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Clapeyron equation

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Water content (θ) as liquid estimated with the Clausius–<span class="search-highlight">Clapeyron</span> <span class="search-highlight">equation</span> ...
Published: 01 May 2016
Fig. 10. Water content (θ) as liquid estimated with the Clausius–Clapeyron equation and water retention curve as ice estimated with changes in volumetric heat capacity and as total from the sum of the liquid water content and the ice content at selected depths. The results at other depths
Journal Article
Published: 01 May 2016
Vadose Zone Journal (2016) 15 (5): vzj2015.11.0154.
... conductivity of frozen soils has been limited. Therefore, it is often estimated from the unsaturated hydraulic conductivity of unfrozen soil using temperature and the Clausius–Clapeyron equation, with inadequate validation. In this study, we simultaneously measured the unfrozen water content and hydraulic...
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Journal Article
Published: 01 November 2013
Vadose Zone Journal (2013) 12 (4): vzj2012.0162.
... depression was included by combining an expression for osmotic head with the Clapeyron equation and the van Genuchten soil water retention function. The coupled water flow and heat transport equations were solved using the Thomas algorithm and Picard iteration. Ice pressure was always assumed zero, and frost...
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Journal Article
Published: 01 April 1999
American Mineralogist (1999) 84 (4): 465–476.
... from this study are also compared to that obtained using the Clausius-Clapeyron equation. GeoRef, Copyright 2004, American Geological Institute. 1999 ...
Journal Article
Published: 01 November 2005
American Mineralogist (2005) 90 (11-12): 1835–1839.
... of the Clapeyron equation for a boundary between a solid phase and a more compressible liquid phase or largely liquid phase assemblage. Raman spectroscopy has been applied to ikaite only once before by Mikkelsen et al. (1999) . That study did not use high pressure to synthesize ikaite, but rather precipitated...
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Journal Article
Published: 01 February 1968
American Mineralogist (1968) 53 (1-2): 346–347.
... of the Clausius-Clapeyron equation. I am grateful to Dr. R. G. J. Strens of the University of Leeds for drawing my attention to this error. Copyright © 1968 by the Mineralogical Society of America 1968 Mineralogical Society of America ...
Journal Article
Published: 01 April 1962
American Mineralogist (1962) 47 (3-4_Part_1): 371–378.
...Boyd G. Ellis; M. M. Mortland Abstract A discussion is presented concerning the factors which affect calibration of a differential thermal analysis apparatus for determination of heats of reaction and the factors affecting the determination of heats of reaction by use of the Clausius-Clapeyron...
Series: GSA Special Papers
Published: 01 January 1942
DOI: 10.1130/SPE36-p175
... 3. Liquid-vapor critical data 185 In systems containing a single component, the change Δ T of the temperature of equilibrium between two phases resulting from a change of hydrostatic pressure Δ P upon the two phases is given by Clapeyron’s equation, Δ T /Δ P = T Δ V /Δ H , where T...
Image
Desorption water isotherms plot of two shales at two temperatures. As to be...
Published: 11 February 2014
Figure 4. Desorption water isotherms plot of two shales at two temperatures. As to be expected, the shales illustrate that at a given relative humidity ( p / p o ), the sample at the higher temperature has a lower WC. The arrows point to the inputs for the Clausius-Clapeyron
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Olivine (yellow), pyroxenes (brown and violet) and spinel (black) as seen i...
Published: 01 October 2010
Olivine (yellow), pyroxenes (brown and violet) and spinel (black) as seen in a thin section of peridotite from Saint Thibéry (Languedoc, France). As embodied in the Clausius-Clapeyron equation, the stability of spinel indicates a source 30 to 60 km deep. P hotograph by N icole S antarelli
Journal Article
Published: 01 May 2004
Vadose Zone Journal (2004) 3 (2): 693–704.
.... Edlefsen and Andersen (1943) later tried to describe the mutual dependence of temperature, water content, and solutes by means of a generalized and extended Clapeyron equation using thermodynamic equilibrium theory. The original form of the Clapeyron equation, which relates changes in pressures...
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Journal Article
Published: 01 February 2013
Vadose Zone Journal (2013) 12 (1): vzj2012.0049.
...) , and Everett (1961) . This theory relies on the Clapeyron equation describing thermodynamic equilibrium in a system at temperature T and containing ice at pressure P i and water at P w ( Prigogine and Defay, 1954 ; Jackson and Chalmers, 1958 ; Black, 1995 ): where L f is the latent heat...
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Journal Article
Published: 01 February 2013
Vadose Zone Journal (2013) 12 (1): vzj2012.0051.
... and to illustrate diversions in thinking. We will then comment on their relevance to a unifying theory using the Clapeyron equation and a new heave index. The Konrad publication defined a segregation potential: SP = v (Grad T f ) − 1 ( Konrad, 1993 , Eq. 74.1), where v is the upward Darcy flux...
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Measured soil volumetric liquid water content (v/v) versus temperature and ...
Published: 01 November 2007
F ig . 4. Measured soil volumetric liquid water content (v/v) versus temperature and fitted freezing characteristic curve using the combination of the van Genuchten (1980) equation and the general Clapeyron relation.
Journal Article
Published: 01 January 2005
Geological Magazine (2005) 142 (1): 141–142.
... with a section on changing atmosphere composition over geological time. In Chapter Nine thermodynamics is dealt with explicitly again, but now in the context of changing pressures and temperatures. The Clapeyron equation, Raoult’s and Henry’s laws are introduced and the practical application, thermobarometry...
Journal Article
Published: 01 February 2024
American Mineralogist (2024) 109 (2): 243–254.
...-crystal neutron diffraction data were collected at ambient- T and 685 °C. A fit of the experimental V-T data with a thermal equation of state yielded a thermal expansion coefficient at ambient conditions: α V 25°C = 1/ V 0 ·(∂ V /∂ T ) P ,25°C = 1.74(3)·10 –5 K –1 . A comparative analysis of the elastic...
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Journal Article
Published: 01 February 2015
American Mineralogist (2015) 100 (2-3): 378–384.
... with synchrotron radiation. The phase boundary between Na-pyroxene and Na-majorite was determined over the temperature interval of 1073–1973 K and was described by a linear equation P (GPa) = 12.39 + 0.0018× T (K). The Clapeyron slope (d P /d T ) determined in this study is similar to the one predicted by computer...
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Journal Article
Published: 01 May 2002
American Mineralogist (2002) 87 (5-6): 803–804.
... equations of thermodynamics and even derives the Clausius-Clapeyron equation. In later chapters he gives equations describing flow, and magmatic segregation, but uses none of his equations to prove any specific points or add to student understanding. So, he falls short of his goal to “leave students...
Journal Article
Published: 01 July 2020
American Mineralogist (2020) 105 (7): 1014–1020.
... and 215 GPa. This indicates that previous local density approximation (LDA) results underestimate the transition pressure by 10–15 GPa. Density functional perturbation theory calculations, carried out using GGA within the quasi-harmonic approximations, give Clapeyron slopes of 5.4 and −2.8 MPa/K for the β...
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Journal Article
Published: 01 April 2014
Vadose Zone Journal (2014) 13 (4): vzj2013.04.0071.
... with the differential form of the generalized Clapeyron equation (e.g., Black, 1995 ) for T < T f . Here, T f < T 0 is the freezing temperature, p l0 is the liquid pressure at the initiation of freezing, and ice pressure is assumed equal to atmospheric pressure p a at the initiation...
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