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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.
Phase Transitions
Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019
where ΔVm is the change in volume per kmole. This relation, which gives the slope of the coexistence curve, is called the Clausius-Clapeyron equation. Since L is positive by definition, the sign of ΔVm determines the sign of the slope. For a liquid-gas transition, ΔVm, and hence dpdT, is positive, but for other transitions, this may not be the case. For example, the density of liquid water is greater than that of ice, so for the ice-water transition ΔVm and dpdT are negative. Raising the pressure lowers the melting point of ice.
Phase Equilibria
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
Typically, the liquid–vapor coexistence curve interrupts at the so-called critical point with, of course, well-specified values of temperature and pressure, which for CO2 are Tc = 31°C and pc = 73 atm. At temperatures lower than the critical temperature, it is possible to perform a vapor–liquid phase transition by increasing the pressure, whereas at temperatures above the critical value, the gas does not become liquid under higher pressures, even though its density increases. The existence of the critical point entails the possibility of transforming the vapor into liquid without performing a phase transition, namely, going around the critical point without crossing the coexistence curve. Because of this, it is justified to use the single word fluid to refer to the two phases, liquid and vapor. As already mentioned, one uses the words gas phase for temperatures above and pressures below their critical values. Finally, we say supercritical gas for temperatures and pressures both above their critical values.
Molecular simulations of the vapour-liquid coexistence curve of square-well dimer fluids
Published in Molecular Physics, 2023
Francisco Sastre, Felipe J. Blas
From the vapour-liquid coexistence curve of a system, it is possible to estimate the critical temperature , and the critical density, . To this end, we apply the well-known scaling law [26, 27] given by, and the law of rectilinear diameter given by, Here β is the corresponding critical exponent, [32] with a universal value of in Equation (8). Equation (9) is the well-known law of rectilinear diameters. A, B, and are four unknown constants obtained by fitting to the simulation results. and are the liquid and vapour coexistence densities at the corresponding temperature T, respectively. Critical temperature, , and density, , can be easily obtained by fitting the simulation results of the vapour and liquid coexistence densities to Equations (8) and (9). We estimate the uncertainties of and from the estimation of the uncertainties of the slope and intercept of the corresponding linear fitting, taking also into account the uncertainties associated to the vapour and liquid coexistence densities at different temperatures. The corresponding values for SW dimers interacting with potential ranges and (b) are provided in Table 3.
Simulation of droplet evaporation under the dual influence of surface wettability and nucleate boiling
Published in International Journal of Green Energy, 2023
Borui Zhang, Jin Wang, Yanwei Hu, Yurong He
As the number of iterations increases, the liquid and gas phases gradually separate. Figure 2 is the p-v curve at a certain temperature (Yuan and Schaefer 2006). Figure 3 shows the gas–liquid coexistence curve.