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Ehrenfest Equations
Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. The Clausius–Clapeyron relation does not make sense for second-order phase transitions,Sivuhin D.V. General physics course. V.2. ''Thermodynamics and molecular physics''. 2005 as both specific entropy and specific volume do not change in second-order phase transitions. Quantitative consideration Ehrenfest equations are the consequence of continuity of specific entropy s and specific volume v, which are first derivatives of specific Gibbs free energy – in second-order phase transitions. If one considers specific entropy s as a function of temperature and pressure, then its differential is: ds = \left( \right)_P dT + \left( \right)_T dP. As \left( \right)_P = , \left( \right)_T = - \left( \right)_P , then the differential of specific entropy also is: d = dT - \left( \right)_P dP, where i= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Ehrenfest
Paul Ehrenfest (; 18 January 1880 – 25 September 1933) was an Austrian Theoretical physics, theoretical physicist who made major contributions to statistical mechanics and its relation to quantum physics, quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. He befriended Albert Einstein on a visit to Prague in 1912 and became a professor in Leiden, where he frequently hosted Einstein. Suffering from depression, in 1933 Ehrenfest killed his disabled son, Wassik, and then himself. Biography Paul Ehrenfest was born on 18 January 1880 in Vienna to Ashkenazi Jews, Jewish parents, who were originally from Loštice in Moravia (now part of the Czech Republic). His parents, Sigmund Ehrenfest and Johanna Jellinek, managed a grocery store. Although the family was not overly religious, Paul studied Hebrew language, Hebrew and Jewish history. Later, he always emphasized his Jewish ancestry. Ehrenfest excelled in grade school but did not do well at the Akad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Heat Capacity
In thermodynamics, the specific heat capacity (symbol ) of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of of water by is , so the specific heat capacity of water is . Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about at 20 °C; but that of ice, just below 0 °C, is only . The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 J⋅kg−1⋅K−1, and 143 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Volume
In thermodynamics, the specific volume of a substance (symbol: , nu) is the quotient of the substance's volume () to its mass (): :\nu = \frac It is a mass-specific intrinsic property of the substance. It is the reciprocal of density (rho) and it is also related to the molar volume and molar mass: :\nu = \rho^ = \frac The standard unit of specific volume is cubic meters per kilogram (m3/kg), but other units include ft3/lb, ft3/slug, or mL/g. Specific volume for an ideal gas is related to the molar gas constant () and the gas's temperature (), pressure (), and molar mass (): : \nu = \frac It's based on the ideal gas law, PV = , and the amount of substance In chemistry, the amount of substance (symbol ) in a given sample of matter is defined as a ratio () between the particle number, number of elementary entities () and the Avogadro constant (). The unit of amount of substance in the International ..., n = m/M Applications Specific volume is commonly applied to: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transitions
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clausius–Clapeyron Relation
The Clausius–Clapeyron relation, in chemical thermodynamics, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matter of a single constituent. It is named after Rudolf Clausius and Benoît Paul Émile Clapeyron. However, this relation was in fact originally derived by Sadi Carnot in his '' Reflections on the Motive Power of Fire'', which was published in 1824 but largely ignored until it was rediscovered by Clausius, Clapeyron, and Lord Kelvin decades later. Kelvin said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning." Kelvin and his brother James Thomson confirmed the relation experimentally in 1849–50, and it was historically important as a very early successful application of theoretical thermodynamics. Its relevance to meteorology and climatology is the increase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change and information systems including the transmission of information in telecommunication. Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible. The thermodynami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Free Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–volume work, pressure–volume work, that may be performed by a closed system, thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as G(p,T) = U + pV - TS = H - TS where: * U is the internal energy of the system * H is the enthalpy of the system * S is the entropy of the system * T is the temperature of the system * V is the volume of the system * p is the pressure of the system (which must be equal to that of the surroundings for mechanical equilibrium). The Gibbs free energy change (, measured in joules in International System of Units, SI) is the ''maximum'' amount of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called ''centigrade''), the Fahrenheit scale (°F), and the Kelvin scale (K), with the third being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics. It would be impossible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various #Units, units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the International System of Units, SI unit of pressure, the Pascal (unit), pascal (Pa), for example, is one newton (unit), newton per square metre (N/m2); similarly, the Pound (force), pound-force per square inch (Pound per square inch, psi, symbol lbf/in2) is the traditional unit of pressure in the imperial units, imperial and United States customary units, US customary systems. Pressure ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Of A Function
In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined by dy = f'(x)\,dx, where f'(x) is the derivative of with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equation dy = \frac\, dx holds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writes df(x) = f'(x)\,dx. The precise meaning of the variables dy and dx depends on the context of the application and the required level of mathematical rigor. The domain of these variables may take on a particular geometrical significance if the differential is regarded as a particular differential form, or analytical significance if the differential is regarded as a linear approximation to the increment of a function. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transition
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
