientific consensus report on Drinking Water Disinfectants published by the International Programme on Chemical Safety of the WHO.
- [http://www.hkc22.com/residentialwater.html Residential water problems and markets] Study paper from Helmut Kaiser Consultancy
- [http://www.hkc22.com/watermarketsworldwide.html Water markets worldwide] Study paper from Helmut Kaiser Consultancy
- [http://www.worldwaterforum.org/ World Water Forum]
- [http://www.unesco.org/water/wwap/ World Water Assessment Program]
- [http://unesdoc.unesco.org/images/0012/001295/129556e.pdf United Nations' World Water Development Report]
- [http://www.gemswater.org/ United Nations GEMS/Water Programme]
- [http://www.lsbu.ac.uk/water/ Water Structure and Behaviour]
- [http://www.wateraid.org/ WaterAid]
- [http://www.sahra.arizona.edu/newswatch/ SAHRA—Global Water Newswatch]
- [http://www.siwi.org/ Stockholm International Water Institute] (SIWI)
- [http://www.c-win.org/ California Water Impact Network (C-WIN)]
- [http://news.bbc.co.uk/2/hi/science/nature/3752590.stm BBC: The water debate]
- [http://www.geocities.com/tapvsbottled/ Tap Water Vs Bottled Water] - Interesting site providing facts about tap and bottled water.
- [http://www.emagazine.com/september-october_2003/0903feat1.html E the Environmental Magazine piece on bottled water] (Oct 2003).
- [http://www.iapws.org/ International Association for the Properties of Water and Steam]
- [http://ga.water.usgs.gov/edu/watercycle.html US Geological Survey: Comprehensive discussion of the water cycle, in many languages]
- [http://www.dartmouth.edu/~etrnsfer/water.htm Why is water blue?]
- [http://www.water.org.uk/home/resources-and-links/water-for-health/ask-about/adults Water requirements in adults]
- [http://www.hkc22.com/environmentaltechnology.html/ Climate change raises markets for environmental technology, drinking water and clean energies]

References

- OA Jones, JN Lester and N Voulvoulis, Pharmaceuticals: a threat to drinking water? TRENDS in Biotechnology 23(4): 163, 2005
- Category:Beverages Category:Hydrology Category:Materials Category:Natural resources Category:Nutrition zh-min-nan:Chúi als:Wasser ko:물 ja:水 ms:Air simple:Water th:น้ำ

Melting point

The melting point of a solid is the temperature at which it changes state from solid to liquid. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point. For most substances, melting and freezing points are equal. For example, the melting point and freezing point of the element mercury is 234.32 kelvins (−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from 32 to 40 °C (89.6 to 104 °F); this phenomenon is known as hysteresis. Certain materials, such as glass, may harden without crystalizing; this is called an amorphous solid. Unlike the boiling point, the melting point is relatively insensitive to pressure. The material with the highest known melting point at atmospheric pressure is graphite, with a melting point of 3,948 kelvins (3,674.8 °C or 6,646.5 °F). Water's Melting/Freezing point is 0 C, or 32 F. Melting point is often used to ascertain purity of and characterise organic compounds. The melting point of a pure substance is always higher than the melting point of an impure sample of that particular substance. When two chemical substances are mixed, the melting point of the resultant mixture will be lower than the melting point of either constituent. The mixing ratio that results in the lowest possible melting point is known as the eutectic point.

William Thomson, 1st Baron Kelvin

The Right Honourable William Thomson, 1st Baron Kelvin, GCVO, OM, PC, PRS (26 June 1824–17 December 1907) was a Scottish-Irish mathematical physicist and engineer, an outstanding leader in the physical sciences of the 19th century. He did important work in the mathematical analysis of electricity and thermodynamics, and did much to unify the emerging discipline of physics in its modern form. He is also credited for the discovery of the atom. He also enjoyed a second career as a telegraph engineer and inventor, a career that propelled him into the public eye and ensured his fame and honour.

Early life and work

Family

William's father was Dr. James Thomson, the son of a Belfast farmer. James received little youthful instruction in Ireland but, when 24 years old, started to study for half the year at the University of Glasgow, Scotland, while working as a teacher back in Belfast for the other half. On graduating, he became a mathematics teacher at the Royal Belfast Academical Institution. He married Margaret Gardner in 1817 and, of their children four boys and two girls survived infancy. William, and his elder brother James, were tutored at home by their father while the younger boys were tutored by their elder sisters. James was intended to benefit from the major share of his father's encouragement, affection and financial support and was prepared for a fashionable career in engineering. However, James was a sickly youth and proved unsuited to a sequence of failed apprenticeships. William soon became his father's favourite. In 1832, the father was appointed professor of mathematics at Glasgow and the family relocated there in October 1833. The Thomson children were introduced to a broader cosmopolitan experience than their father's rural upbringing, spending the summer of 1839 in London and, the boys, being tutored in French in Paris. The summer of 1840 was spent in Germany and the Netherlands. Language study was given a high priority.

Youth

William began study at Glasgow University in 1834 at the age of 10, not out of any precociousness; the University provided many of the facilities of an elementary school for abler pupils and this was a typical starting age. In 1839, John Pringle Nichol, the professor of astronomy, took the chair of natural philosophy. Nichol updated the curriculum, introducing the new mathematical works of Jean Baptiste Joseph Fourier. The mathematical treatment much impressed Thomson. In the academic year 1839-1840, Thomson won the class prize in astronomy for his Essay on the figure of the Earth which showed an early facility for mathematical analysis and creativity. Throughout his life, he would work on the problems raised in the essay as a coping strategy at times of personal stress. Thomson became intrigued with Fourier's Théorie analytique de la chaleur and committed himself to study the "Continental" mathematics resisted by a British establishment still working in the shadow of Sir Isaac Newton. Unsurprisingly, Fourier's work had been attacked by domestic mathematicians, Philip Kelland authoring a critical book. The book motivated Thomson to write his first published scientific paper under the pseudonym P.Q.R., defending Fourier, and submitted to the Cambridge Mathematical Journal by his father. A second P.Q.R paper followed almost immediately. While vacationing with his family in Lamlash in 1841, he wrote a third, more substantial, P.Q.R. paper On the uniform motion of heat in homogeneous solid bodies, and its connection with the mathematical theory of electricity. In the paper he made remarkable connections between the mathematical theories of heat conduction and electrostatics, an analogy that James Clerk Maxwell was ultimately to describe as one of the most valuable science-forming ideas.

Cambridge

William's father was able to make a generous provision for his favourite son's education and, in 1841, installed him, with extensive letters of introduction and ample accommodation, at Peterhouse, Cambridge. In 1845 Thomson graduated as second wrangler. However, he won a Smith's Prize, sometimes regarded as a better test of originality than the tripos. Robert Leslie Ellis, one of the examiners, is said to have declared to another examiner You and I are just about fit to mend his pens. While at Cambridge, Thomson was active in sports and athletics. He won the Silver Sculls, and rowed in the winning boat of the Oxford and Cambridge Boat Race. He also took a lively interest in the classics, music, and literature; but the real love of his intellectual life was the pursuit of science. The study of mathematics, physics, and in particular, of electricity, had captivated his imagination. In 1845 he gave the first mathematical development of Faraday's idea that electric induction takes place through an intervening medium, or "dielectric", and not by some incomprehensible "action at a distance". He also devised a hypothesis of electrical images, which became a powerful agent in solving problems of electrostatics, or the science which deals with the forces of electricity at rest. It was partly in response to his encouragement that Faraday undertook the research in September of 1845 that led to the discovery of the Faraday effect, which established that light and magnetic (and thus electric) phenomena were related. On gaining a fellowship at his college, he spent some time in the laboratory of the celebrated Henri Victor Regnault, at Paris; but in 1846 he was appointed to the chair of natural philosophy in the University of Glasgow. At twenty-two he found himself wearing the gown of a learned professor in one of the oldest Universities in the country, and lecturing to the class of which he was a freshman but a few years before.

Thermodynamics

philosophy By 1847, Thomson had already gained a reputation as a precocious and maverick scientist when he attended the British Association for the Advancement of Science annual meeting in Oxford. At that meeting, he heard James Prescott Joule making yet another of his, so far, ineffective attempts to discredit the caloric theory of heat and the theory of the heat engine built upon it by Sadi Carnot and Émile Clapeyron. Joule argued for the mutual convertibility of heat and mechanical work and for their mechanical equivalence. Thomson was intrigued but skeptical. Though he felt that Joule's results demanded theoretical explanation, he retreated into an even deeper commitment to the Carnot-Clapeyron school. He predicted that the melting point of ice must fall with pressure, otherwise its expansion on freezing could be exploited in a perpetuum mobile. Experimental confirmation in his laboratory did much to bolster his beliefs. In 1848, he extended the Carnot-Clapeyron theory still further through his dissatisfaction that the gas thermometer provided only an operational definition of temperature. He proposed an absolute temperature scale in which a unit of heat descending from a body A at the temperature T° of this scale, to a body B at the temperature (T-1)°, would give out the same mechanical effect [work], whatever be the number T. Such a scale would be quite independent of the physical properties of any specific substance. By employing such a "waterfall", Thomson postulated that a point would be reached at which no further heat (caloric) could be transferred, the point of absolute zero about which Guillaume Amontons had speculated in 1702. Thomson used data published by Regnault to calibrate his scale against established measurements. In his publication, Thomson wrote: :"... the conversion of heat (or caloric) into mechanical effect is probably impossible, certainly undiscovered" - but a footnote signaled his first doubts about the caloric theory, referring to Joule's very remarkable discoveries. Surprisingly, Thomson did not send Joule a copy of his paper but when Joule eventually read it he wrote to Thomson on October 6, claiming that his studies had demonstrated conversion of heat into work but that he was planning further experiments. Thomson replied on the 27th, revealing that he was planning his own experiments and hoping for a reconciliation of their two views. Thomson returned to critique Carnot's original publication and read his analysis to the Royal Society of Edinburgh in January 1849, still convinced that the theory was fundamentally sound. However, though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's. In February 1851 he sat down to articulate his new thinking. However, he was uncertain of how to frame his theory and the paper went through several drafts before he settled on an attempt to reconcile Carnot and Joule. During his rewriting, he seems to have considered ideas that would subsequently give rise to the second law of thermodynamics. In Carnot's theory, lost heat was absolutely lost but Thomson contended that it was "lost to man irrecoverably; but not lost in the material world". Moreover, his theological beliefs led to speculation about the heat death of the universe. :"I believe the tendency in the material world is for motion to become diffused, and that as a whole the reverse of concentration is gradually going on - I believe that no physical action can ever restore the heat emitted from the sun, and that this source is not inexhaustible; also that the motions of the earth and other planets are losing vis viva which is converted into heat; and that although some vis viva may be restored for instance to the earth by heat received from the sun, or by other means, that the loss cannot be precisely compensated and I think it probable that it is under compensated." Compensation would require a creative act or an act possessing similar power. In final publication, Thomson retreated from a radical departure and declared "the whole theory of the motive power of heat is founded on ... two ... propositions, due respectively to Joule, and to Carnot and Clausius." Thomson went on to state a form of the second law: :"It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects." In the paper, Thomson supported the theory that heat was a form of motion but admitted that he had been influenced only by the thought of Sir Humphry Davy and the experiments of Joule and Julius Robert von Mayer, maintaining that experimental demonstration of the conversion of heat into work was still outstanding. As soon as Joule read the paper he wrote to Thomson with his comments and questions. Thus began a fruitful, though largely epistolary, collaboration between the two men, Joule conducting experiments, Thomson analyzing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856, its discoveries including the Joule-Thomson effect, and the published results did much to bring about general acceptance of Joule's work and the kinetic theory.

Transatlantic cable

kinetic theory

Calculations on data-rate

Though now eminent in the academic field, Thomson was obscure to the general public. In September 1852, he married childhood sweetheart Margaret Crum but her health broke down on their honeymoon and, over the next seventeen years, Thomson was distracted by her suffering. On October 16, 1854, Stokes wrote to Thomson to try to re-interest him in work by asking his opinion on some experiments of Michael Faraday on the proposed transatlantic telegraph cable. :To understand the technical issues in which Thomson became involved, see Submarine communications cable: Bandwidth problems Faraday had demonstrated how the construction of a cable would limit the rate at which messages could be sent — in modern terms, the bandwidth. Thomson jumped at the problem and published his response that month. He expressed his results in terms of the data rate that could be achieved and the economic consequences in terms of the potential revenue of the transatlantic undertaking. In a further 1855 analysis, Thomson stressed the impact that the design of the cable would have on its profitability. Thomson contended that the speed of a signal through a given core was inversely proportional to the square of the length of the core. Thomson's results were disputed at a meeting of the British Association in 1856 by Wildman Whitehouse, the electrician of the Atlantic Telegraph Company. Whitehouse had possibly misinterpreted the results of his own experiments but was doubtless feeling financial pressure as plans for the cable were already well underway. He believed that Thomson's calculations implied that the cable must be "abandoned as being practically and commercially impossible." Thomson attacked Whitehouse's contention in a letter to the popular Athenaeum magazine, pitching himself into the public eye. Thomson recommended a larger conductor with a larger cross section of insulation. However, he thought Whitehouse no fool and suspected that he may have the practical skill to make the existing design work. Thomson's work had, however, caught the eye of the project's undertakers and in December 1856, he was elected to the board of directors of the Atlantic Telegraph Company.

Scientist to engineer

Thomson became scientific adviser to a team with Whitehouse as chief electrician and Sir Charles Tilston Bright as chief engineer but Whitehouse had his way with the specification, supported by Faraday and Samuel F. B. Morse. Thomson sailed on board the cable-laying ship Agamemnon in August 1857, with Whitehouse confined to land owing to illness, but the voyage ended after just 380 miles when the cable parted. Thomson contributed to the effort by publishing in the Engineer the whole theory of the stresses involved in the laying of a submarine cable, and showed that when the line is running out of the ship, at a constant speed, in a uniform depth of water, it sinks in a slant or straight incline from the point where it enters the water to that where it touches the bottom. Thomson developed a complete system for operating a submarine telegraph that was capable of sending a character every 3.5 seconds. He patented the key elements of his system, the mirror galvanometer and the siphon recorder, in 1858. However, Whitehouse still felt able to ignore Thomson's many suggestions and proposals. It was not until Thomson convinced the board that using a purer copper for replacing the lost section of cable would improve data capacity, that he first made a difference to the execution of the project. The board insisted that Thomson join the 1858 cable-laying expedition, without any financial compensation, and take an active part in the project. In return, Thomson secured a trial for his mirror galvanometer, about which the board had been unenthusiastic, alongside Whitehouse's equipment. However, Thomson found the access he was given unsatisfactory and the Agamemnon had to return home following the disastrous storm of June 1858. Back in London, the board was on the point of abandoning the project and mitigating their losses by selling the cable. Thomson, Cyrus Field and Curtis M. Lampson argued for another attempt and prevailed, Thomson insisting that the technical problems were tractable. Though employed in an advisory capacity, Thomson had, during the voyages, developed real engineer's instincts and skill at practical problem-solving under pressure, often taking the lead in dealing with emergencies and being unafraid to lend a hand in manual work. A cable was finally completed in August 5.

Disaster and triumph

Thomson's fears were realised and Whitehouse's apparatus proved insufficiently sensitive and had to be replaced by Thomson's mirror galvanometer. Whitehouse continued to maintain that it was his equipment that was providing the service and started to engage in desperate measures to remedy some of the problems. He only succeded in fatally damaging the cable by applying 2,000 V. When the cable failed completely Whitehouse was dismissed, though Thomson objected and was reprimanded by the board for his interference. Thomson subsequently regretted that he had acquiesced too readily to many of Whitehouse's proposals and had not challenged him with sufficient energy. A joint committee of inquiry was established by the Board of Trade and the Atlantic Telegraph Company. Most of the blame for the cable's failure was found to rest with Whitehouse. The committee found that, though underwater cables were notorious in their lack of reliability, most of the problems arose from known and avoidable causes. Thomson was appointed one of a five-member committee to recommend a specification for a new cable. The committee reported in October 1863. In July 1865 Thomson sailed on the cable-laying expedition of the SS Great Eastern but the voyage was again dogged with technical problems. The cable was lost after 1,200 miles had been laid and the expedition had to be abandoned. A further expedition in 1866 managed to lay a new cable in two weeks and then go on to recover and complete the 1865 cable. The enterprise was now feted as a triumph by the public and Thomson enjoyed a large share of the adulation. Thomson, along with the other principals of the project, was knighted on November 10, 1866. Thomson's barony was named after the River Kelvin, which ran through the grounds of the University of Glasgow. To exploit his inventions for signalling on long submarine cables, Thomson now entered into a partnership with C.F. Varley and Fleeming Jenkin. In conjunction with the latter, he also devised an automatic curb sender, a kind of telegraph key for sending messages on a cable.

Later expeditions

Thomson took part in the laying of the French Atlantic submarine communications cable of 1869, and with Jenkin was engineer of the Western and Brazilian and Platino-Brazilian cables, assisted by vacation student James Alfred Ewing. He was present at the laying of the Pará to Pernambuco section of the Brazilian coast cables in 1873. Thomson's wife had died on June 17, 1870 and he resolved to make changes in his life. Already addicted to seafaring, in September he purchased a 126-ton schooner, the Lalla Rookh and used it as a base for entertaining friends and scientific colleagues. In June 1873, Thomson and Jenkin were onboard the Hooper, bound for Lisbon with 2,500 miles of cable when the cable developed a fault. An unscheduled 16-day stop-over in Madeira followed and Thomson became good friends with Charles R. Blandy and his three daughters. On May 2 1874 he set sail for Madeira on the Lalla Rookh. As he approached the harbour, he signalled to the Blandy residence Will you marry me? and Fanny signalled back Yes. Tho