
	Where results make sense

Topic: Gibbs phase rule

Related Topics

Phase (matter)

Phase diagram

Triple point

Water vapor

Thermodynamics

Willard Gibbs

Gibbs phenomenon

Water

Definitions of socialism

Capitalism

Quantum mechanics

Hilbert space

Timeline of thermodynamics, statistical mechanics, and random processes

Copenhagen interpretation

Socialism

In the News (Thu 12 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Gibbs' phase rule - Wikipedia, the free encyclopedia
		In chemistry, Gibbs' phase rule describes the possible number of degrees of freedom (F) in a closed system at equilibrium, in terms of the number of separate phases (P) and the number of chemical constituents (C) in the system.
		Gibbs' rule related the number of phases to the number of degrees of freedom in the thermodynamic system, modeling it on the Euler characteristic (pronounced "oiler").
		For the trivial chemical case of a box of gas (single-phase, single component) Gibbs' formula is in some ways a restatement of the universal gas law that had first been developed in the 1830s, which relates pressure, volume, temperature and the number of particles involved.
	en.wikipedia.org /wiki/Gibbs'_phase_rule (545 words)

	Phase (matter) - Wikipedia, the free encyclopedia
		The appearance of magnetic domains is a phase transition, and the new phase is known as a ferromagnet.
		In contrast, in the plasma phase the atoms are dissociated, i.e.
		Gibbs' phase rule relates the number of possible phases, variables such as temperature and pressure, and whether or not an equilibrium will be reached.
	en.wikipedia.org /wiki/Phase_(matter) (2912 words)

	Gibbs' phase rule (Site not responding. Last check: 2007-10-21)
		In chemistry, Gibbs' phase rule describes the possible number of degrees of freedom in a closed system at equilibrium, in terms of the number of separate phases and the number of chemical constituents in the system.
		Gibbs' formula is in some ways a restatement of the universal gas law that had first been developed in the 1830s, which relates pressure, volume, temperature and the number of particles involved.
		Gibbs' phase rule can be syntactically transformed into the polyhedral formula of Leonhard Euler (1707-1784), so that chemical students knowledgeable in Gibbs' phase rule can understand Euler's polyhedral formula, and vice versa.
	www.sciencedaily.com /encyclopedia/gibbs__phase_rule (442 words)

	Gibbs phase rule - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		Gibbs' phase rule (formulated by the American physicist Josiah Willard Gibbs) specifies the number of degrees of freedom for a given system at equilibrium.
		This means that at a given temperature, water in the gas phase will evaporate or condense until the corresponding equilibrium water vapor pressure is reached.
		Thermodynamically, the relation comes about because for phases to be in equilibrium, the chemical potential of each component must be the same in every phase.
	en.wikipedia.org /wiki/Gibbs_phase_rule (401 words)

	Encyclopedia: Phase (matter)
		Amorphous solids, or glasses, are a phase intermediate between solids and liquids.
		Main article: Phase diagram A phase diagram or phase space is a useful construct used in mathematics and physics to demonstrate and visualise the changes in a given system.
		Josiah Willard Gibbs (February 11, 1839 â€“ April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis.
	www.nationmaster.com /encyclopedia/Phase-(matter) (5466 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The phase rule therefore allows us to determine the minimum number of variables that must be fixed in order to perfectly define a particular condition of the system from a knowledge of the number of system components and phases.
		The condensed phase rule is quite helpful in understanding isobaric T-X or isothermal P-X diagrams, and in experimental geochemistry, where either P or T are held constant to investigate the dependence of the system on the other intensive variable.
		The mineralogical phase rule is therefore a practical or empirical application of the Gibbs phase rule, implying that most metamorphic rocks contain "high variance" assemblages, that an f of at least 2 is common.
	www.utm.edu /departments/artsci/ggp/faculty/ElShazly/GeochemNotes/PhaseRule.htm (1132 words)

	Phase
		Its use for the phases of the moon, which repeat in a regular sequence, gave rise to its use for the time sequence of a signal, particularly a sinusoidal signal, where the phase is represented as an angle that steadily increases with time.
		The result is a two-dimensional phase diagram, as for a single substance, where the coordinates are the temperature T and the concentration c.
		A schematic phase diagram for a system in which the constituents are completely miscible in both the liquid and the solid phases is shown at the left.
	www.du.edu /~jcalvert/phys/phase.htm (6901 words)

	Gibbs phase rule Article, Gibbsphaserule Information (Site not responding. Last check: 2007-10-21)
		In thermodynamics the number of degrees of freedom is the smallest number of intensive variables (i.e.pressure, temperature, and concentrations of components in each phase) that must be specified to completely describe the state ofthe system.
		Gibbs' phase rule implies that the number of degrees of freedom increases as the number of components in the system increasesand decreases as the number of phases increases.
		For example the phase rule indicates that a single component system with onlyone phase, such as liquid water, has 2 degrees of freedom.
	www.anoca.org /number/system/gibbs_phase_rule.html (325 words)

	Science in Christian Perspective
		The concept is anticipated by the Gibbs phase rule, according to which the largest number of phases P which can coexist in a thermodynamical system plus the number of degrees of freedom F equals the sum of the components C of the system, plus 2.
		Equilibrium between two phases occurs along the mutual boundary of the phase regions, and equilibrium among all three phases occurs at the intersection of the regions.
		Further, the phases of the triple point are locked together in a state of dynamic equilibrium which prohibits individual manifestation of the states matter except by destruction of the triple point.
	www.asa3.org /ASA/PSCF/1987/PSCF3-87Bozack.html (2009 words)

	FuelCellStore.com Thermodynamic demonstration device (Site not responding. Last check: 2007-10-21)
		The standard Gibbs free energy change is the maximum reversible work that can be obtained from a mole of ideal gas at standard temperature against the resistance of standard atmospheric pressure.
		Figure 3 is ideal in that the 2 solid phase region or "plateau" is perfectly flat and represents both absorption and desorption of hydrogen.
		Hydrogen, in the gaseous phase, dissolved in metal, or part of a metal hydride crystal, is a single component.
	www.fuelcellstore.com /products/hci/toy.html (2425 words)

	Applied Synergetics Main Page (Site not responding. Last check: 2007-10-21)
		Gibbs' phase rule defines the degrees of energetic freedom available and how much energy needs to be added (or subtracted) locally to bring about other states [27].
		Gibbs' phase rule determines the number of degrees of energetic freedom that are available to the system based on the initial energy conditions and the given framework topology as described by Euler's formula.
		Gibbs' phase rule will also be used to determine how and under what circumstances the system can change state.
	www.applied-synergetics.com /ashp/html/paper2.html (5761 words)

	ME 481/581 Homework Three (Site not responding. Last check: 2007-10-21)
		b) The Gibbs Phase Rule is rewritten as F = 1, because C = 2 (two components, Ag and Cu), and P = 2 (two phaes, liquid and solid-BETA are present at the liquidus line, though the amount of BETA is infinitesimally small).
		c) The Gibbs Phase Rule is rewritten as F = 1, because C = 2 (two components, Ag and Cu), and P = 2 (two phaes, liquid and solid-BETA are present, and the lever rule could be used to determine the relative amounts of the two phases).
		For a temperature of 505 K we are at the melting temperature of pure Sn, and the two phases have an equal free energy at the pure Sn axis.
	oregonstate.edu /instruction/me481/Homework/F99/ME481Hmwk3.html (1280 words)

	ENGR 321: Homework Set 3
		1) Use the Gibbs Phase Rule: P + F = C + 1 (since we only consider T to be a variable, with pressure fixed at one atmosphere).
		At 250 C, the alloy is on a two phase region, with an equilibrium between BETA phase solid, and LIQUID.
		At 500C the alloy is in the two phase ALPHA and Fe3C (cementite, or iron-carbide) region.
	oregonstate.edu /instruct/engr321/Homework/HomeworkW97/HW4.html (848 words)

	Gibbs phase rule -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Gibbs phase rule -- Facts, Info, and Encyclopedia article
		In (The branch of physics concerned with the conversion of different forms of energy) thermodynamics the number of degrees of freedom is the smallest number of intensive variables (i.e.
		Such a system is only possible at the temperature and pressure corresponding to the (Click link for more info and facts about triple point) triple point.
	www.absoluteastronomy.com /encyclopedia/g/gi/gibbs_phase_rule.htm (263 words)

	Gibbs' Phase Rule (Site not responding. Last check: 2007-10-21)
		The Phase Rule describes the possible number of degrees of freedom in a (closed) system at equilibrium, in terms of the number of separate phases and the number of chemical constituents in the system.
		A system with one component and one phase (a balloon full of carbon dioxide, perhaps) has two degrees of freedom: temperature and pressure, say, can be varied independently.
		If you have two phases -- liquid and vapour for instance -- you lose a degree of freedom, and there is only one possible pressure for each temperature.
	jwgibbs.cchem.berkeley.edu /phase_rule.html (361 words)

	Binary Phase Equilibria Tutorial
		The phase rule is best understood by thinking of the conditions of equilibrium as a set of simultaneous equations that nature must solve.
		The phase rule tells us that if A, B, and C all coexist in a binary system then the variance is one, so this should only be possible along a line or curve in P-T space.
		(X) curve of a third phase (phase D in Figure 8) moves around, the point of tangency where the fatter of the two coincident phases and the third phase are in equilibrium may shift so that it becomes equal to the coincident point.
	www.gps.caltech.edu /~asimow/tutorial2.html (3006 words)

	Materials Engineering.Courses
		Phase diagrams, the lever rule, Gibbs phase rule.
		Phase diagrams, Gibbs phase rule, range of stability, reactions in systems of solid phases, reaction kinetics.
		Classification of transformations; homogeneous and heterogeneous nucleation; spinodal decomposition; grain growth; mechanisms of phase transformation; diffusional phase transformation, precipitation in solid solution; transformation with constant composition; order-disorder transformations; thermodynamics and kinetics of shear transformation.
	www.bgu.ac.il /eng/Courses/MatE.Courses.html (2049 words)

	Applications (Engineering Thermodynamics) - Wikibooks
		Gibbs phase rule states that for a system with C components in P phases, the degree of freedom F = C + 2 − P.
		Also, the heat transfer in the boiler takes place mainly as a result of a phase change, compared to the isothermal heating of the ideal gas in the Carnot cycle, so that the efficiency is quite good (even though it is still less than the Carnot efficiency).
		The amount of heat transferred as the liquid is heated to its boiling point is very small compared to the heat transfer during phase change.
	en.wikibooks.org /wiki/Applications_(Engineering_Thermodynamics) (2831 words)

	Model Tests (Site not responding. Last check: 2007-10-21)
		The final assemblage of solids, liquid phase components, and gases should obey Gibbs' phase rule.
		If a liquid phase exists, then the relative humidity and partial pressures of any trace gases partitioned between the condensed and vapour phases should agree with equilibrium values calculated from the liquid phase activities.
		If there is a liquid phase then the saturation ratios of any solids present should be equal to unity.
	mae.ucdavis.edu /~wexler/aim/tests.htm (348 words)

	NORTHEASTE'RN UNIVERSTTY (Site not responding. Last check: 2007-10-21)
		Apply Gibbs phase rule to one and two component systems to obtain the number of degrees of freedom for equilibrium between various numbers of phases.
		Given a binary phase diagram, calculate the amount and composition of any phase or phases in equilibrium at any temperature in any alloy.
		Calculate the composition and amounts of the primary phase and eutectic mixture in an alloy having undergone the eutectic transformation.
	www.coe.neu.edu /~rjmurphy/courses/mim1240/obj_ph1.html (119 words)

	Introduction to Chemical Engineering: Single Phase Systems Summary (Site not responding. Last check: 2007-10-21)
		We all know, however, that changing the process variable (T and P) can cause a material to change phases (boil/condense or freeze/melt) and that under certain conditions we can have multiple phases coexisting (for example: solid water (ice) in a glass of liquid water; water vapor bubbles in liquid water (boiling)).
		A phase diagram is a plot of one system variable versus another which shows the conditions at which the substance is a solid, liquid, gas, or s.c.
		We also noted that for the phase diagrams above (and equations of state in the last chapter) we only needed to specify (at most) 2 varibles before our system was completely specified.
	granular.che.pitt.edu /~mccarthy/che0035/MB/multi/phasediags.html (609 words)

	Gibbs Phase Rule (Site not responding. Last check: 2007-10-21)
		What is the largest number of phases to coexist?
		In binary solutions four phases can coexist in a special point!
		The maximum number of phases in equilibrium is two plus the number of components.
	www.plmsc.psu.edu /~www/matsc597c-1997/phases/Lecture1/node3.html (67 words)

	Chpt7
		A problem in which the Gibbs phase rule must be used to determine the number of degrees of freedom.
		Another problem based on the Gibbs phase rule.
		A third problem based on the Gibbs phase rule.
	www.chem.uky.edu /courses/che442g/chpt07.html (220 words)

	Basic principles
		Each also has implicit assumptions: rules which are as fundamental as the explicit assumptions, but which are usually omitted from the lists of postulates.
		Implicit assumptions of thermodynamics are made visible by the usual proof of Gibbs' phase rule, whose inductive cycle fails when one tries to compare the one-component, one-phase system with something simpler.
		The derivation of Gibbs' Phase Rule, as presented below, invokes an implicit assumption of thermodynamics, namely that a normal single-component, single-phase system has two degrees of freedom.
	users.wpi.edu /~phillies/stat2/node2.html (921 words)

	Water vapor
		Radio waves used for broadcasting and other communication tend to suffer the same effect.
		Water vapor reflects radar to a less extent than do water's other two phases.
		In the form of drops and ice crystals, water acts as a prism, which it does not do as a gas.
	www.brainyencyclopedia.com /encyclopedia/w/wa/water_vapor.html (875 words)

	Conditions for the Appearance of a New Phase
		Last time, it was observed that a a soluble species (i.e, salt) cannot continue to be added to a phase (i.e.
		This can be qualitatively understood by considering the behavior of the molar Gibbs free energy of forming a solution as a function of the amount of solute
		To quantify the conditions for the appearance of new phases, consider the thermodynamics of binary (i.e.
	pruffle.mit.edu /3.00/Lecture_28_web/node1.html (198 words)

	[No title]
		At this condition, or state, the metal exists only in two phases in equilibrium, that is solid and liquid phases simultaneously.
		Phase diagrams are used for binary (2 Component; C= 2) and ternary diagrams (3 component systems; C=3) Phase diagrams are maps of the equilibrium phases associated with the various combinations of temperature and composition.
		Concern is to change phases and associated microstructure that follow changes in temperature and composition.
	www.csuchico.edu /~jpgreene/itec104/m104_ch09-02_files/m104_ch09-02.ppt (1052 words)

Try your search on: Qwika (all wikis)