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2019
At the critical point one has \(\left( \partial p/\partial V_M\right) _T =0\) and \(\left( \partial ^2 p/\partial V_M^2\right) _T=0\). By calculating the derivative of the van der Waals equation with respect to \(V_M\), we find that the first condition reads \(p_c-a/V_{Mc}^2+2ab/V_{Mc}^3=0\).
Primož Ziherl, Gregor Skačej
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At the critical point one has \(\left( \partial p/\partial V_M\right) _T =0\) and \(\left( \partial ^2 p/\partial V_M^2\right) _T=0\). By calculating the derivative of the van der Waals equation with respect to \(V_M\), we find that the first condition reads \(p_c-a/V_{Mc}^2+2ab/V_{Mc}^3=0\).
Primož Ziherl, Gregor Skačej
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Nuclear Physics A, 2014
Abstract The quark–gluon plasma (QGP), the deconfined high-temperature phase of QCD, is currently under extensive investigation in heavy-ion collision experiments at RHIC and LHC. The transition from the hadronic, low-temperature phase to the QGP is a rapid crossover, manifested by a significant change in bulk thermodynamic quantities.
Bazavov, Alexei +28 more
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Abstract The quark–gluon plasma (QGP), the deconfined high-temperature phase of QCD, is currently under extensive investigation in heavy-ion collision experiments at RHIC and LHC. The transition from the hadronic, low-temperature phase to the QGP is a rapid crossover, manifested by a significant change in bulk thermodynamic quantities.
Bazavov, Alexei +28 more
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2004
The equations of state appropriate to the interiors of most stars are simple in one major respect: they may be derived using the assumption that the radiation, gas, fluid, or even solid, is in a state of local thermodynamic equilibrium or LTE. By this we mean that at a particular position in the star complete thermodynamic equilibrium is as very nearly
Carl J. Hansen +2 more
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The equations of state appropriate to the interiors of most stars are simple in one major respect: they may be derived using the assumption that the radiation, gas, fluid, or even solid, is in a state of local thermodynamic equilibrium or LTE. By this we mean that at a particular position in the star complete thermodynamic equilibrium is as very nearly
Carl J. Hansen +2 more
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Derivatives for the equations of state
2007Derivation of partial derivatives for isothermal multi-component mixtures needed for development of universal models for multi-phase multi-component flows is presented. The equations of state and the derivative approximations as functions of temperature and pressure for the elementary mixture constituents are assumed to be known.
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2014
This chapter introduces the equation of state, defines the mean molecular weight, discusses the validity of the perfect gas hypothesis, and presents several examples regarding stellar photospheres.
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This chapter introduces the equation of state, defines the mean molecular weight, discusses the validity of the perfect gas hypothesis, and presents several examples regarding stellar photospheres.
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1989
Let us consider a one-component system such as discussed in Section 4.1. At any given temperature, the a(V) curve has a last phase transition region; at volumes larger than those, no more phase transitions occur and the system is said to be a gas. At temperatures above the critical temperature, this definition implies that the gas phase is reached by ...
Gianni Astarita, Gianni Astarita
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Let us consider a one-component system such as discussed in Section 4.1. At any given temperature, the a(V) curve has a last phase transition region; at volumes larger than those, no more phase transitions occur and the system is said to be a gas. At temperatures above the critical temperature, this definition implies that the gas phase is reached by ...
Gianni Astarita, Gianni Astarita
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Equations of State and Constitutive Equations
Journal of Rheology, 1986Equations-of state information in the otherwise undeformed state as a starting point for the development of constitutive equations is considered in addition to thermodynamics, free energy functions, and conceptual difficulties including the definition of reference states for strain.
Robert F. Landel, Steven T. J. Peng
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2001
Having introduced the necessary statistical technique, we are now in a position to establish routes from statistical mechanics to thermodynamics, i.e. to observable macroscopic properties. There are three such routes, provided by energy pressure (virial) compressibility equations of state.
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Having introduced the necessary statistical technique, we are now in a position to establish routes from statistical mechanics to thermodynamics, i.e. to observable macroscopic properties. There are three such routes, provided by energy pressure (virial) compressibility equations of state.
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EQUATIONS OF STATE AS CONSERVATION EQUATIONS [PDF]
Chemical Engineering Communications, 1983 Equations of state are shown to be mathematically equivalent to conservation equations, when the distance-time plane is replaced by the pressure-temperature plane. The Clapeyron equation is consequently developed, as a “shock condition“, based on the discontinuity in molar volume between phases at equilibrium.
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1992
The gas inside a star consists of a mixture of molecules, atoms and electrons. At temperatures higher than a few times 104 K, the atoms have lost part of their electrons (or all their electrons), and are said to be (partly) ionized. The remaining atom is then called an ion.
Claude Doom, C. De Loore
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The gas inside a star consists of a mixture of molecules, atoms and electrons. At temperatures higher than a few times 104 K, the atoms have lost part of their electrons (or all their electrons), and are said to be (partly) ionized. The remaining atom is then called an ion.
Claude Doom, C. De Loore
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