Generalized Clausius-Clapeyron Equation Research Articles

Similarity of soil freezing characteristic and soil water characteristic: Application in saline frozen soil hydraulic properties prediction

Accurate prediction of hydraulic properties in frozen soils is of importance for the role of frozen soil water dynamics in cold region water cycles. Furthermore, the existence of solute is known to complicate the water, heat and solute transport in frozen soils. To predict hydraulic properties in saline frozen soils more accurately, experiments on soil water characteristic curves (SWCCs) and soil freezing characteristic curves (SFCCs) were conducted under five solute types combined with five solute content levels. Results showed that, under low salinity conditions (e.g., no higher than 1.0% g/g dry soil), the conversion of SFCCs to SWCCs (or SWCCs to SFCCs) was possible by using generalized Clausius-Clapeyron equation (GCCE). The combination of these two curves could predict more reliable hydraulic parameters for the compensation in experimental data ranges. Comparison of the combining method with other direct or indirect experimental results indicated that accurate and integral θl − h relationships could result in accurate estimation in hydraulic parameters in frozen saline soils. This study has proposed an improved method for predicting hydraulic parameters in saline frozen soils, and more validation work with experiments under various soil and solute conditions is needed before incorporating it into frozen soil properties predicting frameworks.

A New Type of Phase Transition Based on the Clausius-Clapeyron Relation Involving a Change in Spatial Dimension

Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transitions from dimension of space, n, to dimension of space, (n - 1), and vice versa, from (n - 1) to n -dimensional space. For the former we can calculate a specific release of latent heat, a decrease in entropy, and a change in volume. For the latter, we derive an expression for the absorption of heat, the increase in entropy, and the difference in volume. Total energy is conserved in this transformation process. We apply this model to black-body radiation in the early universe and find that for a transition from n = 4 to (n - 1) = 3, there is an immense decrease in entropy accompanied by a tremendous change in volume, much like condensation. However, unlike condensation, the volume change is not three-dimensional. The volume changes from V4, a four-dimensional construct, to V3, a three-dimensional entity, which can be considered a subspace of V4. As a specific example of how the equation works, we consider a transition temperature of 3 × 1027 Kelvin, and assume, furthermore, that the latent heat release in three-dimensional space is 1.8 × 1094 Joules. We find that for this transition, the internal energy densities, the entropy densities, and the volumes assume the following values (photons only). In four-dimensional space, we obtain, u4 = 1.15×10125 J⋅ m-4, s4 = 4.81×1097 J⋅ m-4⋅ K-1, and V4 = 2.14×10-31 m4. In three-dimensional space, we have u3 = 6.13×1094 J⋅ m-3, s3 = 2.72×1067 J⋅ m-3⋅ K-1, and V3 = 0.267 m3. The subscripts 3 and 4 refer to three-dimensional and four-dimensional quantities, respectively. We speculate, based on the tremendous change in volume, the explosive release of latent heat, and the magnitudes of the other quantities calculated, that this type of transition might have a connection to inflation. With this work, we prove that space, in and of itself, has an inherent energy content. This is so because giving up space releases latent heat, and buying space costs latent heat, which we can quantify. This is in addition to the energy contained within that space due to radiation. We can determine the specific amount of heat exchanged in transitioning between different spatial dimensions with our generalized Clausius-Clapeyron equation.

Electrocaloric effect in BaTiO3 at all three ferroelectric transitions: Anisotropy and inverse caloric effects

We study the electrocaloric (EC) effect in bulk BaTiO$_3$ (BTO) using molecular dynamics simulations of a first principles-based effective Hamiltonian, combined with direct measurements of the adiabatic EC temperature change in BTO single crystals. We examine in particular the dependence of the EC effect on the direction of the applied electric field at all three ferroelectric transitions, and we show that the EC response is strongly anisotropic. Most strikingly, an inverse caloric effect, i.e., a temperature increase under field removal, can be observed at both ferroelectric-ferroelectric transitions for certain orientations of the applied field. Using the generalized Clausius-Clapeyron equation, we show that the inverse effect occurs exactly for those cases where the field orientation favors the higher temperature/higher entropy phase. Our simulations show that temperature changes of around 1 K can in principle be obtained at the tetragonal-orthorhombic transition close to room temperature, even for small applied fields, provided that the applied field is strong enough to drive the system across the first order transition line. Our direct EC measurements for BTO single crystals at the cubic-tetragonal and at the tetragonal-orthorhombic transitions are in good qualitative agreement with our theoretical predictions, and in particular confirm the occurrence of an inverse EC effect at the tetragonal-orthorhombic transition for electric fields applied along the [001] pseudo-cubic direction.

Basic Study on the Frost Heave Pressure of Rocks

Frost heave in rocks is caused by the frost heave pressure (pore ice pressure) generated by the freezing of pore water, which then cracks the rock. The present work attempts to clarify the frost heave pressure of rocks by experiments at four temperature conditions. Ohya tuff and Kimachi sandstone, in which the occurrence of frost heave has previously been confirmed, were used as specimens.Measurements of these experiments were the internal temperature of the rocks during the freezing process and the location where the ice lens formed.These two parameters made it possible to determine the temperature of the location where the ice lens formed. A generalized Clausius-Clapeyron equation was used to calculate the pore ice pressure. The results indicated that the temperature at the location of ice lens formation depends on the types of rock, but not on the temperature gradient during freezing.It was also confirmed that frost heave in rocks with a higher tensile strength appears at locations with a lower temperature, while that in rocks with a lower tensile strength appears at location of temperatures close to 0°C.These findings suggest that the location and temperature of the ice lens formation are dependent on the strength of the rock.

The Value of A Smile

The physical behaviors of water in the interface are the fundamental to discovering the engineering properties and environmental effects of aqueous porous media (e.g., soils). The pore water pressure (PWP) is a key parameter to characterize the pore water state (PWS) and its phase transition in the micro interface. Traditionally, the water in the interface is frequently believed to be uniform, negative in pressure and tensile based on macroscopic tests and Gibbs interface model. However, the water in the interface is a non-uniform and compressible fluid (part of tensile and part of compressed), forming a spatial profile of density and PWP depending on its distance from the substrate interface. Herein, we introduced the static and dynamic theory methods of non-uniform water based on diffuse interface model to analyze non-uniform water state dynamics and water density and PWP. Based on the theory of non-uniform water, we gave a clear stress analysis on soil water and developed the concepts of PWS, PWP and matric potential in classical soil mechanics. In addition, the phase transition theory of non-uniform water is also examined. In nature, the generalized Clausius-Clapeyron equation (GCCE) is consistent with Clapeyron equation. Therefore, a unified interpretation is proposed to justify the use of GCCE to represent frozen soil water dynamics. Furthermore, the PWP description of non-uniform water can be well verified by some experiments focusing on property variations in the interface area, including the spatial water density profile and unfrozen water content variations with decreasing temperature and other factors. In turn, PWP spatial distribution of non-uniform water and its states can well explain some key phenomena on phase transition during ice or hydrate formation, including the discrepancies of phase transition under a wide range of conditions

A General Approach to First Order Phase Transitions and the Anomalous Behavior of Coexisting Phases in the Magnetic Case

AbstractFirst order phase transitions for materials with exotic properties are usually believed to happen at fixed values of the intensive parameters (such as pressure, temperature, etc.) characterizing their properties. It is also considered that the extensive properties of the phases (such as entropy, volume, etc.) have discontinuities at the transition point, but that for each phase the intensive parameters remain constant during the transition. These features are a hallmark for systems described by two thermodynamic degrees of freedom. In this work it is shown that first order phase transitions must be understood in the broader framework of thermodynamic systems described by three or more degrees of freedom. This means that the transitions occur along intervals of the intensive parameters, that the properties of the phases coexisting during the transition may show peculiar behaviors characteristic of each system, and that a generalized Clausius–Clapeyron equation must be obeyed. These features for the magnetic case are confirmed, and it is shown that experimental calorimetric data agree well with the magnetic Clausius–Clapeyron equation for MnAs. An estimate for the point in the temperature‐field plane where the first order magnetic transition turns to a second order one is obtained (the critical parameters) for MnAs and Gd5Ge2Si2 compounds. Anomalous behavior of the volumes of the coexisting phases during the magnetic first order transition is measured, and it is shown that the anomalies for the individual phases are hidden in the behavior of the global properties as the volume.

A theoretical framework of one-dimensional sharp phase fronts in shape memory alloys

In this paper, we propose a one-dimensional (1D) sharp phase front-based theoretical framework for shape memory alloys (SMAs). An assumption of equality of the chemical potential at the phase front leads to a generalized Clausius–Clapeyron equation, which then gives the condition for the evolution of the phase front during phase transformation. The theoretical framework is general enough to incorporate any Helmholtz free energy function, and for that reason, if the Helmholtz free energy function is completely characterized, then so is the entire system of equations (including the condition for the phase boundary evolution). The small strain, quasistatic approximation of the theory in conjunction with a trilinear Helmholtz free energy function is used to predict the following two experiments: (i) constant deformation-rate phase transformation in a SMA single crystal; and (ii) constant load, temperature-induced transformation in a SMA polycrystalline wire.

Theoretical study of vapor pressure of pure liquids in porous media

There are reports in the literature describing vapor pressure reduction in capillaries or porous materials that is substantially in excess of that predicted by the classical Kelvin equation, which relates the vapor pressure over the curved vapor–liquid interface inside a pore to its radius of curvature. However, this effect is negligible except for pores of radii less than 0.1 μm. In fact, substantial vapor pressure reduction has been observed in larger pores. This is explained here on the basis of the effect of long-range surface forces exerted by the solid on the liquid, while the application of the Kelvin equation to capillary-held liquids tacitly assumes the solid to exert no influence. A generalized Clausius–Clapeyron equation in the presence of external force fields is first obtained. The resulting excess enthalpy of vaporization is next semi-quantitatively related to the molar polarization of the liquid and the porous solid based on a molecular approach.

A Thermodynamic Study of Liquid Transportation in Freezing Porous Media.

A dynamic equation of state at the solid-liquid interface for a lipuid-saturated solid-liquid-porous system has been derived from a thermodynamic study modeling simultaneous heat and mass transfer through purous media from the liquid supply front to the solid-liquid interface. This is the first step in building a mathematical model which macroscopically describes a freezing expansion phenomenon with mass transfer in saturated porous media. It has been revealed that the derived dynamic equation of state generalizes the so-called generalized Clausius-Clapeyron equation, i.e.the static equation of state for porous media without mass transfer, and that mechanical energy produced at the solid-liquid interface is equal to mechanical energy dissipation due to the mass transfer.

多孔質体間隙における動的固液相平衡に関する実験的研究

The so-called generalized Clausius-Clapeyron equation (GCCE), i.e., the static equation of state for solid-liquid-porous media systems without liquid flow through the pores, has been experimentally examined by measuring the pore liquid pressure at the solid-liquid interface, in order to verify the accuracy of our method for measuring the unfrozen pore liquid pressure. Several series of experiments were carried out using water-saturated Ohya-tuff as a porous medium specimen which was cooled from the top down. In these experiments the solid-liquid interface was always fixed on the top surface of the specimen. The experimental results imply that the measurement method should be useful for determining the relative value of the unfrozen pore liquid pressure.

A Thermodynamic Study of Liquid Transortation in Freezing Porous Media.

A dynamic equation of state at the interface for a liquid-saturated solid-liquid porous system has been derived from a thermodynamic study modeling simultaneous heat and mass transfer through porous media from the liquid supply front to the interface, as the very first step in building a mathematical model which may macroscopically describe a freezing expansion phenomenon with mass transfer in saturated porous media. It has been revealed that the derived dynamic equation of state generalizes the so-called generalized Clausius-Clapeyron equation, i.e. the static equation of state for porous media without mass transfer, and that mechanical energy produced at the interface is equal to mechanical energy dissipation due to the mass transfer.

An Experimental Study of Static Solid-Liquid Phase Equilibrium in the Pores of a Porous Medium.

The so-called generalized Clausius-Clapeyron equation (GCCE), i.e., the static equation of state for "solid-liquid-porous media" systems without liquid flow through the pores, has been experimentally examined by measuring the pore liquid pressure at the solid-liquid interface, in order to verify the accuracy of our method for measuring the unfrozen pore liquid pressure. Several series of experiments were carried out using water-saturated Ohya-tuff as a porous medium specimen which was cooled from the top down. In these experiments the solid-liquid interface was always fixed on the top surface of the specimen. The experimental results imply that the measurement method should be useful for determining the relative value of the unfrozen pore liquid pressure.