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Critical Variables
Critical variables are defined, for example in thermodynamics, in terms of the values of variables at the critical point. On a PV diagram, the critical point is an inflection point. Thus: : \left(\frac\right)_=0 : \left(\frac\right)_=0 For the van der Waals equation The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is an equation of state that relates the pressure, volume, Avogadro's law, number of molecules, and temperature in a fluid. The equation modifies ..., the above yields: : P_C=\frac : \displaystyle : T_C=\frac References {{DEFAULTSORT:Critical Variable Thermodynamic properties Conformal field theory ...
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Thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantity, physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the thermodynamic efficiency, efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win ...
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Critical Point (physics)
In thermodynamics, a critical point (or critical state) is the end point of a phase Equilibrium (thermodynamics), equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas comes into a supercritical fluid, supercritical phase, and so cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''c and a ''critical pressure'' ''p''c, phase (matter), phase boundaries vanish. Other examples include the Upper critical solution temperature, liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field. Liquid–vapor critical point Overview For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the vapor–liquid cr ...
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Inflection Point
In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa. For the graph of a function of differentiability class (its first derivative , and its second derivative , exist and are continuous), the condition can also be used to find an inflection point since a point of must be passed to change from a positive value (concave upward) to a negative value (concave downward) or vice versa as is continuous; an inflection point of the curve is where and changes its sign at the point (from positive to negative or from negative to positive). A point where the second derivative vanishes but does not change its sign is sometimes called a point of undulation or und ...
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Van Der Waals Equation
The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is an equation of state that relates the pressure, volume, Avogadro's law, number of molecules, and temperature in a fluid. The equation modifies the ideal gas law in two ways: first, it considers particles to have a finite diameter (whereas an ideal gas consists of point particles); second, its particles interact with each other (unlike an ideal gas, whose particles move as though alone in the volume). The equation is named after Dutch physicist Johannes Diderik van der Waals, who first derived it in 1873 as part of his doctoral thesis. Van der Waals based the equation on the idea that fluids are composed of discrete particles, which few scientists believed existed. However, the equation accurately predicted the behavior of a fluid around its Critical point (thermodynamics), critical point, which had been discovered a few years earlier. Its qualitative and quantitative agreement w ...
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Thermodynamic Properties
In thermodynamics, a physical property is any property that is measurable, and whose value describes a state of a physical system. Thermodynamic properties are defined as characteristic features of a system, capable of specifying the system's state. Some constants, such as the ideal gas constant, , do not describe the state of a system, and so are not properties. On the other hand, some constants, such as (the freezing point depression constant, or cryoscopic constant), depend on the identity of a substance, and so may be considered to describe the state of a system, and therefore may be considered physical properties. "Specific" properties are expressed on a per mass basis. If the units were changed from per mass to, for example, per mole, the property would remain as it was (i.e., intensive or extensive). Regarding work and heat Work and heat are not thermodynamic properties, but rather ''process quantities:'' flows of energy across a system boundary. Systems do not ''co ...
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