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Interaction Between Soil Particles and Soil Solution
Published in Shingo Iwata, Toshio Tabuchi, Benno P. Warkentin, Soil-Water Interactions, 2020
Shingo Iwata, Toshio Tabuchi, Benno P. Warkentin
The driving force for water migration in frozen soils in this theory is the pressure difference produced by the temperature difference. However, the theory does not define the physical mechanism causing the pressure difference. This is a weak point recognized generally in applying the Clausius-Clapeyron relation to a system. In addition, it should be noted that such an application of the Clausius-Clapeyron relation is thermodynamically correct only when pressure and temperature are the only variables defining the state of the system, or when state variables other than temperature and pressure, such as the solute concentration, the electric strength, and the intermolecular force field, are kept constant.
Introduction to Thermodynamics
Published in Caroline Desgranges, Jerome Delhommelle, A Mole of Chemistry, 2020
Caroline Desgranges, Jerome Delhommelle
Let us add that Clapeyron is also known for an equation bearing his name, later called the Clausius–Clapeyron relation. This time, Clapeyron concentrates his efforts on the PT plane. He succeeds in determining “phase diagrams”, which delimit regions in the PT plane where the different states of matter (liquid, solid, vapor) exist. Thanks to this representation, it is thus possible to know if, for example, ice is converted into water for a given temperature and pressure. We can then easily define the changes in states, such as vaporization (transition from a liquid state to a vapor state), condensation (vapor to liquid), solidification (liquid to solid), fusion (solid to liquid) and sublimation (solid to gas). The Clausius–Clapeyron relation gives the slope of the tangents of this curve: dP/dT = L/(TdV), where dP/dT is the slope of the tangent to the coexistence curve at any point, L the latent heat and dV is the specific volume change of the phase transition. Nowadays, latent heat is called enthalpy of change and is defined as the necessary quantity of energy for 1 mole or 1 kg of a pure body to change its state.
Condensation, Evaporation, and Boiling
Published in Anthony F. Mills, Heat and Mass Transfer, 2018
It is important to note that this definition is stated in terms of the vapor saturation temperature Tsat(pv)and not the temperature of the vapor molecules incident on the surface, Tv. The latter differs from the condensate surface temperature Ts by what is essentially the temperature “jump” defined for the slip flow regime of rarefied gas flow. This difference is negligible in most situations of concern. Also, since there is usually a negligible pressure gradient normal to the surface, the vapor undergoes supersaturation at constant pressure before condensing. The Clausius-Clapeyron relation relates vapor pressure and temperature along the saturation line: () dPdT=ρvhfgT
Simulation of diesel spray combustion using LES and a multicomponent vapourisation model
Published in Combustion Theory and Modelling, 2019
Xiaohua Ren, Lei Zhang, Zhongli Ji
Subscripts ‘L’ and ‘V’ denote liquid phase and vapour phase, respectively. P is the ambient pressure. PV(I) is the vapour pressure of the continuously distributed fuel component and is also determined by drop surface temperature. Based on the Clausius–Clapeyron relation, the vapour pressure can be related to the normal boiling point. Using a linear relation of normal boiling point with the molecular weight, namely, , the expression of vapour pressure can be obtained as [18] Patm is the atmospheric pressure. A and B are parameters determined by the drop surface temperature. Using Equation (19), the integration of Equation (18) can be performed to calculate the total mole fraction of the fuel vapour. Multiply both sides of Equation (18) by I and I2, respectively, the expressions of the first two moments of fuel vapour at drop surface can be obtained as
Analytical theory study on latent heat coefficient of grain water vaporization
Published in Drying Technology, 2021
The Clausius-Clapeyron relation (1843) developed equilibrium thermodynamics in 1843 and established the theoretical expression (Equation (1)) of the relations between pressure and temperature change rate under phase equilibrium conditions for a single component system under phase equilibrium conditions. where P is the vapor pressure (kPa), T is the absolute temperature (K), Δh is the specific enthalpy difference (kJ/kg), Δv is the specific volume difference (m3/kg), v0 is the specific volume of water at the same temperature (m3/kg).