Pressure also must be in absolute terms. The air still in a tire at a gage pressure of 0 kPa expands too as it gets hotter. It is not uncommon for engineers to overlook that one must work in terms of absolute pressure when compensating for temperature. For instance, a dominant manufacturer of aircraft tires published a document on temperature-compensating tire pressure, which used gage pressure in the formula. However, the high gage pressures involved (180 psi; 12.4 bar; 1.24 MPa) means the error would be quite small. With low-pressure automobile tires, where gage pressures are typically around 2 bar (200 kPa), failing to adjust to absolute pressure results in a significant error. "Aircraft tire ratings"(PDF). Air Michelin. Archived from the original(PDF) on 2010-02-15.[better source needed]
aps.org
pra.aps.org
Absolute zero's relationship to zero-point energy While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanicalzero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid HeliumArchived 2008-02-12 at the Wayback Machine by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero (T = 0) is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two T = 0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620 pm between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = 1×10−24 K). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1animation above. Before being given the kinetic kick, both T = 0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At T = 0, no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at T = 0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a T = 0 system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than T = 0, heat will flow inward, and if the surrounding environment is at 'T = 0, there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at T = 0 with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847.
archive-it.org
wayback.archive-it.org
When measured at constant-volume since different amounts of work must be performed if measured at constant-pressure. Nitrogen's CvH (100 kPa, 20 °C) equals 20.8 J⋅mol–1⋅K–1 vs. the monatomic gases, which equal 12.4717 J mol–1 K–1. Freeman, W. H. "Part 3: Change". Physical Chemistry(PDF). Exercise 21.20b, p. 787. Archived from the original(PDF) on 2007-09-27. See also Nave, R. "Molar Specific Heats of Gases". HyperPhysics. Georgia State University.
arxiv.org
Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. Oechslin, R.; Janka, H.-T. (2006). "Torus formation in neutron star mergers and well-localized short gamma-ray bursts". Monthly Notices of the Royal Astronomical Society. 368 (4): 1489–1499. arXiv:astro-ph/0507099v2. Bibcode:2006MNRAS.368.1489O. doi:10.1111/j.1365-2966.2006.10238.x. S2CID15036056. For a summary, see "Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars". Max-Planck-Institut für Astrophysik. Retrieved 24 September 2024.
Absolute zero's relationship to zero-point energy While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanicalzero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid HeliumArchived 2008-02-12 at the Wayback Machine by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero (T = 0) is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two T = 0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620 pm between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = 1×10−24 K). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1animation above. Before being given the kinetic kick, both T = 0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At T = 0, no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at T = 0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a T = 0 system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than T = 0, heat will flow inward, and if the surrounding environment is at 'T = 0, there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at T = 0 with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847.
calphysics.org
Absolute zero's relationship to zero-point energy While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanicalzero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid HeliumArchived 2008-02-12 at the Wayback Machine by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero (T = 0) is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two T = 0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620 pm between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = 1×10−24 K). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1animation above. Before being given the kinetic kick, both T = 0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At T = 0, no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at T = 0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a T = 0 system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than T = 0, heat will flow inward, and if the surrounding environment is at 'T = 0, there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at T = 0 with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847.
Kastberg, A.; et al. (27 February 1995). "Adiabatic Cooling of Cesium to 700 nK in an Optical Lattice". Physical Review Letters. 74 (9): 1542–1545. Bibcode:1995PhRvL..74.1542K. doi:10.1103/PhysRevLett.74.1542. PMID10059055. A record cold temperature of 450 pK in a Bose–Einstein condensate of sodium atoms (achieved by A. E. Leanhardt et al.. of MIT){{cn|{{subst:DATE}} equates to an average vector-isolated atom velocity of 0.4 mm/s and an average atom speed of 0.7 mm/s.
A record cold temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium (23Na) atoms was achieved in 2003 by researchers at MIT. Leanhardt, A. E.; et al. (12 September 2003). "Cooling Bose–Einstein Condensates Below 500 Picokelvin". Science. 301 (5639): 1515. Bibcode:2003Sci...301.1513L. doi:10.1126/science.1088827. PMID12970559. The thermal velocity of the atoms averaged about 0.4 mm/s. This record's peak emittance black-body radiation wavelength of 6,400 kilometers is roughly the radius of Earth.
Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41 GK (309 ±35 keV) for 3 ns (ns 112 through 115). Haines, M. G.; et al. (2006). "Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2 × 109 Kelvin". Physical Review Letters. 96 (7): 075003. Bibcode:2006PhRvL..96g5003H. doi:10.1103/PhysRevLett.96.075003. PMID16606100. No. 075003. For a press summary of this article, see "Sandia's Z machine exceeds two billion degrees Kelvin". Sandia. March 8, 2006. Archived from the original on 2006-07-02.
Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. Oechslin, R.; Janka, H.-T. (2006). "Torus formation in neutron star mergers and well-localized short gamma-ray bursts". Monthly Notices of the Royal Astronomical Society. 368 (4): 1489–1499. arXiv:astro-ph/0507099v2. Bibcode:2006MNRAS.368.1489O. doi:10.1111/j.1365-2966.2006.10238.x. S2CID15036056. For a summary, see "Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars". Max-Planck-Institut für Astrophysik. Retrieved 24 September 2024.
Nearly half of the 92 naturally occurring chemical elements that can freeze under a vacuum also have a closest-packed crystal lattice. This set includes beryllium, osmium, neon, and iridium (but excludes helium), and therefore have zero latent heat of phase transitions to contribute to internal energy (symbol: U). In the calculation of enthalpy (formula: {{{1}}}), internal energy may exclude different sources of thermal energy (particularly ZPE) depending on the nature of the analysis. Accordingly, all T = 0 closest-packed matter under a perfect vacuum has either minimal or zero enthalpy, depending on the nature of the analysis. Alberty, Robert A. (2001). "Use of Legendre Transforms In Chemical Thermodynamics"(PDF). Pure and Applied Chemistry. 73 (8): 1349. doi:10.1351/pac200173081349.
A difference of 100 kPa is used here instead of the 101.325 kPa value of one standard atmosphere. In 1982, the International Union of Pure and Applied Chemistry (IUPAC) recommended that for the purposes of specifying the physical properties of substances, the standard pressure (atmospheric pressure) should be defined as precisely 100 kPa (≈ 750.062 Torr). Besides being a round number, this had a very practical effect: relatively few people live and work at precisely sea level; 100 kPa equates to the mean pressure at an altitude of about 112 meters, which is closer to the 194–meter, worldwide median altitude of human habitation. For especially low-pressure or high-accuracy work, true atmospheric pressure must be measured. "Standard pressure". Compendium of Chemical Terminology (online 3rd ed.). International Union of Pure and Applied Chemistry. 2014. doi:10.1351/goldbook.S05921.
When measured at constant-volume since different amounts of work must be performed if measured at constant-pressure. Nitrogen's CvH (100 kPa, 20 °C) equals 20.8 J⋅mol–1⋅K–1 vs. the monatomic gases, which equal 12.4717 J mol–1 K–1. Freeman, W. H. "Part 3: Change". Physical Chemistry(PDF). Exercise 21.20b, p. 787. Archived from the original(PDF) on 2007-09-27. See also Nave, R. "Molar Specific Heats of Gases". HyperPhysics. Georgia State University.
Kastberg, A.; et al. (27 February 1995). "Adiabatic Cooling of Cesium to 700 nK in an Optical Lattice". Physical Review Letters. 74 (9): 1542–1545. Bibcode:1995PhRvL..74.1542K. doi:10.1103/PhysRevLett.74.1542. PMID10059055. A record cold temperature of 450 pK in a Bose–Einstein condensate of sodium atoms (achieved by A. E. Leanhardt et al.. of MIT){{cn|{{subst:DATE}} equates to an average vector-isolated atom velocity of 0.4 mm/s and an average atom speed of 0.7 mm/s.
A record cold temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium (23Na) atoms was achieved in 2003 by researchers at MIT. Leanhardt, A. E.; et al. (12 September 2003). "Cooling Bose–Einstein Condensates Below 500 Picokelvin". Science. 301 (5639): 1515. Bibcode:2003Sci...301.1513L. doi:10.1126/science.1088827. PMID12970559. The thermal velocity of the atoms averaged about 0.4 mm/s. This record's peak emittance black-body radiation wavelength of 6,400 kilometers is roughly the radius of Earth.
Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41 GK (309 ±35 keV) for 3 ns (ns 112 through 115). Haines, M. G.; et al. (2006). "Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2 × 109 Kelvin". Physical Review Letters. 96 (7): 075003. Bibcode:2006PhRvL..96g5003H. doi:10.1103/PhysRevLett.96.075003. PMID16606100. No. 075003. For a press summary of this article, see "Sandia's Z machine exceeds two billion degrees Kelvin". Sandia. March 8, 2006. Archived from the original on 2006-07-02.
Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. Oechslin, R.; Janka, H.-T. (2006). "Torus formation in neutron star mergers and well-localized short gamma-ray bursts". Monthly Notices of the Royal Astronomical Society. 368 (4): 1489–1499. arXiv:astro-ph/0507099v2. Bibcode:2006MNRAS.368.1489O. doi:10.1111/j.1365-2966.2006.10238.x. S2CID15036056. For a summary, see "Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars". Max-Planck-Institut für Astrophysik. Retrieved 24 September 2024.
Nearly half of the 92 naturally occurring chemical elements that can freeze under a vacuum also have a closest-packed crystal lattice. This set includes beryllium, osmium, neon, and iridium (but excludes helium), and therefore have zero latent heat of phase transitions to contribute to internal energy (symbol: U). In the calculation of enthalpy (formula: {{{1}}}), internal energy may exclude different sources of thermal energy (particularly ZPE) depending on the nature of the analysis. Accordingly, all T = 0 closest-packed matter under a perfect vacuum has either minimal or zero enthalpy, depending on the nature of the analysis. Alberty, Robert A. (2001). "Use of Legendre Transforms In Chemical Thermodynamics"(PDF). Pure and Applied Chemistry. 73 (8): 1349. doi:10.1351/pac200173081349.
goldbook.iupac.org
A difference of 100 kPa is used here instead of the 101.325 kPa value of one standard atmosphere. In 1982, the International Union of Pure and Applied Chemistry (IUPAC) recommended that for the purposes of specifying the physical properties of substances, the standard pressure (atmospheric pressure) should be defined as precisely 100 kPa (≈ 750.062 Torr). Besides being a round number, this had a very practical effect: relatively few people live and work at precisely sea level; 100 kPa equates to the mean pressure at an altitude of about 112 meters, which is closer to the 194–meter, worldwide median altitude of human habitation. For especially low-pressure or high-accuracy work, true atmospheric pressure must be measured. "Standard pressure". Compendium of Chemical Terminology (online 3rd ed.). International Union of Pure and Applied Chemistry. 2014. doi:10.1351/goldbook.S05921.
lsbu.ac.uk
Water's enthalpy of fusion is 6.0095 kJ⋅mol−1 K−1 (0 °C, 101.325 kPa). Chaplin, Martin. "Water Properties (including isotopologues)". Water Structure and Science. London South Bank University. Archived from the original on 2020-11-21. The only metals with enthalpies of fusion not in the range of 6–30 J mol−1 K−1 are (on the high side): Ta, W, and Re; and (on the low side) most of the group 1 (alkaline) metals plus Ga, In, Hg, Tl, Pb, and Np.
H2O specific heat capacity, Cp = 0.075327 kJ⋅mol−1⋅K−1 (25 °C); enthalpy of fusion = 6.0095 kJ/mol (0 °C, 101.325 kPa); enthalpy of vaporization (liquid) = 40.657 kJ/mol (100 °C). Chaplin, Martin. "Water Properties (including isotopologues)". Water Structure and Science. London South Bank University. Archived from the original on 2020-11-21.
mpg.de
mpa-garching.mpg.de
Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. Oechslin, R.; Janka, H.-T. (2006). "Torus formation in neutron star mergers and well-localized short gamma-ray bursts". Monthly Notices of the Royal Astronomical Society. 368 (4): 1489–1499. arXiv:astro-ph/0507099v2. Bibcode:2006MNRAS.368.1489O. doi:10.1111/j.1365-2966.2006.10238.x. S2CID15036056. For a summary, see "Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars". Max-Planck-Institut für Astrophysik. Retrieved 24 September 2024.
nasa.gov
nssdc.gsfc.nasa.gov
"Sun Fact Sheet". NASA Space Science Center Coordinated Archive. Retrieved 2023-08-27.
newscientist.com
Battersby, Stephen (2 March 2011). "Eight extremes: The hottest thing in the universe". New Scientist. While the details of this process are currently unknown, it must involve a fireball of relativistic particles heated to something in the region of a trillion kelvin.
nih.gov
pubmed.ncbi.nlm.nih.gov
Kastberg, A.; et al. (27 February 1995). "Adiabatic Cooling of Cesium to 700 nK in an Optical Lattice". Physical Review Letters. 74 (9): 1542–1545. Bibcode:1995PhRvL..74.1542K. doi:10.1103/PhysRevLett.74.1542. PMID10059055. A record cold temperature of 450 pK in a Bose–Einstein condensate of sodium atoms (achieved by A. E. Leanhardt et al.. of MIT){{cn|{{subst:DATE}} equates to an average vector-isolated atom velocity of 0.4 mm/s and an average atom speed of 0.7 mm/s.
A record cold temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium (23Na) atoms was achieved in 2003 by researchers at MIT. Leanhardt, A. E.; et al. (12 September 2003). "Cooling Bose–Einstein Condensates Below 500 Picokelvin". Science. 301 (5639): 1515. Bibcode:2003Sci...301.1513L. doi:10.1126/science.1088827. PMID12970559. The thermal velocity of the atoms averaged about 0.4 mm/s. This record's peak emittance black-body radiation wavelength of 6,400 kilometers is roughly the radius of Earth.
Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41 GK (309 ±35 keV) for 3 ns (ns 112 through 115). Haines, M. G.; et al. (2006). "Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2 × 109 Kelvin". Physical Review Letters. 96 (7): 075003. Bibcode:2006PhRvL..96g5003H. doi:10.1103/PhysRevLett.96.075003. PMID16606100. No. 075003. For a press summary of this article, see "Sandia's Z machine exceeds two billion degrees Kelvin". Sandia. March 8, 2006. Archived from the original on 2006-07-02.
The cited emission wavelengths are for true black bodies in equilibrium. In this table, only the sun so qualifies. CODATA recommended value of 2.897771955...×10−3 m⋅K used for Wien displacement law constant b.
The 350 MK value is the maximum peak fusion fuel temperature in a thermonuclear weapon of the Teller–Ulam configuration (commonly known as a "hydrogen bomb"). Peak temperatures in Gadget-style fission bomb cores (commonly known as an "atomic bomb") are in the range of 50 to 100 MK. "Nuclear Weapons Frequently Asked Questions". 3.2.5 Matter At High Temperatures.[full citation needed] All referenced data was compiled from publicly available sources.
sandia.gov
Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41 GK (309 ±35 keV) for 3 ns (ns 112 through 115). Haines, M. G.; et al. (2006). "Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2 × 109 Kelvin". Physical Review Letters. 96 (7): 075003. Bibcode:2006PhRvL..96g5003H. doi:10.1103/PhysRevLett.96.075003. PMID16606100. No. 075003. For a press summary of this article, see "Sandia's Z machine exceeds two billion degrees Kelvin". Sandia. March 8, 2006. Archived from the original on 2006-07-02.
semanticscholar.org
api.semanticscholar.org
Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. Oechslin, R.; Janka, H.-T. (2006). "Torus formation in neutron star mergers and well-localized short gamma-ray bursts". Monthly Notices of the Royal Astronomical Society. 368 (4): 1489–1499. arXiv:astro-ph/0507099v2. Bibcode:2006MNRAS.368.1489O. doi:10.1111/j.1365-2966.2006.10238.x. S2CID15036056. For a summary, see "Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars". Max-Planck-Institut für Astrophysik. Retrieved 24 September 2024.
spiess-verlage.de
Lambert, Johann Heinrich (1779). Pyrometrie. Berlin: Haude & Spener.
ualberta.ca
phys.ualberta.ca
Absolute zero's relationship to zero-point energy While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanicalzero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid HeliumArchived 2008-02-12 at the Wayback Machine by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero (T = 0) is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two T = 0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620 pm between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = 1×10−24 K). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1animation above. Before being given the kinetic kick, both T = 0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At T = 0, no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at T = 0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a T = 0 system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than T = 0, heat will flow inward, and if the surrounding environment is at 'T = 0, there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at T = 0 with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847.
Absolute zero's relationship to zero-point energy While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanicalzero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid HeliumArchived 2008-02-12 at the Wayback Machine by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero (T = 0) is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two T = 0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620 pm between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = 1×10−24 K). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1animation above. Before being given the kinetic kick, both T = 0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At T = 0, no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at T = 0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a T = 0 system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than T = 0, heat will flow inward, and if the surrounding environment is at 'T = 0, there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at T = 0 with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847.
Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41 GK (309 ±35 keV) for 3 ns (ns 112 through 115). Haines, M. G.; et al. (2006). "Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2 × 109 Kelvin". Physical Review Letters. 96 (7): 075003. Bibcode:2006PhRvL..96g5003H. doi:10.1103/PhysRevLett.96.075003. PMID16606100. No. 075003. For a press summary of this article, see "Sandia's Z machine exceeds two billion degrees Kelvin". Sandia. March 8, 2006. Archived from the original on 2006-07-02.
Water's enthalpy of fusion is 6.0095 kJ⋅mol−1 K−1 (0 °C, 101.325 kPa). Chaplin, Martin. "Water Properties (including isotopologues)". Water Structure and Science. London South Bank University. Archived from the original on 2020-11-21. The only metals with enthalpies of fusion not in the range of 6–30 J mol−1 K−1 are (on the high side): Ta, W, and Re; and (on the low side) most of the group 1 (alkaline) metals plus Ga, In, Hg, Tl, Pb, and Np.
H2O specific heat capacity, Cp = 0.075327 kJ⋅mol−1⋅K−1 (25 °C); enthalpy of fusion = 6.0095 kJ/mol (0 °C, 101.325 kPa); enthalpy of vaporization (liquid) = 40.657 kJ/mol (100 °C). Chaplin, Martin. "Water Properties (including isotopologues)". Water Structure and Science. London South Bank University. Archived from the original on 2020-11-21.
Pressure also must be in absolute terms. The air still in a tire at a gage pressure of 0 kPa expands too as it gets hotter. It is not uncommon for engineers to overlook that one must work in terms of absolute pressure when compensating for temperature. For instance, a dominant manufacturer of aircraft tires published a document on temperature-compensating tire pressure, which used gage pressure in the formula. However, the high gage pressures involved (180 psi; 12.4 bar; 1.24 MPa) means the error would be quite small. With low-pressure automobile tires, where gage pressures are typically around 2 bar (200 kPa), failing to adjust to absolute pressure results in a significant error. "Aircraft tire ratings"(PDF). Air Michelin. Archived from the original(PDF) on 2010-02-15.[better source needed]
For xenon, available values range from 2.3 to 3.1 kJ/mol. "Xenon – 54Xe: the essentials". WebElements. Retrieved 24 September 2024. Helium's heat of fusion of only 0.021 kJ/mol is so weak of a bonding force that zero-point energy prevents helium from freezing unless it is under a pressure of at least 25 atmospheres.
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When measured at constant-volume since different amounts of work must be performed if measured at constant-pressure. Nitrogen's CvH (100 kPa, 20 °C) equals 20.8 J⋅mol–1⋅K–1 vs. the monatomic gases, which equal 12.4717 J mol–1 K–1. Freeman, W. H. "Part 3: Change". Physical Chemistry(PDF). Exercise 21.20b, p. 787. Archived from the original(PDF) on 2007-09-27. See also Nave, R. "Molar Specific Heats of Gases". HyperPhysics. Georgia State University.
Thomson, William (October 1848). "On an Absolute Thermometric Scale". Philosophical Magazine. Also published in Thomson, William (1882). Mathematical and Physical Papers. Vol. 1. Cambridge University Press. pp. 100–106.
