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Kelvin

The kelvin (symbol: K) is the SI base unit of thermodynamic temperature, defined by fixing the numerical value of the Boltzmann constant k at exactly $1.380\,649 \times 10^{-23} J K^{-1}, where the joule is the SI unit of energy.^[1] This definition, adopted in the 2019 revision of the International System of Units (SI), establishes the kelvin as an absolute scale with 0 K corresponding to absolute zero—the theoretical lowest temperature at which the entropy of a perfect crystal reaches its minimum value and all thermal motion ceases.^[2] The unit is named after William Thomson, 1st Baron Kelvin (1824–1907), a British physicist and engineer who first proposed an absolute temperature scale in 1848 to resolve inconsistencies in the Carnot heat engine theory.^[3] The kelvin scale aligns closely with the Celsius scale, differing only by a constant shift: a temperature interval of 1 K equals 1 °C, and the conversion is given by T(\text{K}) = t(°\text{C}) + 273.15, with the triple point of water measured at 273.16 K.^[4] Historically, the kelvin's magnitude was originally set by the triple point of water (0.01 K above the ice point) until the 2019 redefinition, which decoupled it from any physical artifact for greater precision and universality.^[3] This unit is fundamental in fields like physics, chemistry, and engineering, enabling precise measurements of phenomena such as blackbody radiation, ideal gas behavior, and quantum effects near absolute zero.^[2]

Definition and Fundamentals

Absolute Scale Characteristics

The kelvin, symbol K, is the base unit of the International System of Units (SI) for thermodynamic temperature. Prior to the 2019 revision of the SI, the kelvin was defined as exactly 1/273.16 of the thermodynamic temperature of the triple point of water, which served as a reproducible fixed point for calibration.^[5] Following the 26th General Conference on Weights and Measures in 2018, the kelvin was redefined by fixing the numerical value of the Boltzmann constant k to exactly $1.380649 \times 10^{-23} when expressed in the unit J K^{-1}, where the joule is defined in terms of the hertz and second.^[6] This redefinition maintains the triple point of water at exactly 273.16 K while linking the unit directly to a fundamental physical constant, ensuring long-term stability independent of material artifacts.^[7] The Kelvin scale is an absolute thermodynamic scale, with its zero point at absolute zero, defined as 0 K—the theoretical lower limit of temperature at which the thermal motion of particles in a perfect crystalline substance reaches its minimum, approaching complete rest.^[4] Unlike empirical interval scales such as the Celsius scale, which allow negative values relative to an arbitrary zero, the Kelvin scale prohibits negative temperatures and exhibits additivity for temperature intervals, enabling consistent measurement of thermal energy differences regardless of the reference point.^[8] This absolute nature ensures that thermodynamic temperature T, expressed in kelvins, behaves as an invariant state function under reversible processes, preserving its value across equilibrium transformations.^[5] A key application of the Kelvin scale arises in fundamental thermodynamic relations, such as the ideal gas law, which relates pressure P, volume V, amount of substance n, and temperature T through

PV = nRT,

where R is the molar gas constant.^[5] Here, T in kelvins directly scales with the average kinetic energy of gas particles, proportional to kT per degree of freedom, underscoring the scale's connection to microscopic energy distributions.^[7] The relation to the Celsius scale is given by T (in K) = t (in °C) + 273.15, facilitating practical conversions without altering the absolute properties.^[4]

Conversion to Other Temperature Scales

The Kelvin scale is an absolute temperature scale, allowing straightforward conversions to other scales like Celsius and Fahrenheit through defined offsets and ratios.^[4] To convert from Kelvin to Celsius, subtract 273.15 from the Kelvin value, as the Celsius scale is shifted by this exact amount relative to Kelvin:

T(°C) = T(K) - 273.15

This offset arises because the triple point of water, where solid, liquid, and vapor phases coexist in equilibrium, is defined as exactly 273.16 K, corresponding to 0.01 °C; thus, 0 °C is precisely 273.15 K.^[9] The reverse conversion adds 273.15:

T(K) = T(°C) + 273.15

For Fahrenheit, which is based on a non-absolute scale with an arbitrary zero point (32 °F for the freezing point of water) and a degree size of 5/9 that of Celsius, the conversion from Kelvin first shifts to Celsius and then applies the Fahrenheit ratio:

T(°F) = (T(K) - 273.15) \times \frac{9}{5} + 32

This simplifies to T(°F) = T(K) \times \frac{9}{5} - 459.67, where -459.67 °F marks absolute zero.^[4] The reverse formula is:

T(K) = (T(°F) + 459.67) \times \frac{5}{9}

Practical examples illustrate these conversions: the boiling point of water at standard atmospheric pressure is 373.15 K, equivalent to 100 °C or 212 °F,^[4] while absolute zero is 0 K, or -273.15 °C and -459.67 °F.^[9] A key feature of the Kelvin and Celsius scales is that their degree intervals are identical, so a temperature change of 1 K equals a change of 1 °C; however, a 1 K change corresponds to 1.8 °F due to Fahrenheit's different degree size.^[4]

Historical Development

Precursors and Early Concepts

The development of concepts leading to an absolute temperature scale began with early experiments on gas behavior. In 1703, French physicist Guillaume Amontons constructed an air thermometer of constant volume, observing that the pressure of trapped air increased linearly with temperature rises above a reference point, such as the freezing point of water.^[10] By extrapolating this linear relationship downward, Amontons inferred a theoretical "extreme cold" at which pressure would reach zero, approximately 240 degrees below the freezing point on his scale, marking an initial conception of absolute zero derived from pressure-volume observations in gases.^[11] Building on such empirical foundations, Jacques Alexandre César Charles conducted unpublished experiments around 1787, noting that the volume of a gas held at constant pressure expands proportionally with increasing temperature. This relationship, expressed as V \propto T where T is absolute temperature, implied that the ratio V/T remains constant for a given quantity of ideal gas, further supporting the idea of an absolute zero at which volume would theoretically vanish.^[12] Charles's observations suggested a temperature scale independent of arbitrary fixed points, though they remained private until later dissemination. In 1802, Joseph Louis Gay-Lussac publicly refined and quantified Charles's findings through meticulous measurements on various gases, confirming that their volumes increase by approximately 1/273 of the value at 0°C for each degree Celsius rise at constant pressure. Gay-Lussac's work extended the proportionality to multiple gases, excluding those soluble in water, and highlighted the universality of the effect, thereby strengthening the empirical basis for an absolute scale.^[12] Concurrently, John Dalton's emerging atomic theory, formalized in his 1808 publication A New System of Chemical Philosophy, posited gases as collections of discrete atoms whose repulsive forces and motions underpin volume and pressure changes with temperature, offering a rudimentary kinetic interpretation that aligned gas laws with particulate behavior.^[13] During the early 1800s, efforts to formalize absolute scales drew on these gas laws, as seen in Pierre-Simon Laplace's collaborations with Antoine Lavoisier on caloric theory and specific heats, which explored heat as a fluid influencing gas expansion without yet defining a fixed, reproducible unit for absolute temperature.^[13] These precursors established the linear gas thermometry principle but lacked a standardized reference, setting the stage for subsequent theoretical unification.

Lord Kelvin's Contributions

William Thomson, later known as Lord Kelvin, proposed the first absolute temperature scale in his 1848 paper "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations."^[14] In this work, Thomson utilized Sadi Carnot's theorem on the efficiency of heat engines, which posits that the maximum efficiency depends solely on the temperature difference between the source and sink, to define an absolute measure of temperature independent of any particular substance.^[15] He argued that the mechanical effect produced by heat transfer between two bodies is proportional to the temperature interval on this scale, providing a universal standard for thermometry.^[14] Thomson's initial formulation relied on the air thermometer as a practical reference, extrapolating to absolute zero using Charles's law, which describes the linear expansion of gases with temperature.^[3] By extending the air thermometer's readings downward, he determined absolute zero to be approximately -273°C on the conventional scale, establishing 0 on the new scale at this point where molecular motion theoretically ceases.^[14] To calibrate the scale, Thomson incorporated Henri Victor Regnault's experimental data on the physical properties of air and vapors, calculating that the temperature of the ice point (freezing of water at standard pressure) corresponded to about 273 units above absolute zero, while the boiling point of water was around 373 units.^[16] This setup ensured the absolute scale's degrees matched those of the air thermometer between 0°C and 100°C, offering a consistent framework for thermodynamic calculations.^[14] The development of this thermodynamic temperature concept was significantly influenced by James Prescott Joule's experimental demonstrations that heat is a form of energy convertible to mechanical work, challenging the caloric theory underlying Carnot's original assumptions.^[17] Thomson, who had encountered Joule's findings around 1847, integrated this insight in subsequent writings, refining the absolute scale to align with the conservation of energy and establishing temperature as a measure tied to the average kinetic energy of particles.^[16] This synthesis bridged empirical gas laws with emerging thermodynamic principles, laying the groundwork for modern temperature measurement.^[15]

Standardization and Triple Point

The practical realization of the Kelvin scale prior to 1954 relied on the normal hydrogen thermometer, a constant-volume gas thermometer using hydrogen gas to approximate the ideal gas law for measuring absolute temperatures, calibrated against the ice point of water at 0 °C and 1 atm pressure.^[18] This method provided a reproducible but indirect approach to the thermodynamic scale, with the kelvin defined as equivalent to the degree interval on the Celsius scale extrapolated from absolute zero.^[8] In 1954, the 10th Conférence Générale des Poids et Mesures (CGPM) adopted Resolution 3, formally defining the kelvin as the unit of thermodynamic temperature such that the temperature of the triple point of water, denoted T_\text{t}, is exactly 273.16 K, establishing the triple point as the fundamental fixed point for the scale.^[19] This single-point definition replaced earlier two-point calibrations (such as ice and steam points) to enhance precision and universality in thermometry. The triple point of water represents the unique condition of thermodynamic equilibrium where its solid (ice), liquid, and vapor phases coexist, occurring at a temperature of 0.01 °C (exactly 273.16 K) and a vapor pressure of 611.657 Pa.^[20] This state is realized in sealed cells containing high-purity water, providing an exceptionally reproducible reference temperature with uncertainties as low as 0.1 mK when properly prepared, far surpassing the variability of single-phase transitions like the ice point under atmospheric pressure.^[21] The selection of the triple point over single-phase points, such as the ice point, was driven by its superior precision for primary thermometry, as the coexistence of three phases yields a sharp, unambiguous phase boundary that minimizes measurement errors from impurities, pressure variations, or supercooling effects.^[22] In 1967–1968, the 13th CGPM further refined this through Resolution 3, officially naming the unit "kelvin" (symbol K) rather than "degree Kelvin" (°K) and explicitly defining it as \frac{1}{273.16} of the thermodynamic temperature at the triple point of water, solidifying its role in the International System of Units.^[23] This adjustment also aligned practical temperature scales, like the International Practical Temperature Scale of 1968 (IPTS-68), with the triple point as the anchor for calibrations above 0 K, improving consistency across global metrology.^[18]

2019 SI Redefinition

The 26th General Conference on Weights and Measures (CGPM), held in November 2018, adopted Resolution 1 approving the redefinition of the kelvin as part of the broader revision of the International System of Units (SI), with the change taking effect on May 20, 2019.^[24]^[25] Under this redefinition, the kelvin is now defined by fixing the numerical value of the Boltzmann constant k to exactly $1.380\,649 \times 10^{-23} joules per kelvin (J/K), thereby linking the unit directly to a fundamental physical constant rather than a material artifact.^[26]^[9] This shift was motivated by the desire to base the SI on invariant constants of nature, such as the Planck constant h, to ensure long-term stability and universality, while addressing limitations of the prior definition tied to the triple point of water, which suffered from reproducibility challenges due to isotopic variations in water samples that could cause temperature discrepancies of up to about 0.2 mK.^[27]^[9] As a result, the triple point of water, previously exactly 273.16 K by definition, is now an approximate value of 273.16 K, measured relative to the fixed Boltzmann constant, which enhances the scale's independence from material properties and improves consistency across global measurements.^[7]^[9] The redefinition has no immediate impact on existing temperature values or calibration practices, as the numerical value of k was chosen to preserve continuity with prior measurements.^[7] However, it promotes greater precision in fields like low-temperature physics by facilitating primary thermometry methods that directly link measurements to the Boltzmann constant, potentially ushering in advanced techniques for realizing the kelvin without reliance on secondary standards.^[28]^[29]

Practical Applications

Thermodynamic and Scientific Uses

In thermodynamics, the Kelvin scale serves as the absolute temperature measure essential for fundamental equations describing gas behavior and energy transfer. The ideal gas law, expressed as PV = nRT, relates pressure P, volume V, amount of substance n, and temperature T in kelvins, with R as the gas constant; this formulation ensures thermodynamic consistency by avoiding negative temperatures inherent in other scales.^[30] Similarly, the Stefan-Boltzmann law states that the total power radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature, j = \sigma T^4, where \sigma is the Stefan-Boltzmann constant and T is in kelvins; this relation underpins calculations of thermal radiation in high-temperature environments.^[31] Wien's displacement law further illustrates the Kelvin scale's role, asserting that the wavelength \lambda_{\max} at which black-body radiation peaks satisfies \lambda_{\max} T = b, with b \approx 2.897 \times 10^{-3} m·K as Wien's displacement constant; this enables determination of source temperatures from spectral peaks.^[32] The Kelvin scale is indispensable in specialized scientific domains requiring precise low- or high-temperature assessments. In cryogenics, phenomena like superconductivity emerge at temperatures near absolute zero, such as the 4.2 K transition in mercury, where electrical resistance vanishes below critical thresholds; the scale's origin at 0 K facilitates studies of quantum effects in materials cooled to millikelvins.^[33] Atmospheric science employs kelvins to quantify lapse rates, the rate of temperature decrease with altitude, typically around 6.5 K/km in the troposphere under standard conditions, aiding models of convection and weather patterns.^[34] In stellar physics, surface temperatures of stars are routinely expressed in kelvins, ranging from about 2,500 K for cool red dwarfs to over 50,000 K for hot O-type stars, allowing astrophysicists to classify spectral types and infer evolutionary stages via black-body approximations.^[35] Accurate temperature measurement in scientific contexts relies on devices calibrated against the Kelvin scale for traceability to the International Temperature Scale of 1990 (ITS-90). Thermocouples, which generate voltage from the Seebeck effect across dissimilar metals, are calibrated over wide ranges (e.g., type K from 0 K to 1,700 K) to ensure precision in dynamic environments like engines or reactors.^[36] Resistance thermometers, particularly platinum models, exhibit resistance changes proportional to temperature and are standardized at fixed points like the triple point of water (273.16 K), achieving uncertainties below 0.001 K for cryogenic and high-accuracy applications.^[37] The Kelvin scale also anchors the third law of thermodynamics, which posits that the entropy S of a perfect crystalline substance approaches a minimum value—typically zero—as temperature T nears 0 K, implying unattainability of absolute zero through finite processes; this establishes an absolute entropy reference for thermodynamic calculations.^[38]

Color Temperature in Lighting and Imaging

Color temperature describes the color appearance of a light source by referencing the absolute temperature, in kelvins, at which a theoretical blackbody radiator would emit light of comparable chromaticity on the CIE 1931 chromaticity diagram.^[39] For instance, warm incandescent bulbs typically have a color temperature around 2700 K, producing a yellowish-reddish hue, while midday daylight approximates 6500 K, yielding a neutral to bluish-white tone.^[40] This metric is perceptual rather than a direct measure of physical heat, focusing on visual similarity to blackbody radiation.^[41] The perceived warmth or coolness of light arises from the spectral power distribution governed by Planck's law, which dictates that lower temperatures shift the emission peak toward longer, redder wavelengths, while higher temperatures favor shorter, bluer wavelengths.^[42] As temperature increases, the blackbody spectrum broadens and intensifies in the visible range, enhancing blue content and reducing red dominance, thus altering chromaticity from warm (e.g., below 4000 K) to cool (above 5000 K).^[43] For sources deviating from ideal blackbody spectra, such as LEDs or fluorescent lamps, correlated color temperature (CCT) is used instead, defined as the temperature of the nearest point on the Planckian locus to the source's chromaticity coordinates.^[44] In lighting design, color temperature guides selections for ambiance and functionality, with LEDs often specified by CCT ranges like 3000 K for residential warmth or 5000 K for task-oriented coolness in offices.^[39] Photography relies on matching film or sensor white balance to source CCT to avoid color casts, as emulsions or digital profiles are calibrated for specific temperatures like 3200 K tungsten or 5500 K daylight.^[40] Similarly, display technologies set white points using CCT standards, such as 6500 K for sRGB to simulate daylight viewing, ensuring consistent color reproduction across devices.^[45] The concept of color temperature for illuminants emerged in the 1930s, with early work correlating non-blackbody sources to blackbody equivalents for standardized description, distinct from thermodynamic measurements.^[44]

Noise Temperature in Electronics

In electronics, particularly in radio frequency (RF) and microwave systems, noise temperature quantifies the level of thermal noise generated by a device or system, expressed in kelvin (K). It represents the temperature at which a hypothetical resistor would produce the same noise power as the actual noise source under consideration. This concept is fundamental to characterizing the performance of sensitive receivers where unwanted noise can degrade signal quality. The noise power P_n delivered by such a resistor into a matched load across a bandwidth B is given by the Nyquist formula:

P_n = k T B

where T is the noise temperature in kelvin and k is the Boltzmann constant, fixed at $1.380649 \times 10^{-23} J/K since the 2019 SI redefinition. This formula derives from the statistical mechanics of thermal agitation of charge carriers in conductors, providing a direct link between noise and an equivalent thermal equilibrium temperature. For a device with noise temperature T_n, the effective noise power matches that of a resistor at T_n, enabling standardized comparisons across components.^[46]^[47] Unlike physical temperature, which measures the actual kinetic energy of particles, noise temperature is a metaphorical quantity that solely describes the statistical equivalent of noise fluctuations in terms of power spectral density. It does not imply literal heating of the device; instead, it serves as a convenient metric for noise analysis in non-equilibrium or active systems, such as amplifiers, where physical cooling may reduce but not eliminate other noise sources. This distinction allows engineers to model total system noise without directly measuring thermal states.^[48] In practical applications, noise temperature is essential for designing antennas, receivers, and low-noise amplifiers (LNAs) in high-sensitivity systems. For antennas, it accounts for contributions from sky noise, ground emissions, and atmospheric effects, helping to optimize signal-to-noise ratios in radio astronomy or deep-space communications. In receivers, the overall system noise temperature combines contributions from the antenna, feed lines, and front-end electronics, influencing the noise figure—a dimensionless measure of degradation defined relative to a 290 K reference. LNAs, often cryogenic to minimize their own noise, are critical in satellite communications, where low noise temperatures (e.g., below 10 K at microwave frequencies) enable detection of weak signals from distant spacecraft. For instance, NASA's Deep Space Network employs cooled LNAs with noise temperatures under 4 K at 8.4 GHz to support interplanetary missions.^[49]^[48]^[50] Representative examples highlight the scale of noise temperatures in advanced systems. The cosmic microwave background (CMB) radiation, a pervasive noise source in radio receivers, has an effective antenna temperature of 2.725 K, as precisely measured by the Cosmic Background Explorer (COBE) satellite's Far Infrared Absolute Spectrophotometer (FIRAS). This uniform background sets a fundamental limit for low-frequency observations. In quantum computing, cryogenic amplifiers operating at millikelvin physical temperatures achieve noise temperatures as low as 2.3 K across 1–11 GHz, enabling readout of superconducting qubits with minimal added noise and preserving quantum coherence. These ultra-low values are vital for scaling quantum processors, where even slight noise can cause decoherence.^[51]^[52]

Units and Notation

Derived Units and SI Prefixes

The kelvin serves as the base unit for thermodynamic temperature in the International System of Units (SI) and is integral to several derived units that quantify thermal phenomena.^[9] One key derived unit is heat capacity, expressed as joule per kelvin (J/K), which measures the heat energy required to increase the temperature of a system or substance by one kelvin at constant volume or pressure.^[9] Another is thermal conductivity, given in watts per meter kelvin (W/(m·K)), representing the rate of heat transfer through a unit area of material per unit temperature gradient along the direction of heat flow.^[9] Additionally, temperature differences or intervals are expressed in kelvins, with the unit symbol K used identically for both absolute temperatures and differences, ensuring numerical consistency with degree Celsius intervals.^[9] SI prefixes may be attached to the kelvin to form decimal multiples and submultiples, facilitating the expression of extreme temperatures across scientific domains, though such prefixed units are not coherent SI units.^[9] For cryogenic applications, the millikelvin (mK) is commonly employed; for example, dilution refrigerators routinely achieve base temperatures around 10 mK, enabling experiments in quantum materials and low-temperature physics.^[53] In cosmology, the microkelvin (μK) describes minute temperature fluctuations in the cosmic microwave background radiation, which are on the order of ±200 μK and provide insights into the early universe's structure.^[54] At the opposite extreme, prefixes like kilokelvin (kK) and megakelvin (MK) are used for high-temperature regimes in astrophysics and plasma physics; Big Bang nucleosynthesis, for instance, occurred at approximately 10⁹ K during the universe's first few minutes.^[55] While SI prefixes are permitted with the kelvin for both absolute temperatures and intervals according to the official SI guidelines, some contexts—particularly in engineering or traditional thermometry—avoid prefixing temperature differences to prevent ambiguity, though this is not a formal restriction.^[9]^[56]

Orthography and Symbol Usage

The kelvin, symbol K, is the SI base unit of thermodynamic temperature, with the symbol written as an uppercase K without any preceding degree sign (°). The unit name is spelled "kelvin" in lowercase letters when used in running text, following the general convention for SI unit names treated as common nouns.^[9]^[57] The plural form of the unit name is "kelvins," applied according to standard English grammar rules for countable quantities greater than one. Numerical values are expressed with a non-breaking space between the number and the symbol (e.g., 273 K), and the symbol remains unchanged in the plural (e.g., 25 K). In textual descriptions, temperatures can be written out fully as "25 kelvins" or using the symbol as "25 K," but the phrase "degrees Kelvin" or "degrees kelvin" is incorrect and prohibited. Examples include the triple point of water at exactly 273.16 K or room temperature approximated as 293 K.^[58]^[57]^[9] Historically, the notation "°K" and the term "degree Kelvin" were used but were officially deprecated by the 13th General Conference on Weights and Measures (CGPM) in 1967, which adopted the current symbol K and name "kelvin" to align with SI principles and avoid confusion with interval units like the degree Celsius.^[9] The unit name "kelvin" is the standard in English-language publications, but the symbol K is universally adopted across all languages in accordance with SI conventions, ensuring consistent international communication. In scientific equations, thermodynamic temperature is conventionally denoted by the italicized variable T, expressed in kelvins, to distinguish it from other quantities that may share the letter T (such as time or tension) based on contextual usage. For instance, the ideal gas law is written as pV = nRT, where T represents temperature in K.^[9]^[58]

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Light and Color - Color Temperature - Molecular Expressions
Nov 13, 2015 · Imagine that the black body radiator is heated to the temperature of freezing water, equal to 273 kelvins (or K), zero degrees Celsius, or 32 ...Missing: Kelvin | Show results with:Kelvin
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[PDF] Terms related to Planckian radiation temperature for light sources
If the stimulus is a blackbody, the colour temperature is equivalent to the thermodynamic temperature. This equivalence is a means to determine the temperature ...<|control11|><|separator|>
[42]
Blackbody Radiation - HyperPhysics
Stars approximate blackbody radiators and their visible color depends upon the temperature of the radiator. The curves show blue, white, and red stars.Missing: definition Kelvin
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[PDF] Color Temperature Estimation of Scene Illumination
Figure 1 shows the spectral-power distributions of a black body radiator at absolute color temperatures ranging from. 1000K to 10,000K in 500K steps. Figure 1 ...
[44]
[PDF] A correlated color temperature for illuminants
from 2,000° to 3,100° K. With one of the filters the color temperature range is from 2,650° to 5,000° K. and with the other, from 4,000° to.
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[PDF] T.A.Clark, P.E. , G.A.Salazar, P.E. , G.C. Brainard, Ph.D. , A ...
Correlated Color Temperature. CCT shows how the apparent color of the ambient lighting system is overcome by the content of the display. Note, however, that ...<|control11|><|separator|>
[46]
[PDF] The Nyquist Theorem - UCSB Physics
The rate at which energy comes off the line in one direction is (29.5) ET Af. but V I(2R), so that T²R = kT Aƒ, (29.6) v2/R www 4k T Af, which is the Nyquist ...
[47]
[PDF] Johnson Noise Thermometry
Johnson noise thermometers infer thermodynamic temperature from measurements of the thermally-induced current fluctuations that occur in all electrical ...
[48]
[PDF] Noise in Antennas
Note that the definition of noise figure depends on Ts, which is usually taken as 290 K, corresponding approximately to room temperature. For low noise ...
[49]
[PDF] Low-Noise Systems in the Deep Space Network - DESCANSO
noise temperature of the antenna and the low noise amplifier (LNA). Then Top is given by. Top. = Tmw +TB. = Tmw +Tatm +. Tcosmic. Latm. (6.4-4). Given Eqs. (6.4 ...
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Cryogenic, X-band and Ka-band InP HEMT based LNAs for the ...
To date, the lowest noise LNA modules developed for the DSN have demonstrated noise temperatures of under 4 K at 8.4 GHz and 11 K at 32 GHz.Missing: satellite | Show results with:satellite
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Cosmic Background Explorer - Nasa Lambda
FIRAS - The cosmic microwave background (CMB) spectrum is that of a nearly perfect blackbody with a temperature of 2.725 +/- 0.002 K.
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(PDF) Precision measurement method for cryogenic amplifier noise ...
Aug 5, 2025 · The particular amplifier that was measured exhibits a noise temperature below 5.5 K from 1 to 11 GHz, attaining a minimum value of 2.3 K±0.3 K ...
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Nanoelectronic primary thermometry below 4 mK - Nature
Jan 27, 2016 · The lowest temperature reported by the CBT is below 3.7 mK when ... Simple design for dilution refrigerator with base temperature of 2.3mK.
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Microwaves - NASA Science
Aug 3, 2023 · The observed +/-200 microKelvin temperature fluctuations, shown as color differences in the image, are the seeds that grew to become clusters of ...
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ESA - So, how did everything start? - European Space Agency
This is called 'primordial nucleosynthesis' and it lasts several minutes. Three minutes after the Big Bang the temperature is a thousand million degrees. It ...
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NIST Guide to the SI, Chapter 4: The Two Classes of SI Units and ...
Jan 28, 2016 · The kelvin and its symbol K are also used to express the value of a temperature interval or a temperature difference (see Sec. 8.5). Table 1. SI ...
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NIST Guide to the SI, Chapter 9: Rules and Style Conventions for ...
Jan 28, 2016 · The following eight sections give rules and style conventions related to spelling the names of units.Missing: orthography | Show results with:orthography
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NIST Guide to the SI, Chapter 7: Rules and Style Conventions for ...
Jan 28, 2016 · In keeping with Ref. [4: ISO 31-0], this Guide takes the position that it is acceptable to use the internationally recognized symbol % (percent) ...