Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater

2006 ◽  
Vol 23 (12) ◽  
pp. 1709-1728 ◽  
Author(s):  
David R. Jackett ◽  
Trevor J. McDougall ◽  
Rainer Feistel ◽  
Daniel G. Wright ◽  
Stephen M. Griffies
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermodynamic Potential ◽  
Potential Temperature ◽  
Inverse Function ◽  
Freezing Temperature ◽  
Ocean Models ◽  
The Difference ◽  
New Equation ◽  
Density Equation

Abstract Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

scholarly journals Materials in thermodynamic potential gradients

2003 ◽  
Vol 75 (7) ◽  
pp. 889-903 ◽  
Author(s):  
M. Martin
Keyword(s):  
Thermodynamic Potential ◽  
Potential Temperature ◽  
Electrical Potential ◽  
Potential Gradient ◽  
Ionic Conductivities ◽  
Transport Processes ◽  
Morphological Stability ◽  
Potential Gradients ◽  
The Difference ◽  
Ion Conducting

In materials that are exposed to thermodynamic potential gradients (i.e., gradients of chemical potentials, electrical potential, temperature, or pressure), transport processes of the mobile components occur. These transport processes and the coupling between different processes are not only of fundamental interest, but are also the origin of degradation processes, such as kinetic demixing and decomposition and changes in the morphology of the material, all of which are of great practical relevance.Two classes of materials will be considered: semi-and ion-conducting oxides and ion-conducting halides. In oxides, kinetic demixing of the cations in a multicomponent oxide and kinetic decomposition of the oxide under the influence of an applied thermodynamic potential gradient will be considered for homovalent oxide solid solutions and for heterovalently doped oxides. In ion-conducting halides, the morphological stability of solid/solid interfaces, which are driven by an external electrical potential gradient, is studied. Monte Carlo simulations show that the morphological stability of the interface is determined by the difference in the ionic conductivities of the two crystals.

scholarly journals The interpretation of temperature and salinity variables in numerical ocean model output, and the calculation of heat fluxes and heat content

2021 ◽  
Author(s):  
Trevor J. McDougall ◽  
Paul M. Barker ◽  
Ryan M. Holmes ◽  
Rich Pawlowicz ◽  
Stephen M. Griffies ◽  
...  
Keyword(s):  
Equation Of State ◽  
Potential Temperature ◽  
Heat Content ◽  
Coupled Model ◽  
Heat Fluxes ◽  
Ocean Heat Content ◽  
Global Ocean ◽  
Volume Integral ◽  
Meridional Heat Transport ◽  
Ocean Models

Abstract. The 2010 international thermodynamic equation of seawater, TEOS-10, defined the enthalpy and entropy of seawater, thus enabling the global ocean heat content to be calculated as the volume integral of the product of in situ density, ρ, and potential enthalpy, h0 (with reference sea pressure of 0 dbar). In terms of Conservative Temperature, Θ, ocean heat content is the volume integral of ρcp0Θ, where cp0 is a constant isobaric heat capacity. However, several ocean models in CMIP6 (as well as all of those in previous Coupled Model Intercomparison Project phases, such as CMIP5) have not been converted from EOS-80 (Equation of State - 1980) to TEOS-10, so the question arises of how the salinity and temperature variables in these models should be interpreted. In this article we address how heat content, surface heat fluxes and the meridional heat transport are best calculated in these models, and also how these quantities should be compared with the corresponding quantities calculated from observations. We conclude that even though a model uses the EOS-80 equation of state which expects potential temperature as its input temperature, the most appropriate interpretation of the model's temperature variable is actually Conservative Temperature. This interpretation is needed to ensure that the air-sea heat flux that leaves/arrives-in the atmosphere is the same as that which arrives-in/leaves the ocean. We also show that the salinity variable carried by TEOS-10 based models is Preformed Salinity, while the prognostic salinity of EOS-80 based models is also proportional to Preformed Salinity. These interpretations of the salinity and temperature variables in ocean models are an update on the comprehensive Griffies et al. (2016) paper that discusses the interpretation of many aspects of coupled model runs.

scholarly journals Experimental Study of the Space–Time Effect of a Double-Pipe Frozen Curtain Formation with Different Groundwater Velocities

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3830
Author(s):  
Shicheng Sun ◽  
Chuanxin Rong ◽  
Hua Cheng ◽  
Bin Wang ◽  
Xiaogang Jiang ◽  
...  
Keyword(s):  
Freezing Temperature ◽  
Physical Model Test ◽  
Sand Layer ◽  
Test Results ◽  
Groundwater Velocity ◽  
Test Platform ◽  
The Difference ◽  
Freezing Test ◽  
Double Pipe ◽  
Thermal Physical Properties

Groundwater velocity has significant effects on the formation of a frozen curtain during freezing. In order to study the influence of the velocity on a frozen curtain, a large physical model test platform was established for double-pipe freezing. Based on this platform, freezing tests for different velocities were carried out. Quartz sand was selected as a similar material. The freezing temperature of the saturated sand layer was found by analyzing the results of the nuclear magnetic resonance (NMR). Based on the study of the thermal physical properties of the sand layer, the freezing test results were analyzed, and the results showed that the flow led to the differential development of the temperature between the upstream and downstream sections of the freezing pipes. Moreover, the larger the velocity, the greater the difference. The flow prolonged the overlapping time of the frozen curtains. Additionally, the flow slowed down the development of the frozen curtain area and the frozen curtain thickness. The larger the flow velocity, the greater the inhibition of the flow on the development of the frozen curtain. The test results can provide more references for the design and construction of freezing engineering with flowing groundwater.

A New Equation of State for Fluids

1928 ◽  
Vol 63 (5) ◽  
pp. 229 ◽  
Author(s):  
James A. Beattie ◽  
Oscar C. Bridgeman
Keyword(s):  
Equation Of State ◽  
New Equation

scholarly journals Analysis of Equation of State for Carbon Nanotubes

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jeewan Chandra ◽  
Pooja Kapri Bhatt ◽  
Kuldeep Kholiya
Keyword(s):  
Experimental Data ◽  
Carbon Nanotubes ◽  
Thermal Expansion ◽  
Carbon Nanotube ◽  
Equation Of State ◽  
Compression Behavior ◽  
Nanotube Bundles ◽  
The Individual

Compression behavior of carbon nanotube bundles and individual carbon nanotubes within the bundle has been studied by using the Suzuki, Shanker, and usual Tait formulations. It is found that the Suzuki formulation is not capable of explaining the compression behavior of nanomaterials. Shanker formulation slightly improves the results obtained by the Suzuki formulation, but only usual Tait’s equation (UTE) of state gives results in agreement to the experimental data. The present study reveals that the product of bulk modules and the coefficient of volume thermal expansion remain constant for carbon nanotubes. It has also been found that the individual carbon nanotubes are less compressible than bundles of carbon nanotubes.

scholarly journals A NEW EQUATION OF STATE

1929 ◽  
Vol 15 (1) ◽  
pp. 11-18 ◽  
Author(s):  
H. J. Brennen
Keyword(s):  
Equation Of State ◽  
New Equation

The Field Measure of Special Strata Freezing Temperature in West Area

2012 ◽  
Vol 170-173 ◽  
pp. 1207-1210
Author(s):  
Jun Hao Chen ◽  
Rui Zhang
Keyword(s):  
Engineering Design ◽  
Freezing Temperature ◽  
Design Requirement ◽  
Shaft Sinking ◽  
Design Requirements ◽  
Security Information ◽  
Frozen Wall ◽  
The Difference ◽  
Circle Tube ◽  
Field Measure

A new round of upsurge of mine well construction were set off in the west area, but there are many problems, this article through the field measure of special strata freezing temperature in Bo-jiang-hai-zi coal mine airshaft, use the freezing shaft sinking security information network visualization platform that developed by Anhui University of Science and Technology, analysis several different strata, obtain the overall temperatre decline rate, and compare the difference between in-site shaft well temperature and the calculation value at different position, and difference is very small, it shows that the platform can good response the actual situation. Through calculation, the frozen wall thickness, average of frozen wall temperature, shaft well temperature are meet the engineering design requirement, so propose that in west area at the freezing method mine well construction, the main purpose is waterproof, and use single circle tube freezing can satisfy engineering design requirements.

scholarly journals THE ACCUMULATION OF ELECTROLYTES

1932 ◽  
Vol 15 (6) ◽  
pp. 667-689 ◽  
Author(s):  
W. J. V. Osterhout ◽  
W. M. Stanley
Keyword(s):  
Steady State ◽  
Osmotic Pressure ◽  
Aqueous Phase ◽  
Thermodynamic Potential ◽  
Ph Value ◽  
Molecular Form ◽  
External Solution ◽  
Aqueous Layer ◽  
The Difference ◽  
Pass Through

Inasmuch as attempts to explain accumulation by the Donnan principle have failed in the case of Valonia, a hypothesis of the steady state has been formulated to explain what occurs. In order to see whether this hypothesis is in harmony with physico-chemical laws attempts have been made to imitate its chief features by means of a model. The model consists of a non-aqueous layer (representing the protoplasmic surface) placed between an alkaline aqueous phase (representing the external solution) and a more acid aqueous phase (representing the cell sap). The model reproduces most of the features of the hypothesis. Attention may be called to the following points. 1. The semipermeable surface is a continuous non-aqueous phase. 2. Potassium penetrates by combining with an acid HX in the non-aqueous layer to form KX which in turn reacts with an acid HA in the sap to form KA. Since KX is little dissociated in the non-aqueous layer potassium appears to pass through it chiefly in molecular form. 3. The internal composition depends on permeability, e.g., sodium penetrates less rapidly than potassium and in consequence potassium predominates over sodium in the "artificial sap." The order of penetration in the model is the same as in Valonia, i.e., K > Na > Ca > Mg, and Cl > SO4, but the quantitative resemblance is not close, e.g., the difference between potassium and sodium, and chloride and sulfate is much less in the model. 4. The formation of KA and NaA in the sap raises its osmotic pressure and water enters. 5. The concentration of potassium and sodium and the osmotic pressure become much greater inside than outside. For example, potassium may become 200 times as concentrated inside as outside. 6. No equilibrium occurs but a steady state is reached in which water and salt enter at the same rate so that the composition of the sap remains constant as its volume increases. 7. Since no equilibrium occurs there is a difference of thermodynamic potential between inside and outside. At the start the thermodynamic potential of KOH is much greater outside than inside. This difference gradually diminishes and in the steady state has about the same value as in Valonia. The difference in pH value between the internal and external solutions is also similar in both cases (about 2 pH units). 8. Accumulation does not depend on the presence of molecules or ions inside which are unable to pass out. One important feature of the hypothesis is not seen in the model: this is the exchange of HCO3 for Cl-. Experiments on this point are in progress.

The Equation of State and the Temperature, Pressure, and Shear Dependence of Viscosity for a Highly Viscous Reference Liquid, Dipentaerythritol Hexaisononanoate

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Scott Bair ◽  
Tsuyoshi Yamaguchi
Keyword(s):  
Molecular Weight ◽  
Shear Stress ◽  
Equation Of State ◽  
High Molecular Weight ◽  
Free Volume ◽  
Newtonian Limit ◽  
Scaling Models ◽  
The Difference ◽  
Better Than ◽  
Low Shear

Measurements are reported for dipentaerythritol hexaisononanoate (DiPEiC9) of pressure–volume–temperature (pVT) response to pressures to 400 MPa and temperatures to 100 °C, and of viscosity at pressures to 700 MPa and temperatures to 90 °C and shear stress to 18 MPa. These data complement the low-shear viscosities published by Harris to pressures to 200 MPa and the compressions by Fandiño et al. to 70 MPa. The improved Yasutomi correlation reproduces all viscosity measurements with accuracy better than the Doolittle free volume and the Bair and Casalini thermodynamic scaling models which require an equation of state (EoS). The interaction parameter for thermodynamic scaling, γ = 3.6, is less than that reported by Harris (γ = 4.2) and the difference is primarily in the choice of EoS. The shear stress at the Newtonian limit, about 6 MPa, is exceptionally large given the high molecular weight of DiPEiC9. The large Newtonian limit is also seen in the oscillatory shear response.

Sign in / Sign up

Export Citation Format

Share Document