1.
Phase space
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For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré. For every possible state of the system, or allowed combination of values of the systems parameters, the systems evolving state over time traces a path through the high-dimensional space. As a whole, the diagram represents all that the system can be. A phase space may contain a number of dimensions. For instance, a gas containing many molecules may require a separate dimension for each x, y and z positions. In classical mechanics, any choice of generalized coordinates qi for the position defines conjugate generalized momenta pi which together define co-ordinates on phase space, the motion of an ensemble of systems in this space is studied by classical statistical mechanics. The local density of points in such systems obeys Liouvilles Theorem, within the context of a model system in classical mechanics, the phase space coordinates of the system at any given time are composed of all of the systems dynamic variables. Because of this, it is possible to calculate the state of the system at any time in the future or the past. For simple systems, there may be as few as one or two degrees of freedom, the simplest non-trivial examples are the exponential growth model/decay and the logistic growth model. In this case, a sketch of the portrait may give qualitative information about the dynamics of the system. Here, the horizontal axis gives the position and vertical axis the velocity, as the system evolves, its state follows one of the lines on the phase diagram. Classic examples of phase diagrams from chaos theory are, the Lorenz attractor population growth parameter plane of quadratic polynomials with Mandelbrot set. A plot of position and momentum variables as a function of time is called a phase plot or a phase diagram. In quantum mechanics, the p and q of phase space normally become hermitian operators in a Hilbert space. But they may retain their classical interpretation, provided functions of them compose in novel algebraic ways. With J E Moyal, these completed the foundations of the phase space formulation of quantum mechanics, in thermodynamics and statistical mechanics contexts, the term phase space has two meanings, It is used in the same sense as in classical mechanics. In this sense, as long as the particles are distinguishable, N is typically on the order of Avogadros number, thus describing the system at a microscopic level is often impractical
2.
Physical chemistry
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Some of the relationships that physical chemistry strives to resolve include the effects of, Intermolecular forces that act upon the physical properties of materials. Reaction kinetics on the rate of a reaction, the identity of ions and the electrical conductivity of materials. Surface chemistry and electrochemistry of cell membranes, interaction of one body with another in terms of quantities of heat and work called thermodynamics. Number of phases, number of components and degree of freedom can be correlated with one another with help of phase rule, the key concepts of physical chemistry are the ways in which pure physics is applied to chemical problems. Predicting the properties of compounds from a description of atoms. To describe the atoms and bonds precisely, it is necessary to know both where the nuclei of the atoms are, and how electrons are distributed around them, spectroscopy is the related sub-discipline of physical chemistry which is specifically concerned with the interaction of electromagnetic radiation with matter. Another set of important questions in chemistry concerns what kind of reactions can happen spontaneously and it can frequently be used to assess whether a reactor or engine design is feasible, or to check the validity of experimental data. To a limited extent, quasi-equilibrium and non-equilibrium thermodynamics can describe irreversible changes, however, classical thermodynamics is mostly concerned with systems in equilibrium and reversible changes and not what actually does happen, or how fast, away from equilibrium. Which reactions do occur and how fast is the subject of chemical kinetics, in general, the higher the barrier, the slower the reaction. A second is that most chemical reactions occur as a sequence of elementary reactions, the precise reasons for this are described in statistical mechanics, a specialty within physical chemistry which is also shared with physics. Statistical mechanics also provides ways to predict the properties we see in everyday life from molecular properties without relying on empirical correlations based on chemical similarities. The term physical chemistry was coined by Mikhail Lomonosov in 1752, modern physical chemistry originated in the 1860s to 1880s with work on chemical thermodynamics, electrolytes in solutions, chemical kinetics and other subjects. One milestone was the publication in 1876 by Josiah Willard Gibbs of his paper and this paper introduced several of the cornerstones of physical chemistry, such as Gibbs energy, chemical potentials, and Gibbs phase rule. Other milestones include the subsequent naming and accreditation of enthalpy to Heike Kamerlingh Onnes, together with Svante August Arrhenius, these were the leading figures in physical chemistry in the late 19th century and early 20th century. All three were awarded with the Nobel Prize in Chemistry between 1901–1909, developments in the following decades include the application of statistical mechanics to chemical systems and work on colloids and surface chemistry, where Irving Langmuir made many contributions. Another important step was the development of quantum mechanics into quantum chemistry from the 1930s, cathedrals of Science The Cambridge History of Science, The modern physical and mathematical sciences
3.
Engineering
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The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, lever, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbours and he was also a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics
4.
Mineralogy
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Mineralogy is a subject of geology specializing in the scientific study of chemistry, crystal structure, and physical properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, the German Renaissance specialist Georgius Agricola wrote works such as De re metallica and De Natura Fossilium which began the scientific approach to the subject. Systematic scientific studies of minerals and rocks developed in post-Renaissance Europe, the modern study of mineralogy was founded on the principles of crystallography and to the microscopic study of rock sections with the invention of the microscope in the 17th century. Nicholas Steno first observed the law of constancy of interfacial angles in quartz crystals in 1669 and this was later generalized and established experimentally by Jean-Baptiste L. Romé de lIslee in 1783. In 1814, Jöns Jacob Berzelius introduced a classification of minerals based on their chemistry rather than their crystal structure, james D. Dana published his first edition of A System of Mineralogy in 1837, and in a later edition introduced a chemical classification that is still the standard. It, however, retains a focus on the structures commonly encountered in rock-forming minerals. An initial step in identifying a mineral is to examine its physical properties and these can be classified into density, measures of mechanical cohesion, macroscopic visual properties, magnetic and electric properties, radioactivity and solubility in hydrogen chloride. If the mineral is crystallized, it will also have a distinctive crystal habit that reflects the crystal structure or internal arrangement of atoms. It is also affected by crystal defects and twinning. Many crystals are polymorphic, having more than one crystal structure depending on factors such as pressure and temperature. ”Examples of polymorphs are calcite and aragonite - two minerals with identical chemical composition, distinguished by their crystallography, calcite is rhombohedral and aragonite is orthorhombic. The crystal structure is the arrangement of atoms in a crystal and it is represented by a lattice of points which repeats a basic pattern, called a unit cell, in three dimensions. The lattice can be characterized by its symmetries and by the dimensions of the unit cell and these dimensions are represented by three Miller indices. The lattice remains unchanged by certain symmetry operations about any point in the lattice, reflection, rotation, inversion, and rotary inversion. Together, they make up an object called a crystallographic point group or crystal class. There are 32 possible crystal classes, in addition, there are operations that displace all the points, translation, screw axis, and glide plane. In combination with the point symmetries, they form 230 possible space groups, most geology departments have X-ray powder diffraction equipment to analyze the crystal structures of minerals. X-rays have wavelengths that are the order of magnitude as the distances between atoms. In a sample that is ground to a powder, the X-rays sample a random distribution of all crystal orientations, powder diffraction can distinguish between minerals that may appear the same in a hand sample, for example quartz and its polymorphs tridymite and cristobalite
5.
Materials science
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The interdisciplinary field of materials science, also commonly termed materials science and engineering, involves the discovery and design of new materials, with an emphasis on solids. Materials science still incorporates elements of physics, chemistry, and engineering, as such, the field was long considered by academic institutions as a sub-field of these related fields. Materials science is a syncretic discipline hybridizing metallurgy, ceramics, solid-state physics and it is the first example of a new academic discipline emerging by fusion rather than fission. Many of the most pressing scientific problems humans currently face are due to the limits of the materials that are available, thus, breakthroughs in materials science are likely to affect the future of technology significantly. Materials scientists emphasize understanding how the history of a material influences its structure, the understanding of processing-structure-properties relationships is called the § materials paradigm. This paradigm is used to advance understanding in a variety of areas, including nanotechnology, biomaterials. Such investigations are key to understanding, for example, the causes of various accidents and incidents. The material of choice of a given era is often a defining point, phrases such as Stone Age, Bronze Age, Iron Age, and Steel Age are great examples. Originally deriving from the manufacture of ceramics and its putative derivative metallurgy, materials science is one of the oldest forms of engineering, modern materials science evolved directly from metallurgy, which itself evolved from mining and ceramics and the use of fire. Materials science has driven, and been driven by, the development of technologies such as rubbers, plastics, semiconductors. Before the 1960s, many materials science departments were named metallurgy departments, reflecting the 19th, a material is defined as a substance that is intended to be used for certain applications. There are a myriad of materials around us—they can be found in anything from buildings to spacecraft, Materials can generally be divided into two classes, crystalline and non-crystalline. The traditional examples of materials are metals, semiconductors, ceramics, New and advanced materials that are being developed include nanomaterials and biomaterials, etc. The basis of science involves studying the structure of materials. Once a materials scientist knows about this structure-property correlation, they can go on to study the relative performance of a material in a given application. The major determinants of the structure of a material and thus of its properties are its constituent chemical elements and these characteristics, taken together and related through the laws of thermodynamics and kinetics, govern a materials microstructure, and thus its properties. As mentioned above, structure is one of the most important components of the field of materials science, Materials science examines the structure of materials from the atomic scale, all the way up to the macro scale. Characterization is the way materials scientists examine the structure of a material, structure is studied at various levels, as detailed below
6.
Chart
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A chart, also called a graph, is a graphical representation of data, in which the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart. A chart can represent tabular numeric data, functions or some kinds of qualitative structure, the term chart as a graphical representation of data has multiple meanings, A data chart is a type of diagram or graph, that organizes and represents a set of numerical or qualitative data. Maps that are adorned with extra information for a purpose are often known as charts, such as a nautical chart or aeronautical chart. Other domain specific constructs are sometimes called charts, such as the chart in music notation or a record chart for album popularity. Charts are often used to understanding of large quantities of data. Charts can usually be more quickly than the raw data. They are used in a variety of fields, and can be created by hand or by computer using a charting application. Certain types of charts are useful for presenting a given data set than others. For example, data that presents percentages in different groups are displayed in a pie chart. On the other hand, data that represents numbers that change over a period of time might be best shown as a line chart. A chart can take a variety of forms, however there are common features that provide the chart with its ability to extract meaning from data. Typically the data in a chart is represented graphically, since humans are able to infer meaning from pictures quicker than from text. Text is generally used only to annotate the data, one of the most important uses of text in a graph is the title. A graphs title usually appears above the graphic and provides a succinct description of what the data in the graph refers to. Dimensions in the data are displayed on axes. If a horizontal and an axis are used, they are usually referred to as the x-axis and y-axis respectively. Each axis will have a scale, denoted by periodic graduations, each axis will typically also have a label displayed outside or beside it, briefly describing the dimension represented. If the scale is numerical, the label will often be suffixed with the unit of scale in parentheses
7.
Phase (matter)
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In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization, a simple description is that a phase is a region of material that is chemically uniform, physically distinct, and mechanically separable. In a system consisting of ice and water in a jar, the ice cubes are one phase, the water is a second phase. The glass of the jar is another separate phase, the term phase is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the phase is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Distinct phases may be described as different states of such as gas, liquid, solid. Useful mesophases between solid and liquid form other states of matter, distinct phases may also exist within a given state of matter. As shown in the diagram for iron alloys, several phases exist for both the solid and liquid states, phases may also be differentiated based on solubility as in polar or non-polar. A mixture of water and oil will separate into two phases. Water has a low solubility in oil, and oil has a low solubility in water. Solubility is the amount of a solute that can dissolve in a solvent before the solute ceases to dissolve. A mixture can separate into more than two phases and the concept of phase separation extends to solids, i. e. solids can form solid solutions or crystallize into distinct crystal phases. Metal pairs that are mutually soluble can form alloys, whereas metal pairs that are mutually insoluble cannot, as many as eight immiscible liquid phases have been observed. Mutually immiscible liquid phases are formed from water, hydrophobic solvents, perfluorocarbons, silicones, several different metals. Not all organic solvents are completely miscible, e. g. a mixture of ethylene glycol, phases do not need to macroscopically separate spontaneously. Emulsions and colloids are examples of immiscible phase pair combinations that do not physically separate, left to equilibration, many compositions will form a uniform single phase, but depending on the temperature and pressure even a single substance may separate into two or more distinct phases. Within each phase, the properties are uniform but between the two phases properties differ, water in a closed jar with an air space over it forms a two phase system. Most of the water is in the phase, where it is held by the mutual attraction of water molecules
8.
Triple point
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In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium. For example, the point of mercury occurs at a temperature of −38.83440 °C. In addition to the point for solid, liquid, and gas phases. Helium-4 is a case that presents a triple point involving two different fluid phases. The triple point of water is used to define the kelvin, the value of the triple point of water is fixed by definition, rather than measured. The triple points of substances are used to define points in the ITS-90 international temperature scale. The term triple point was coined in 1873 by James Thomson, at that point, it is possible to change all of the substance to ice, water, or vapor by making arbitrarily small changes in pressure and temperature. Strictly speaking, the surfaces separating the different phases should also be perfectly flat, the gas–liquid–solid triple point of water corresponds to the minimum pressure at which liquid water can exist. At pressures below the point, solid ice when heated at constant pressure is converted directly into water vapor in a process known as sublimation. Above the triple point, solid ice when heated at constant pressure first melts to form liquid water, for most substances the gas–liquid–solid triple point is also the minimum temperature at which the liquid can exist. For water, however, this is not true because the point of ordinary ice decreases as a function of pressure. At temperatures just below the point, compression at constant temperature transforms water vapor first to solid. The triple point pressure of water was used during the Mariner 9 mission to Mars as a point to define sea level. More recent missions use laser altimetry and gravity measurements instead of pressure to define elevation on Mars, at high pressures, water has a complex phase diagram with 15 known phases of ice and several triple points including ten whose coordinates are shown in the diagram. For example, the point at 251 K and 210 MPa corresponds to the conditions for the coexistence of ice Ih, ice III and liquid water. There are also triple points for the coexistence of three phases, for example ice II, ice V and ice VI at 218 K and 620 MPa. For those high-pressure forms of ice which can exist in equilibrium with liquid, at temperatures above 273 K, increasing the pressure on water vapor results first in liquid water and then a high-pressure form of ice. In the range 251–273 K, ice I is formed first, followed by water and then ice III or ice V
9.
Kelvin
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The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm. When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 7002273160280000000♠0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 7003130000000000000♠1300 K. In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 6977138065049999999♠1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 7003400000000000000♠4000 K appear reddish, whereas those above about 7003750000000000000♠7500 K appear bluish
10.
Pascal (unit)
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The pascal is the SI derived unit of pressure used to quantify internal pressure, stress, Youngs modulus and ultimate tensile strength. It is defined as one newton per square meter and it is named after the French polymath Blaise Pascal. Common multiple units of the pascal are the hectopascal which is equal to one millibar, the unit of measurement called standard atmosphere is defined as 101,325 Pa and approximates to the average pressure at sea-level at the latitude 45° N. Meteorological reports typically state atmospheric pressure in hectopascals, the unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre by the 14th General Conference on Weights, one pascal is the pressure exerted by a force of magnitude one newton perpendicularly upon an area of one square metre. The unit of measurement called atmosphere or standard atmosphere is 101325 Pa and this value is often used as a reference pressure and specified as such in some national and international standards, such as ISO2787, ISO2533 and ISO5024. In contrast, IUPAC recommends the use of 100 kPa as a standard pressure when reporting the properties of substances, geophysicists use the gigapascal in measuring or calculating tectonic stresses and pressures within the Earth. Medical elastography measures tissue stiffness non-invasively with ultrasound or magnetic resonance imaging, in materials science and engineering, the pascal measures the stiffness, tensile strength and compressive strength of materials. In engineering use, because the pascal represents a small quantity. The pascal is also equivalent to the SI unit of energy density and this applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields. In measurements of sound pressure, or loudness of sound, one pascal is equal to 94 decibels SPL, the quietest sound a human can hear, known as the threshold of hearing, is 0 dB SPL, or 20 µPa. The airtightness of buildings is measured at 50 Pa, the units of atmospheric pressure commonly used in meteorology were formerly the bar, which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals unit, exceptions include Canada and Portugal, which use kilopascals. In many other fields of science, the SI is preferred, many countries also use the millibar or hectopascal to give aviation altimeter settings. In practically all fields, the kilopascal is used instead. Centimetre of water Metric prefix Orders of magnitude Pascals law
11.
Slurry
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A slurry is a thin sloppy mud or cement or, in extended use, any fluid mixture of a pulverized solid with a liquid, often used as a convenient way of handling solids in bulk. Slurries behave in ways like thick fluids, flowing under gravity but are also capable of being pumped if not too thick. It contains large amount of catalyst, in form of sediments hence the denomination of slurry. C, a General Theory of the Hydraulic Transport of Solids in Full Suspension Ravelet, F. Bakir, F. Khelladi, S. Rey, R. Experimental study of transport of large particles in horizontal pipes. Ming, G. Ruixiang, L. Fusheng, N. Liqun, X. Hydraulic Transport of Coarse Gravel—A Laboratory Investigation Into Flow Resistance
12.
Freezing point
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The melting point of a solid is the temperature at which it changes state from solid to liquid at atmospheric pressure. At the melting point the solid and liquid phase exist in equilibrium, the melting point of a substance depends on pressure and is usually specified at standard pressure. When considered as the temperature of the change from liquid to solid. Because of the ability of some substances to supercool, the point is not considered as a characteristic property of a substance. For most substances, melting and freezing points are approximately equal, for example, the melting point and freezing point of mercury is 234.32 kelvins. However, certain substances possess differing solid-liquid transition temperatures, for example, agar melts at 85 °C and solidifies from 31 °C to 40 °C, such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is close to 0 °C. In the presence of nucleating substances the freezing point of water is the same as the melting point, the chemical element with the highest melting point is tungsten, at 3687 K, this property makes tungsten excellent for use as filaments in light bulbs. Many laboratory techniques exist for the determination of melting points, a Kofler bench is a metal strip with a temperature gradient. Any substance can be placed on a section of the strip revealing its thermal behaviour at the temperature at that point, differential scanning calorimetry gives information on melting point together with its enthalpy of fusion. A basic melting point apparatus for the analysis of crystalline solids consists of an oil bath with a transparent window, the several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated and with the aid of the melting of the individual crystals at a certain temperature can be observed. In large/small devices, the sample is placed in a heating block, the measurement can also be made continuously with an operating process. For instance, oil refineries measure the point of diesel fuel online, meaning that the sample is taken from the process. This allows for more frequent measurements as the sample does not have to be manually collected, for refractory materials the extremely high melting point may be determined by heating the material in a black body furnace and measuring the black-body temperature with an optical pyrometer. For the highest melting materials, this may require extrapolation by several hundred degrees, the spectral radiance from an incandescent body is known to be a function of its temperature. An optical pyrometer matches the radiance of a body under study to the radiance of a source that has been previously calibrated as a function of temperature, in this way, the measurement of the absolute magnitude of the intensity of radiation is unnecessary. However, known temperatures must be used to determine the calibration of the pyrometer, for temperatures above the calibration range of the source, an extrapolation technique must be employed
13.
Boiling point
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The boiling point of a substance is the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. The boiling point of a liquid varies depending upon the environmental pressure. A liquid in a vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a boiling point than when that liquid is at atmospheric pressure. For a given pressure, different liquids boil at different temperatures, for example, water boils at 100 °C at sea level, but at 93.4 °C at 2,000 metres altitude. The normal boiling point of a liquid is the case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level,1 atmosphere. At that temperature, the pressure of the liquid becomes sufficient to overcome atmospheric pressure. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar, the heat of vaporization is the energy required to transform a given quantity of a substance from a liquid into a gas at a given pressure. Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation, evaporation is a surface phenomenon in which molecules located near the liquids edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, a saturated liquid contains as much thermal energy as it can without boiling. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase, the liquid can be said to be saturated with thermal energy. Any addition of energy results in a phase transition. If the pressure in a system remains constant, a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy is removed, similarly, a liquid at saturation temperature and pressure will boil into its vapor phase as additional thermal energy is applied. The boiling point corresponds to the temperature at which the pressure of the liquid equals the surrounding environmental pressure. Thus, the point is dependent on the pressure. Boiling points may be published with respect to the NIST, USA standard pressure of 101.325 kPa, at higher elevations, where the atmospheric pressure is much lower, the boiling point is also lower. The boiling point increases with increased pressure up to the critical point, the boiling point cannot be increased beyond the critical point. Likewise, the point decreases with decreasing pressure until the triple point is reached
14.
Cartesian coordinate system
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Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair. The coordinates can also be defined as the positions of the projections of the point onto the two axis, expressed as signed distances from the origin. One can use the principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes. In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n and these coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes. The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes can be described by Cartesian equations, algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, a familiar example is the concept of the graph of a function. Cartesian coordinates are also tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering. They are the most common system used in computer graphics, computer-aided geometric design. Nicole Oresme, a French cleric and friend of the Dauphin of the 14th Century, used similar to Cartesian coordinates well before the time of Descartes. The adjective Cartesian refers to the French mathematician and philosopher René Descartes who published this idea in 1637 and it was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. Both authors used a single axis in their treatments and have a length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes La Géométrie was translated into Latin in 1649 by Frans van Schooten and these commentators introduced several concepts while trying to clarify the ideas contained in Descartes work. Many other coordinate systems have developed since Descartes, such as the polar coordinates for the plane. The development of the Cartesian coordinate system would play a role in the development of the Calculus by Isaac Newton. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line, a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative, we say that the line is oriented from the negative half towards the positive half
15.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
16.
Temperature
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A temperature is an objective comparative measurement of hot or cold. It is measured by a thermometer, several scales and units exist for measuring temperature, the most common being Celsius, Fahrenheit, and, especially in science, Kelvin. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, the kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. Temperature is important in all fields of science including physics, geology, chemistry, atmospheric sciences, medicine. The Celsius scale is used for temperature measurements in most of the world. Because of the 100 degree interval, it is called a centigrade scale.15, the United States commonly uses the Fahrenheit scale, on which water freezes at 32°F and boils at 212°F at sea-level atmospheric pressure. Many scientific measurements use the Kelvin temperature scale, named in honor of the Scottish physicist who first defined it and it is a thermodynamic or absolute temperature scale. Its zero point, 0K, is defined to coincide with the coldest physically-possible temperature and its degrees are defined through thermodynamics. The temperature of zero occurs at 0K = −273. 15°C. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, Temperature is one of the principal quantities in the study of thermodynamics. There is a variety of kinds of temperature scale and it may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century, empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a capillary tube, is dependent largely on temperature. Such scales are only within convenient ranges of temperature. For example, above the point of mercury, a mercury-in-glass thermometer is impracticable. A material is of no use as a thermometer near one of its phase-change temperatures, in spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics, nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and they rely on theoretical properties of idealized devices and materials
17.
Solid
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Solid is one of the four fundamental states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume, unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to other, either in a regular geometric lattice or irregularly. The branch of physics deals with solids is called solid-state physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification. The atoms, molecules or ions which make up solids may be arranged in a repeating pattern. Materials whose constituents are arranged in a regular pattern are known as crystals, in some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Almost all common metals, and many ceramics, are polycrystalline, in other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids, examples include polystyrene, whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed. While many common objects, such as an ice cube or a coin, are chemically identical throughout, for example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is an organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties, the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of sodium and chlorine. In diamond or silicon, the atoms share electrons and form covalent bonds, in metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding, metals typically are strong, dense, and good conductors of both electricity and heat
18.
Liquid
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A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a constant volume independent of pressure. As such, it is one of the four states of matter. A liquid is made up of tiny vibrating particles of matter, such as atoms, water is, by far, the most common liquid on Earth. 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, a distinctive property of the liquid state is surface tension, leading to wetting phenomena. The density of a liquid is usually close to that of a solid, therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is in form as interstellar clouds or in plasma form within stars. Liquid is one of the four states of matter, with the others being solid, gas. Unlike a solid, the molecules in a liquid have a greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, a liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, if liquid is placed in a bag, it can be squeezed into any shape. These properties make a suitable for applications such as hydraulics. Liquid particles are bound firmly but not rigidly and they are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its point, the cohesive forces that bind the molecules closely together break. If the temperature is decreased, the distances between the molecules become smaller, only two elements are liquid at standard conditions for temperature and pressure, mercury and bromine. Four more elements have melting points slightly above room temperature, francium, caesium, gallium and rubidium, metal alloys that are liquid at room temperature include NaK, a sodium-potassium metal alloy, galinstan, a fusible alloy liquid, and some amalgams
19.
Gas
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Gas is one of the four fundamental states of matter. A pure gas may be made up of atoms, elemental molecules made from one type of atom. A gas mixture would contain a variety of pure gases much like the air, what distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer, the interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam, the gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention, high-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these states of matter see list of states of matter. The only chemical elements which are stable multi atom homonuclear molecules at temperature and pressure, are hydrogen, nitrogen and oxygen. These gases, when grouped together with the noble gases. Alternatively they are known as molecular gases to distinguish them from molecules that are also chemical compounds. The word gas is a neologism first used by the early 17th-century Flemish chemist J. B. van Helmont, according to Paracelsuss terminology, chaos meant something like ultra-rarefied water. An alternative story is that Van Helmonts word is corrupted from gahst and these four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a relationship among these properties expressed by the ideal gas law. Gas particles are separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another, transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion, the drifting smoke particles in the image provides some insight into low pressure gas behavior
20.
Thermodynamic free energy
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The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering, the free energy is the internal energy of a system minus the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a multiplied by the temperature of the system. Like the internal energy, the energy is a thermodynamic state function. Energy is a generalization of free energy, since energy is the ability to do work which is free energy, free energy is that portion of any first-law energy that is available to perform thermodynamic work, i. e. work mediated by thermal energy. Free energy is subject to loss in the course of such work. Since first-law energy is conserved, it is evident that free energy is an expendable. Several free energy functions may be formulated based on system criteria, free energy functions are Legendre transformations of the internal energy. The Helmholtz free energy has a theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. The historically earlier Helmholtz free energy is defined as A = U − TS, where U is the energy, T is the absolute temperature. Its change is equal to the amount of work done on, or obtainable from. Thus its appellation work content, and the designation A from Arbeit, the Gibbs free energy is given by G = H − TS, where H is the enthalpy. Historically, these terms have been used inconsistently. In physics, free energy most often refers to the Helmholtz free energy, denoted by A, while in chemistry, since both fields use both functions, a compromise has been suggested, using A to denote the Helmholtz function and G for the Gibbs function. While A is preferred by IUPAC, G is sometimes still in use, the use of the words “latent heat” implied a similarity to latent heat in the more usual sense, it was regarded as chemically bound to the molecules of the body. In the adiabatic compression of a gas, the heat remained constant. During the early 19th century, the concept of perceptible or free caloric began to be referred to as “free heat” or heat set free. In 1824, for example, the French physicist Sadi Carnot, in his famous “Reflections on the Motive Power of Fire”, an increasing number of books and journal articles do not include the attachment “free”, referring to G as simply Gibbs energy
21.
Phase transition
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The term phase transition is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma. A phase of a system and the states of matter have uniform physical properties. For example, a liquid may become gas upon heating to the boiling point, the measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions are common in nature and used today in many technologies, the same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid is heated and transforms into a phase and a liquid phase. A spinodal decomposition, in which a phase is cooled. Transition to a mesophase between solid and liquid, such as one of the crystal phases. The transition between the ferromagnetic and paramagnetic phases of materials at the Curie point. The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide, the martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides, the dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron. The emergence of superconductivity in certain metals and ceramics when cooled below a critical temperature, the superfluid transition in liquid helium is an example of this. The breaking of symmetries in the laws of physics during the history of the universe as its temperature cooled. Isotope fractionation occurs during a transition, the ratio of light to heavy isotopes in the involved molecules changes. When water vapor condenses, the heavier water isotopes become enriched in the liquid phase while the lighter isotopes tend toward the vapor phase, Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables. This condition generally stems from the interactions of a number of particles in a system. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, examples include, quantum phase transitions, dynamic phase transitions, and topological phase transitions. In these types of other parameters take the place of temperature
22.
Critical point (thermodynamics)
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In thermodynamics, a critical point is the end point of a phase equilibrium curve. The most prominent example is the critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid. At the critical point, defined by a critical temperature Tc, other examples include the liquid–liquid critical points in mixtures. For simplicity and clarity, the notion of critical point is best introduced by discussing a specific example. This was the first critical point to be discovered, and it is still the best known, the figure to the right shows the schematic PT diagram of a pure substance. The commonly known phases solid, liquid and vapor are separated by phase boundaries, at the triple point, all three phases can coexist. However, the liquid-vapor boundary terminates in an endpoint at some critical temperature Tc, in water, the critical point occurs at around 647 K and 22.064 MPa. In the vicinity of the point, the physical properties of the liquid. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a dielectric constant. At the critical point, only one phase exists, the heat of vaporization is zero. There is a point in the constant-temperature line on a PV diagram. This means that at the point, T = T =0 Above the critical point there exists a state of matter that is continuously connected with both the liquid and the gaseous state. The existence of a point was first discovered by Charles Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860. Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3,000 atm. Solving the above condition T =0 for the van der Waals equation, however, the van der Waals equation, based on a mean field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws, the principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is true for many substances, but becomes increasingly inaccurate for large values of pr. The liquid–liquid critical point of a solution, which occurs at the solution temperature
23.
Supercritical fluid
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A supercritical fluid is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It can effuse through solids like a gas, and dissolve materials like a liquid, in addition, close to the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be fine-tuned. Supercritical fluids are suitable as a substitute for organic solvents in a range of industrial, carbon dioxide and water are the most commonly used supercritical fluids, being used for decaffeination and power generation, respectively. In general terms, supercritical fluids have properties between those of a gas and a liquid, in Table 1, the critical properties are shown for some components, which are commonly used as supercritical fluids. Table 2 shows density, diffusivity and viscosity for typical liquids, gases, in addition, there is no surface tension in a supercritical fluid, as there is no liquid/gas phase boundary. By changing the pressure and temperature of the fluid, the properties can be tuned to be more liquid- or more gas-like, one of the most important properties is the solubility of material in the fluid. Solubility in a supercritical fluid tends to increase with density of the fluid, since density increases with pressure, solubility tends to increase with pressure. The relationship with temperature is a more complicated. At constant density, solubility will increase with temperature, however, close to the critical point, the density can drop sharply with a slight increase in temperature. Therefore, close to the temperature, solubility often drops with increasing temperature. All supercritical fluids are completely miscible with each other so for a mixture a single phase can be guaranteed if the point of the mixture is exceeded. The critical point of a mixture can be estimated as the arithmetic mean of the critical temperatures and pressures of the two components, Tc = x TcA + x TcB. For greater accuracy, the point can be calculated using equations of state, such as the Peng Robinson. Other properties, such as density, can also be calculated using equations of state, figures 1 and 2 show projections of a phase diagram. This can be observed in the phase diagram for carbon dioxide. At well below the temperature, e. g.280 K, as the pressure increases. The system consists of 2 phases in equilibrium, a dense liquid, as the critical temperature is approached, the density of the gas at equilibrium becomes higher, and that of the liquid lower. At the critical point, there is no difference in density, thus, above the critical temperature a gas cannot be liquefied by pressure
24.
Symmetry group
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In abstract algebra, the symmetry group of an object is the group of all transformations under which the object is invariant with composition as the group operation. For a space with a metric, it is a subgroup of the group of the space concerned. If not stated otherwise, this article considers symmetry groups in Euclidean geometry, the objects may be geometric figures, images, and patterns, such as a wallpaper pattern. The definition can be more precise by specifying what is meant by image or pattern. For symmetry of objects, one may also want to take their physical composition into account. The group of isometries of space induces an action on objects in it. The symmetry group is also called full symmetry group in order to emphasize that it includes the orientation-reversing isometries under which the figure is invariant. The subgroup of orientation-preserving isometries that leave the figure invariant is called its symmetry group. The proper symmetry group of an object is equal to its symmetry group if. The proper symmetry group is then a subgroup of the orthogonal group SO. A discrete symmetry group is a group such that for every point of the space the set of images of the point under the isometries in the symmetry group is a discrete set. There are also continuous symmetry groups, which contain rotations of arbitrarily small angles or translations of arbitrarily small distances, the group of all symmetries of a sphere O is an example of this, and in general such continuous symmetry groups are studied as Lie groups. With a categorization of subgroups of the Euclidean group corresponds a categorization of symmetry groups, for example, two 3D figures have mirror symmetry, but with respect to different mirror planes. Two 3D figures have 3-fold rotational symmetry, but with respect to different axes, two 2D patterns have translational symmetry, each in one direction, the two translation vectors have the same length but a different direction. When considering isometry groups, one may restrict oneself to those where for all points the set of images under the isometries is topologically closed. This includes all discrete isometry groups and also involved in continuous symmetries. A figure with this group is non-drawable and up to arbitrarily fine detail homogeneous. The group generated by all translations, this group cannot be the group of a pattern, it would be homogeneous
25.
Slope
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In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The direction of a line is increasing, decreasing, horizontal or vertical. A line is increasing if it goes up from left to right, the slope is positive, i. e. m >0. A line is decreasing if it goes down from left to right, the slope is negative, i. e. m <0. If a line is horizontal the slope is zero, if a line is vertical the slope is undefined. The steepness, incline, or grade of a line is measured by the value of the slope. A slope with an absolute value indicates a steeper line Slope is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points on a line. Sometimes the ratio is expressed as a quotient, giving the number for every two distinct points on the same line. A line that is decreasing has a negative rise, the line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The rise of a road between two points is the difference between the altitude of the road at two points, say y1 and y2, or in other words, the rise is = Δy. Here the slope of the road between the two points is described as the ratio of the altitude change to the horizontal distance between any two points on the line. In mathematical language, the m of the line is m = y 2 − y 1 x 2 − x 1. The concept of slope applies directly to grades or gradients in geography, as a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. When the curve given by a series of points in a diagram or in a list of the coordinates of points, thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of both technology and the built environment. This is described by the equation, m = Δ y Δ x = vertical change horizontal change = rise run. Given two points and, the change in x from one to the other is x2 − x1, substituting both quantities into the above equation generates the formula, m = y 2 − y 1 x 2 − x 1. The formula fails for a line, parallel to the y axis. Suppose a line runs through two points, P = and Q =, since the slope is positive, the direction of the line is increasing
26.
Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
27.
Intermolecular force
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Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields used in molecular mechanics. The investigation of intermolecular forces starts from macroscopic observations which indicate the existence and these observations include non-ideal-gas thermodynamic behavior reflected by virial coefficients, vapor pressure, viscosity, superficial tension, and absorption data. The first reference to the nature of microscopic forces is found in Alexis Clairauts work Theorie de la Figure de la Terre, other scientists who have contributed to the investigation of microscopic forces include, Laplace, Gauss, Maxwell and Boltzmann. The link to microscopic aspects is given by virial coefficients and Lennard-Jones potentials, dipole-dipole interactions are electrostatic interactions between permanent dipoles in molecules. These interactions tend to align the molecules to increase attraction, an example of a dipole-dipole interaction can be seen in hydrogen chloride, the positive end of a polar molecule will attract the negative end of the other molecule and influence its position. Polar molecules have a net attraction between them, examples of polar molecules include hydrogen chloride and chloroform. H δ + − Cl δ − ⋯ H δ + − Cl δ − Often molecules contain dipolar groups and this occurs if there is symmetry within the molecule that causes the dipoles to cancel each other out. This occurs in such as tetrachloromethane and carbon dioxide. The dipole-dipole interaction between two atoms is usually zero, since atoms rarely carry a permanent dipole. Ion-dipole and ion-induced dipole forces are similar to dipole-dipole and induced-dipole interactions but involve ions, ion-dipole and ion-induced dipole forces are stronger than dipole-dipole interactions because the charge of any ion is much greater than the charge of a dipole moment. Ion-dipole bonding is stronger than hydrogen bonding, an ion-dipole force consists of an ion and a polar molecule interacting. They align so that the positive and negative groups are next to one another, an ion-induced dipole force consists of an ion and a non-polar molecule interacting. Like a dipole-induced dipole force, the charge of the ion causes distortion of the cloud on the non-polar molecule. A hydrogen bond is the attraction between the pair of an electronegative atom and a hydrogen atom that is bonded to either nitrogen, oxygen. The hydrogen bond is described as a strong electrostatic dipole-dipole interaction. Intermolecular hydrogen bonding is responsible for the boiling point of water compared to the other group 16 hydrides
28.
Hydrogen bond
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Hydrogen bonds can occur between molecules or within different parts of a single molecule. Depending on geometry and environment, the hydrogen bond free energy content is between 1 and 5 kcal/mol and this makes it stronger than a van der Waals interaction, but weaker than covalent or ionic bonds. This type of bond can occur in molecules such as water and in organic molecules like DNA. Intermolecular hydrogen bonding is responsible for the boiling point of water compared to the other group 16 hydrides that have much weaker hydrogen bonds. Intramolecular hydrogen bonding is responsible for the secondary and tertiary structures of proteins. It also plays an important role in the structure of polymers, in 2011, an IUPAC Task Group recommended a modern evidence-based definition of hydrogen bonding, which was published in the IUPAC journal Pure and Applied Chemistry. An accompanying detailed technical report provides the rationale behind the new definition, a hydrogen atom attached to a relatively electronegative atom will play the role of the hydrogen bond donor. This electronegative atom is usually fluorine, oxygen, or nitrogen, a hydrogen attached to carbon can also participate in hydrogen bonding when the carbon atom is bound to electronegative atoms, as is the case in chloroform, CHCl3. An example of a hydrogen donor is the hydrogen from the hydroxyl group of ethanol. In a hydrogen bond, the electronegative atom not covalently attached to the hydrogen is named proton acceptor, because of the small size of hydrogen relative to other atoms and molecules, the resulting charge, though only partial, represents a large charge density. A hydrogen bond results when this positive charge density attracts a lone pair of electrons on another heteroatom. The hydrogen bond is described as an electrostatic dipole-dipole interaction. These covalent features are more substantial when acceptors bind hydrogens from more electronegative donors, the partially covalent nature of a hydrogen bond raises the following questions, To which molecule or atom does the hydrogen nucleus belong. And Which should be labeled donor and which acceptor, liquids that display hydrogen bonding are called associated liquids. Hydrogen bonds can vary in strength from weak to extremely strong. For example, the central interresidue N−H···N hydrogen bond between guanine and cytosine is much stronger in comparison to the N−H···N bond between the adenine-thymine pair, the length of hydrogen bonds depends on bond strength, temperature, and pressure. The bond strength itself is dependent on temperature, pressure, bond angle, the typical length of a hydrogen bond in water is 197 pm. The ideal bond angle depends on the nature of the hydrogen bond donor, moore and Winmill used the hydrogen bond to account for the fact that trimethylammonium hydroxide is a weaker base than tetramethylammonium hydroxide
29.
Antimony
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Antimony is a chemical element with symbol Sb and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite, Antimony compounds have been known since ancient times and were powdered for use as medicine and cosmetics, often known by the Arabic name, kohl. Metallic antimony was known, but it was erroneously identified as lead upon its discovery. In the West, it was first isolated by Vannoccio Biringuccio, for some time, China has been the largest producer of antimony and its compounds, with most production coming from the Xikuangshan Mine in Hunan. The industrial methods for refining antimony are roasting and reduction with carbon or direct reduction of stibnite with iron, the largest applications for metallic antimony is an alloy with lead and tin and the lead antimony plates in lead–acid batteries. Alloys of lead and tin with antimony have improved properties for solders, bullets, Antimony compounds are prominent additives for chlorine and bromine-containing fire retardants found in many commercial and domestic products. An emerging application is the use of antimony in microelectronics, Antimony is in a pnictogen and has an electronegativity of 2.05. In accordance with periodic trends, it is more electronegative than tin or bismuth, Antimony is stable in air at room temperature, but reacts with oxygen if heated to produce antimony trioxide, Sb2O3. Antimony is resistant to attack by acids, four allotropes of antimony are known, a stable metallic form and three metastable forms. Elemental antimony is a brittle, silver-white shiny metalloid, when slowly cooled, molten antimony crystallizes in a trigonal cell, isomorphic with the gray allotrope of arsenic. A rare explosive form of antimony can be formed from the electrolysis of antimony trichloride, when scratched with a sharp implement, an exothermic reaction occurs and white fumes are given off as metallic antimony forms, when rubbed with a pestle in a mortar, a strong detonation occurs. Black antimony is formed upon cooling of antimony vapor. It has the crystal structure as red phosphorus and black arsenic, it oxidizes in air. At 100 °C, it transforms into the stable form. The yellow allotrope of antimony is the most unstable and it has only been generated by oxidation of stibine at −90 °C. Above this temperature and in ambient light, this metastable allotrope transforms into the more stable black allotrope, elemental antimony adopts a layered structure in which layers consist of fused, ruffled, six-membered rings. The nearest and next-nearest neighbors form an octahedral complex, with the three atoms in each double layer slightly closer than the three atoms in the next. This relatively close packing leads to a density of 6.697 g/cm3
30.
Bismuth
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Bismuth is a chemical element with the symbol Bi and atomic number 83. Bismuth, a pentavalent post-transition metal and one of the pnictogens, chemically resembles its lighter homologs arsenic, elemental bismuth may occur naturally, although its sulfide and oxide form important commercial ores. The free element is 86% as dense as lead and it is a brittle metal with a silvery white color when freshly produced, but surface oxidation can give it a pink tinge. Bismuth is the most naturally diamagnetic element, and has one of the lowest values of thermal conductivity among metals, Bismuth metal has been known since ancient times, although it was often confused with lead and tin, which share some physical properties. Bismuth was long considered the element with the highest atomic mass that is stable, because of its tremendously long half-life, bismuth may still be considered stable for almost all purposes. Bismuth compounds account for half the production of bismuth. They are used in cosmetics, pigments, and a few pharmaceuticals, notably bismuth subsalicylate, bismuths unusual propensity to expand upon freezing is responsible for some of its uses, such as in casting of printing type. Bismuth has unusually low toxicity for a heavy metal, as the toxicity of lead has become more apparent in recent years, there is an increasing use of bismuth alloys as a replacement for lead. The name bismuth dates from around the 1660s, and is of uncertain etymology and it is one of the first 10 metals to have been discovered. Bismuth appears in the 1660s, from obsolete German Bismuth, Wismut, Wissmuth, the New Latin bisemutum is from the German Wismuth, perhaps from weiße Masse, white mass. The element was confused in early times with tin and lead because of its resemblance to those elements, Bismuth has been known since ancient times, so no one person is credited with its discovery. Agricola, in De Natura Fossilium states that bismuth is a metal in a family of metals including tin. This was based on observation of the metals and their physical properties, miners in the age of alchemy also gave bismuth the name tectum argenti, or silver being made, in the sense of silver still in the process of being formed within the Earth. Bismuth was also known to the Incas and used in a bronze alloy for knives. Bismuth is a metal with a white, silver-pink hue, often occurring in its native form. The spiral, stair-stepped structure of crystals is the result of a higher growth rate around the outside edges than on the inside edges. The variations in the thickness of the layer that forms on the surface of the crystal causes different wavelengths of light to interfere upon reflection. When burned in oxygen, bismuth burns with a blue flame and its toxicity is much lower than that of its neighbors in the periodic table, such as lead, antimony, and polonium
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Enthalpy
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Enthalpy /ˈɛnθəlpi/ is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the heat content of a system. It is equal to the energy of the system plus the product of pressure. Enthalpy is defined as a function that depends only on the prevailing equilibrium state identified by the systems internal energy, pressure. The unit of measurement for enthalpy in the International System of Units is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating or work other than expansion work, the total enthalpy, H, of a system cannot be measured directly. The same situation exists in classical mechanics, only a change or difference in energy carries physical meaning. Enthalpy itself is a potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point, therefore what we measure is the change in enthalpy. The ΔH is a change in endothermic reactions, and negative in heat-releasing exothermic processes. For processes under constant pressure, ΔH is equal to the change in the energy of the system. This means that the change in enthalpy under such conditions is the heat absorbed by the material through a reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume standard state, most commonly 1 bar pressure, standard state does not, strictly speaking, specify a temperature, but expressions for enthalpy generally reference the standard heat of formation at 25 °C. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy, real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses. The word enthalpy stems from the Ancient Greek verb enthalpein, which means to warm in and it combines the Classical Greek prefix ἐν- en-, meaning to put into, and the verb θάλπειν thalpein, meaning to heat. The word enthalpy is often attributed to Benoît Paul Émile Clapeyron. This misconception was popularized by the 1927 publication of The Mollier Steam Tables, however, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyrons death. The earliest writings to contain the concept of enthalpy did not appear until 1875, however, Gibbs did not use the word enthalpy in his writings. The actual word first appears in the literature in a 1909 publication by J. P. Dalton
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Entropy
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In statistical thermodynamics, entropy is a measure of the number of microscopic configurations Ω that a thermodynamic system can have when in a state as specified by some macroscopic variables. Formally, S = k B ln Ω, for example, gas in a container with known volume, pressure, and temperature could have an enormous number of possible configurations of the collection of individual gas molecules. Each instantaneous configuration of the gas may be regarded as random, Entropy may be understood as a measure of disorder within a macroscopic system. The second law of thermodynamics states that an isolated systems entropy never decreases, such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environments entropy increases by at least that amount, since entropy is a function of the state of the system, a change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible, however, irreversible processes increase the combined entropy of the system and its environment. The above definition is called the macroscopic definition of entropy because it can be used without regard to any microscopic description of the contents of a system. The concept of entropy has found to be generally useful and has several other formulations. Entropy was discovered when it was noticed to be a quantity that behaves as a function of state and it has the dimension of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units. But the entropy of a substance is usually given as an intensive property—either entropy per unit mass or entropy per unit amount of substance. In statistical mechanics this reflects that the state of a system is generally non-degenerate. Understanding the role of entropy in various processes requires an understanding of how. It is often said that entropy is an expression of the disorder, or randomness of a system, the second law is now often seen as an expression of the fundamental postulate of statistical mechanics through the modern definition of entropy. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy and he made the analogy with that of how water falls in a water wheel. This was an insight into the second law of thermodynamics. g. Clausius described entropy as the transformation-content, i. e. dissipative energy use and this was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, henceforth, the essential problem in statistical thermodynamics, i. e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a definition of irreversibility, in terms of trajectories
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Steam
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Steam is water in the gas phase, which is formed when water boils. Steam is invisible, however, steam often refers to wet steam, at lower pressures, such as in the upper atmosphere or at the top of high mountains, water boils at a lower temperature than the nominal 100 °C at standard pressure. If heated further it becomes superheated steam, piston type steam engines played a central role to the Industrial Revolution and modern steam turbines are used to generate more than 80% of the worlds electricity. If liquid water comes in contact with a hot surface or depressurizes quickly below its vapor pressure. Steam explosions have been responsible for many accidents, and may also have been responsible for much of the damage to the plant in the Chernobyl disaster. Steam is traditionally created by heating a boiler via burning coal and other fuels, water vapor that includes water droplets is described as wet steam. As wet steam is heated further, the droplets evaporate, and at a high temperature all of the water evaporates. Superheated steam is steam at a higher than its boiling point for the pressure. Steam tables contain thermodynamic data for water/steam and are used by engineers and scientists in design. Additionally, thermodynamic phase diagrams for water/steam, such as a diagram or a Mollier diagram shown in this article. Steam charts are used for analysing thermodynamic cycles. In agriculture, steam is used for sterilization to avoid the use of harmful chemical agents. Steams capacity to transfer heat is used in the home, for cooking vegetables, steam cleaning of fabric, carpets and flooring. In each case, water is heated in a boiler, steam is also used in ironing clothes to add enough humidity with the heat to take wrinkles out and put intentional creases into the clothing. About 90% of all electricity is generated using steam as the working fluid, in electric generation, steam is typically condensed at the end of its expansion cycle, and returned to the boiler for re-use. However, in cogeneration, steam is piped into buildings through a heating system to provide heat energy after its use in the electric generation cycle. The worlds biggest steam generation system is the New York City steam system, in other industrial applications steam is used for energy storage, which is introduced and extracted by heat transfer, usually through pipes. Steam is a reservoir for thermal energy because of waters high heat of vaporization
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Refrigerant
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A refrigerant is a substance or mixture, usually a fluid, used in a heat pump and refrigeration cycle. In most cycles it undergoes phase transitions from a liquid to a gas, many working fluids have been used for such purposes. Fluorocarbons, especially chlorofluorocarbons, became commonplace in the 20th century, other common refrigerants used in various applications are ammonia, sulfur dioxide, and non-halogenated hydrocarbons such as propane. The ideal refrigerant would have favorable properties, be noncorrosive to mechanical components. It would not cause ozone depletion or climate change, since different fluids have the desired traits in different degree, choice is a matter of trade-off. Since boiling point and gas density are affected by pressure, refrigerants may be more suitable for a particular application by choice of operating pressures. In order from the highest to the lowest potential of ozone depletion are Bromochlorofluorocarbon, though HFC and PFC are non-ozone depleting, many have global warming potentials that are thousands of times greater than CO2. Some other refrigerants such as propane and ammonia are not inert, new refrigerants were developed in the early 21st century that are safer for the environment, but their application has been held up due to concerns over toxicity and flammability. Early mechanical refrigeration systems employed sulfur dioxide, methyl chloride and ammonia, being toxic, sulfur dioxide and methyl chloride rapidly disappeared from the market with the introduction of CFCs. Occasionally, one may encounter older machines with methyl formate, chloromethane, chlorofluorocarbons were little used for refrigeration until better synthesis methods, developed in the 1950s, reduced their cost. Their domination of the market was called into question in the 1980s by concerns about depletion of the ozone layer and they are currently subject to prohibition discussions on account of their harmful effect on the climate. In 1997, FCs and HFCs were included in the Kyoto Protocol to the Framework Convention on Climate Change, in 2006, the EU adopted a Regulation on fluorinated greenhouse gases, which makes stipulations regarding the use of FCs and HFCs with the intention of reducing their emissions. The provisions do not affect climate-neutral refrigerants, refrigerants such as ammonia, carbon dioxide and non-halogenated hydrocarbons do not deplete the ozone layer and have no or only a low global warming potential. They are used in air-conditioning systems for buildings, in sport and leisure facilities, in the industry, in the automotive industry. In these settings their toxicity is less a concern than in home equipment, emissions from automobile air conditioning are a growing concern because of their impact on climate change. From 2011 on, the European Union will phase out refrigerants with a global warming potential of more than 150 in automotive air conditioning and this will ban potent greenhouse gases such as the refrigerant HFC-134a —which has a GWP of 1410—to promote safe and energy-efficient refrigerants. One of the most promising alternatives is CO2, carbon dioxide is non-flammable, non-ozone depleting, has a global warming potential of 1. R-744 can be used as a fluid in climate control systems for cars, residential air conditioning, hot water pumps, commercial refrigeration
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Thermodynamic cycle
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In the process of passing through a cycle, the working fluid may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source, during a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities, such as heat and work are process dependent, ein might be the work and heat input during the cycle and Eout would be the work and heat output during the cycle. The first law of thermodynamics also dictates that the net heat input is equal to the net work output over a cycle, the repeating nature of the process path allows for continuous operation, making the cycle an important concept in thermodynamics. Thermodynamic cycles are often represented mathematically as quasistatic processes in the modeling of the workings of an actual device, two primary classes of thermodynamic cycles are power cycles and heat pump cycles. Power cycles are cycles which convert some heat input into a mechanical work output, cycles composed entirely of quasistatic processes can operate as power or heat pump cycles by controlling the process direction. On a pressure-volume diagram or temperature-entropy diagram, the clockwise and counterclockwise directions indicate power and heat pump cycles, because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a PV diagram. A PV diagrams Y axis shows pressure and X axis shows volume, if the cyclic process moves clockwise around the loop, then W will be positive, and it represents a heat engine. If it moves counterclockwise, then W will be negative, and this does not exclude energy transfer as work. Isothermal, The process is at a constant temperature during that part of the cycle and this does not exclude energy transfer as heat or work. Isobaric, Pressure in that part of the cycle will remain constant and this does not exclude energy transfer as heat or work. Isochoric, The process is constant volume and this does not exclude energy transfer as heat or work. Isentropic, The process is one of constant entropy and this excludes the transfer of heat but not work. Thermodynamic power cycles are the basis for the operation of heat engines, power cycles can be organized into two categories, real cycles and ideal cycles. Cycles encountered in real world devices are difficult to analyze because of the presence of complicating effects, power cycles can also be divided according to the type of heat engine they seek to model. The most common used to model internal combustion engines are the Otto cycle, which models gasoline engines, and the Diesel cycle. There is no difference between the two except the purpose of the refrigerator is to cool a very small space while the heat pump is intended to warm a house. Both work by moving heat from a space to a warm space
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Carnot cycle
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The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It is not an actual thermodynamic cycle but is a theoretical construct, every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, in the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A system undergoing a Carnot cycle is called a Carnot heat engine, although such an engine is only a theoretical construct. However, a microscopic Carnot heat engine has been designed and run, essentially, there are two systems at temperatures Th and Tc, which are so large that their temperatures are practically unaffected by a single cycle. As such, they are called heat reservoirs, since the cycle is reversible, there is no generation of entropy during the cycle, entropy is conserved. During the cycle, an amount of entropy ΔS is extracted from the hot reservoir. The difference in the two energies ΔS is equal to the work done by the engine, the Carnot cycle when acting as a heat engine consists of the following steps, Reversible isothermal expansion of the gas at the hot temperature, T1. During this step the gas is allowed to expand and it work on the surroundings. The temperature of the gas does not change during the process, the gas expansion is propelled by absorption of heat energy Q1 from the high temperature reservoir and results in an increase of entropy of the gas in the amount Δ S1 = Q1 / T1. For this step the mechanisms of the engine are assumed to be thermally insulated, the gas continues to expand, doing work on the surroundings, and losing an amount of internal energy equal to the work that leaves the system. The gas expansion causes it to cool to the cold temperature, Reversible isothermal compression of the gas at the cold temperature, T2. Once again the mechanisms of the engine are assumed to be thermally insulated, at this point the gas is in the same state as at the start of step 1. In this case, Δ S1 = Δ S2, or and this is true as Q2 and T2 are both lower and in fact are in the same ratio as Q1 / T1. For a simple closed system, any point on the graph represent a particular state of the system. A thermodynamic process will consist of a curve connecting an initial state, the area under the curve will be, Q = ∫ A B T d S which is the amount of thermal energy transferred in the process. If the process moves to greater entropy, the area under the curve will be the amount of absorbed by the system in that process. If the process moves towards lesser entropy, it will be the amount of heat removed, for any cyclic process, there will be an upper portion of the cycle and a lower portion
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Rankine cycle
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The Rankine cycle is a model that is used to predict the performance of steam turbine systems, though the theoretical principle also applies to reciprocating engines such as steam locomotives. The Rankine cycle is a thermodynamic cycle of a heat engine that converts heat into mechanical work. The heat is supplied externally to a loop, which usually uses water as the working fluid. It is named after William John Macquorn Rankine, a Scottish polymath, the Rankine cycle closely describes the process by which steam-operated heat engines commonly found in thermal power generation plants generate power. The heat sources used in power plants are usually nuclear fission or the combustion of fossil fuels such as coal, natural gas. The efficiency of the Rankine cycle is limited by the heat of vaporization of the working fluid. This gives a theoretical maximum Carnot efficiency for the turbine alone of about 63. 8% compared with an actual overall thermal efficiency of up to 42% for a modern coal-fired power station. This low steam turbine entry temperature is why the Rankine cycle is used as a bottoming cycle to recover otherwise rejected heat in combined-cycle gas turbine power stations. The working fluid in a Rankine cycle follows a loop and is reused constantly. This exhaust heat is represented by the Qout flowing out of the side of the cycle shown in the T/s diagram below. Cooling towers operate as heat exchangers by absorbing the latent heat of vaporization of the working fluid. The benefit of this is offset by the low temperatures of steam admitted to the turbine, gas turbines, for instance, have turbine entry temperatures approaching 1500°C. However, the efficiency of actual large steam power stations. There are four processes in the Rankine cycle and these states are identified by numbers in the above T-s diagram. Process 1-2, The working fluid is pumped from low to high pressure, as the fluid is a liquid at this stage, the pump requires little input energy. Process 2-3, The high pressure liquid enters a boiler where it is heated at constant pressure by a heat source to become a dry saturated vapour. The input energy required can be easily calculated graphically, using a chart, or numerically. Process 3-4, The dry saturated vapour expands through a turbine and this decreases the temperature and pressure of the vapour, and some condensation may occur
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Vapor-compression refrigeration
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Refrigeration may be defined as lowering the temperature of an enclosed space by removing heat from that space and transferring it elsewhere. A device that performs this function may also be called an air conditioner, refrigerator, air source heat pump, the vapor-compression uses a circulating liquid refrigerant as the medium which absorbs and removes heat from the space to be cooled and subsequently rejects that heat elsewhere. Figure 1 depicts a typical, single-stage vapor-compression system, all such systems have four components, a compressor, a condenser, a thermal expansion valve, and an evaporator. Circulating refrigerant enters the compressor in the state known as a saturated vapor and is compressed to a higher pressure. This is where the refrigerant rejects heat from the system. The condensed liquid refrigerant, in the state known as a saturated liquid, is next routed through an expansion valve where it undergoes an abrupt reduction in pressure. That pressure reduction results in the flash evaporation of a part of the liquid refrigerant. The cold mixture is then routed through the coil or tubes in the evaporator, a fan circulates the warm air in the enclosed space across the coil or tubes carrying the cold refrigerant liquid and vapor mixture. That warm air evaporates the liquid part of the refrigerant mixture. At the same time, the air is cooled and thus lowers the temperature of the enclosed space to the desired temperature. The evaporator is where the refrigerant absorbs and removes heat which is subsequently rejected in the condenser. To complete the cycle, the refrigerant vapor from the evaporator is again a saturated vapor and is routed back into the compressor. Freon is a name for a family of haloalkane refrigerants manufactured by DuPont. Haloalkanes are also an order of more expensive than petroleum derived flammable alkanes of similar or better cooling performance. Unfortunately, chlorine- and fluorine-bearing refrigerants reach the atmosphere when they escape. In the stratosphere, CFCs break up due to UV radiation and these chlorine free radicals act as catalysts in the breakdown of ozone through chain reactions. One CFC molecule can cause thousands of molecules to break down. This causes severe damage to the layer that shields the Earths surface from the Suns strong UV radiation
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Two-dimensional graph
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A two-dimensional graph is a set of points in two-dimensional space. If the points are real and if Cartesian coordinates are used, with real variables on the axes, each point in the graph depicts the values of two real variables. Alternatively, each point in a graph may depict the value of a complex variable. The function could be a function or a transcendental function. For example, the graph of the polynomial f = x 3 −9 x is. If this set is plotted on a Cartesian plane, the result is a curve, in some cases the relation between two real variables cannot be written in the form y = f. In other words, it is not a function, nevertheless, the set of all points given by the relation is still a two-dimensional graph, as in the accompanying graph of the circle 2 +2 =1. An image of a curve is also a two-dimensional graph. In some contexts it is useful to graph two or more together in the same diagram. An example is the supply and demand graph commonly used in economics, two-dimensional geometric shapes are sets of points bounded by line segments or curves, so a shape can also be constructed by graphs of several equations of its boundary. Polygons are the shapes that are bounded by line segments. These can be visualized by using two-dimensional graphs, graphs of two polygons, a parallelogram and a right triangle, are shown here along with the graph of a circle. Graph Three-dimensional graph List of two-dimensional geometric shapes Analytic geometry Cartesian coordinate system Euclidean space Coordinate system Dimension
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Concentration
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In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished, mass concentration, molar concentration, number concentration, the term concentration can be applied to any kind of chemical mixture, but most frequently it refers to solutes and solvents in solutions. The molar concentration has variants such as concentration and osmotic concentration. To concentrate a solution, one must add more solute, or reduce the amount of solvent, by contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution, at this point, the solution is said to be saturated. If additional solute is added to a solution, it will not dissolve, except in certain circumstances. Instead, phase separation will occur, leading to coexisting phases, the point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute. Concentrations are often called levels, reflecting the mental schema of levels on the axis of a graph. There are four quantities that describe concentration, The mass concentration ρ i is defined as the mass of a constituent m i divided by the volume of the mixture V, ρ i = m i V. The molar concentration c i is defined as the amount of a constituent n i divided by the volume of the mixture V, c i = n i V, however, more commonly the unit mol/L is used. The number concentration C i is defined as the number of entities of a constituent N i in a divided by the volume of the mixture V, C i = N i V. The volume concentration ϕ i is defined as the volume of a constituent V i divided by the volume of the mixture V, ϕ i = V i V. Being dimensionless, it is expressed as a number, e. g.0.18 or 18%, several other quantities can be used to describe the composition of a mixture. Note that these should not be called concentrations, normality is defined as the molar concentration c i divided by an equivalence factor f e q. Since the definition of the equivalence factor depends on context, IUPAC, the SI unit for molality is mol/kg. The mole fraction x i is defined as the amount of a constituent n i divided by the amount of all constituents in a mixture n t o t, x i = n i n t o t. However, the deprecated parts-per notation is used to describe small mole fractions. The mole ratio r i is defined as the amount of a constituent n i divided by the amount of all other constituents in a mixture
