Triple Point and Critical Point

5 Key excerpts on "Triple Point and Critical Point"

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  eBook - PDF

  Principles of Engineering Thermodynamics, SI Edition

  • John Reisel(Author)
  • 2021(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  At the intersection of all three phases, there is a pressure and temperature where all three phases coexist. On a P-T diagram, this is called the triple point; however, it should be noted that this state exists at a range of specific volumes and FIGURE 3.2 A P-v-T surface for substances that contract upon freezing (most substances). Gas Critical Temperature Constant-Temperature Line Constant-Pressure Line Critical State Triple State Solid and Liquid Solid and Vapor Liquid and Vapor Liquid (Pressure) P (Volume) v T (Temperature) Solid FIGURE 3.3 A P-T diagram of water. P T Solid Triple Point Liquid Critical Point Vapor Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 3 Thermodynamic Properties and Equations of State 72 is more appropriately called the triple line (as will be seen on a P-v diagram). Another point of interest is the end of the line dividing the liquid and vapor phases. This point is called the critical point, and it represents the state at which the liquid and vapor phases become indistinct. Recall that substances in both the liquid and the gas phase are free to move, with the primary dif- ference between the phases being the strength of the intermolecular forces. The forces in the gas phase tend to be weak and allow indi- vidual molecules to float freely, whereas the forces in a liquid tend to bind neighboring molecules together. If we start to increase the temperature of a high-pressure liquid, the forces attracting the molecules begin to be weakened by the increasing molecular kinetic energy of the high-temperature molecules.

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  Natural Gas Hydrates

  A Guide for Engineers

  • John Carroll(Author)
  • 2003(Publication Date)
  • Gulf Professional Publishing

    (Publisher)

  In this case, the phase rule says there are zero degrees of freedom. Thus, this is a fixed point in the pressure-temperature plane and is called a triple point . The location of the triple point is at the intersection of the two-phase loci. 3. Three two-phase loci intersect at a triple point, a point where three phases are in equilibrium . As a corollary to Rule 3, the vapor pressure, melting, and sublimation curves intersect at a vapor-liquid-solid triple point. This is the most common triple point, but because multiple solids can exist, there may be other triple points; John J. Carroll 213 however, there cannot be a single-component liquid-liquid-vapor triple point because, as was stated earlier, two liquid phases cannot exist for a pure component. The critical points of components found in natural gas are listed in Table 9-1. This table also lists the vapor-liquid-solid triple points for these substances. Critical points for pure components are fairly well established, and large tabulations are available. One reason for this is that the critical point is an important parameter in the correlation of fluid properties. Water Figure 9-1 shows the pressure-temperature diagram for water. This plot is to scale and shows the vapor pressure, melting curve, and sublimation curve. As was discussed earlier, note how the three loci intersect in a triple point. Also note how the three two-phase loci map out the single-phase regions. For example, the single-phase vapor region is bounded by the vapor + liquid locus and the vapor + solid locus. Similar diagrams could have been constructed for the other components commonly found in natural gas.

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  Supercritical Fluid Nanotechnology

  Advances and Applications in Composites and Hybrid Nanomaterials

  • Concepcion Domingo Pascual, Pascale Subra-Paternault(Authors)
  • 2015(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  2.1 Introduction: The Near-Critical Region of Fluids 2.1.1 What Is a Supercritical Fluid? Before we get into the details of the singularities of the critical point, let’s start with some definitions. A phase is a homogeneous region of matter in which there is no spatial variation in average density, energy, composition, or other macroscopic properties. The coexistence of phases in thermodynamic equilibrium with one another in a system consisting of two or more phases is called phase equilibrium. The simplest examples of phase equilibrium are the equilibrium of a liquid and its saturated vapor, such as liquid water and its vapor, and the equilibrium of a liquid in equilibrium with its solid phase, such as liquid water and ice at the melting point of ice. The temperature at which a phase transition occurs—for example, a boiling point or a melting point—changes if the pressure changes. The temperature change that results from an infinitesimal change in pressure is given by the Clapeyron equation. Graphs that represent the interrelation of the various thermodynamic variables at phase equilibrium are called phase transition curves or surfaces; a set of such curves or surfaces is known as a phase diagram. A phase transition curve may either intersect two other phase transition curves at a triple point or terminate at a critical point. At the critical point the densities of the liquid and gas phases become equal and the distinction between them disappears, resulting in a single phase, called supercritical. A supercritical fluid is then any substance at a temperature and pressure above its critical point. Close to the critical point, small changes in pressure or temperature result in large changes in density. In addition, there is no surface tension in a supercritical fluid, as there is no liquid-/ gas-phase boundary.

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  Liquids and Liquid Mixtures

  Butterworths Monographs in Chemistry

  • J S Rowlinson, F L Swinton, Patrick Perlmutter, A D Buckingham, S Danishefsky(Authors)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 3 The critical state 3.1 Thermodynamics of the critical point The critical state of a fluid is represented by the point on the (p, V, T) surface where the volumes of the gas and liquid phases become identical. The mechanical stability of this state is of a lower order than that required by the inequalities of Section 2.1. Such a point lies on the border separating the stable and unstable parts of a continuous (p,K T) surface. A preliminary discussion of the behaviour of thermodynamic functions at and near this point may therefore be based on the (A 9 V,T) surface. It is impossible to use the (G, p, T) surface, since the condition of mechanical stability cannot be derived from it. Liquid and gas can exist together at equilibrium if the temperatures, pressures and chemical potentials of the two phases are equal. These equalities may be written in terms of the molar Helmholtz free energy of a one-component system : T 1 = T g (3.1) (da/dvf T = (ôa/dvf T (3.2) a 1 -vda/dv) l T = a g -v*(da/dvf T (3.3) Thus a graph of a as a function of v at constant temperature is represented by the full line in Figure 3.1. The volumes of the coexistent phases, A and D, are connected by a straight tie-line of slope (— p) which, by equations (3.2) and (3.3), must be the common tangent to both branches of the curve. Thus the experimental free energy is not a continuous differentiable function of volume at the dew and bubble points. It is, however, convenient to treat it as such a function of the form shown by the dashed curve ABCD. This lies above the full curve and is therefore a less stable state. The instability of the curve ABCD is of two kinds; between B and C the derivative (ê 2 a/dv 2 ) T is negative, or (dp/dv) T is positive. Such a system is mechanically unstable ; the parts of the curve between A and B and between C and D are mechanically stable but are metastable with respect to the two-phase system.

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  Physics of Fluids in Microgravity

  • Rodolfo Monti(Author)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  Critical ana supercritical fluids and related phenomena D. Beysens and Y. Garrabos Fluids are called 'critical' or 'near-critical' when their temperature and pressure are near their gas-liquid critical point (CP). In a wide domain around the CP, important parameters (e.g. isothermal compressibility, density of gas and liquid phases, surface tension) obey universal power laws and are easily varied or scaled by using small changes in temperature. The highly variable properties of near-critical fluids make them very appealing for studying many interesting phenomena that are valid for all fluids. Above the critical temperature and pressure, such fluids are called 'supercritical' (Figure 8.1). In this region, fluids exhibit a number of specific properties (large density, low viscosity, large diffusivity) which make them intermediate between liquids and gases. In addition, their isothermal compressibility can become very large, especially when they approach the critical point. Their use under normal gravity conditions - or under reduced gravity, e.g. for the storage of cryogenic propellants - raises fundamental questions concerning fluid dynamics, heat transfer, interfacial phenomena and chemical process. Experimentation in the ISS is a good opportunity to answer these questions and enhance the knowledge in this field. Figure 8.1 Phase diagram of a pure substance in the plane temperature-pressure. The supercritical 'state' corresponds to a compressed gas that exhibits the density of a liquid. 224 D. Bey sens and Y. Garrabos In the following, we first review the main characteristics of the critical state (The Basics of Critical Point Phenomena in Fluids), then analyse some important hydrodynamics (The Role of Hydrodynamics), considering both the effect of gravity-induced hydrodynamics (External Hydrodynamics due to Gravity) and the effects when gravity is suppressed (Zero-G Hydrodynamics).

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