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Duhem–Margules Equation
The Duhem–Margules equation, named for Pierre Duhem and Max Margules, is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas: : \left ( \frac \right )_ = \left ( \frac \right )_ where ''P''A and ''P''B are the partial vapour pressures of the two constituents and ''xA'' and ''xB'' are the mole fractions of the liquid. The equation gives the relation between changes in mole fraction and partial pressure of the components. Derivation Let us consider a binary liquid mixture of two component in equilibrium with their vapor at constant temperature and pressure. Then from the Gibbs–Duhem equation In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system: :\sum_^I N_i \mathrm\mu_i = - S \mathrmT + V \mathrmp where N_i is the number of moles of com ..., we have Where ''nA'' and ''nB'' are num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Duhem
Pierre Maurice Marie Duhem (; 9 June 1861 – 14 September 1916) was a French theoretical physicist who worked on thermodynamics, hydrodynamics, and the theory of elasticity. Duhem was also a historian of science, noted for his work on the European Middle Ages, which is regarded as having created the field of the history of medieval science. As a philosopher of science, he is remembered principally for his views on the indeterminacy of experimental criteria (see Duhem–Quine thesis). Theoretical physics Among scientists, Duhem is best known today for his work on chemical thermodynamics, and in particular for the Gibbs–Duhem and Duhem–Margules equations. His approach was strongly influenced by the early works of Josiah Willard Gibbs, which Duhem effectively explicated and promoted among French scientists. In continuum mechanics, he is also remembered for his contribution to what is now called the Clausius–Duhem inequality. Duhem was convinced that all physical phenome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Margules
Max Margules (1856-1920) was a mathematician, physicist, and chemist. In 1877 he joined the Central Institute of Meteorology and Geodynamics (ZAMG) in Vienna as a volunteer. After two years he left Vienna to study in Berlin for a year. He returned to Vienna and received his PhD in Electrodynamics. During his doctoral studies he was a : an unpaid position, but one which allowed him to lecture students. Students' fees gave him some income. Later, administration offered this teaching job to someone else after he refused to convert from Judaism to acquire the position, which ended his academic career. In 1882 he returned to ZAMG. During ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Component (thermodynamics)
In thermodynamics, a component is one of a collection of chemically independent constituents of a system. The number of components represents the minimum number of independent chemical species necessary to define the composition of all phases of the system. Calculating the number of components in a system is necessary when applying Gibbs' phase rule in determination of the number of degrees of freedom of a system. The number of components is equal to the number of distinct chemical species (constituents), minus the number of chemical reactions between them, minus the number of any constraints (like charge neutrality or balance of molar quantities). Calculation Suppose that a chemical system has elements and chemical species (elements or compounds). The latter are combinations of the former, and each species can be represented as a sum of elements: : A_i = \sum_j a_E_j, where are the integers denoting number of atoms of element in molecule . Each species is determined by a ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is by far the most common liquid on Earth. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed condensed matte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vapour
In physics, a vapor (American English) or vapour (British English and Canadian English; see spelling differences) is a substance in the gas phase at a temperature lower than its critical temperature,R. H. Petrucci, W. S. Harwood, and F. G. Herring, ''General Chemistry'', Prentice-Hall, 8th ed. 2002, p. 483–86. which means that the vapor can be condensed to a liquid by increasing the pressure on it without reducing the temperature. A vapor is different from an aerosol. An aerosol is a suspension of tiny particles of liquid, solid, or both within a gas. For example, water has a critical temperature of , which is the highest temperature at which liquid water can exist. In the atmosphere at ordinary temperatures gaseous water (known as water vapor) will condense into a liquid if its partial pressure is increased sufficiently. A vapor may co-exist with a liquid (or a solid). When this is true, the two phases will be in equilibrium, and the gas-partial pressure will be equal to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions. Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vapour Pressure
Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or a solid). A substance with a high vapor pressure at normal temperatures is often referred to as '' volatile''. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the kinetic energy of its molecules also increases. As the kinetic energy of the molecules increases, the number of molecules transitioning into a vapor also increases, thereby increasing the vapor pressure. The vapor pressure of any substance increases non-linearly with temperature according ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mole Fraction
In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This expression is given below: :x_i = \frac The sum of all the mole fractions is equal to 1: :\sum_^ n_i = n_\mathrm ; \ \sum_^ x_i = 1. The same concept expressed with a denominator of 100 is the mole percent, molar percentage or molar proportion (mol%). The mole fraction is also called the amount fraction. It is identical to the number fraction, which is defined as the number of molecules of a constituent ''Ni'' divided by the total number of all molecules ''N''tot. The mole fraction is sometimes denoted by the lowercase Greek letter (chi) instead of a Roman ''x''. For mixtures of gases, IUPAC recommends the letter ''y''. The National Institute of Standards and Technology of the United States prefers the term amount-of-substance fraction o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs–Duhem Equation
In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system: :\sum_^I N_i \mathrm\mu_i = - S \mathrmT + V \mathrmp where N_i is the number of moles of component i, \mathrm\mu_i the infinitesimal increase in chemical potential for this component, S the entropy, T the absolute temperature, V volume and p the pressure. I is the number of different components in the system. This equation shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate. When pressure and temperature are variable, only I-1 of I components have independent values for chemical potential and Gibbs' phase rule follows. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena. The equation is named after Josiah Willard Gibbs and Pierre Duhem. Derivation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Atkins
Peter William Atkins (born 10 August 1940) is an English chemist and a Fellow of Lincoln College at the University of Oxford. He retired in 2007. He is a prolific writer of popular chemistry textbooks, including ''Physical Chemistry'', ''Inorganic Chemistry'', and ''Molecular Quantum Mechanics''. Atkins is also the author of a number of popular science books, including ''Atkins' Molecules'', ''Galileo's Finger: The Ten Great Ideas of Science'' and ''On Being''. Career Atkins left school (Dr Challoner's Grammar School, Amersham) at fifteen and took a job at Monsanto as a laboratory assistant. He studied for A-levels by himself and gained a place, following a last-minute interview, at the University of Leicester. Atkins studied chemistry there, obtaining a BSc degree in chemistry, and a PhD degree in 1964 for research into electron spin resonance spectroscopy, and other aspects of theoretical chemistry. Atkins then took a postdoctoral position at UCLA as a Harkness Fellow of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
