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Substituting into the Clapeyron equation =, we can obtain the Clausius–Clapeyron equation [8]: 509 = for low temperatures and pressures, [8]: 509 where is the specific latent heat of the substance. Instead of the specific, corresponding molar values (i.e. L {\\displaystyle L} in kJ/mol and R = 8.31 J/(mol⋅K)) may also be used.
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine (1825–1897). [1]
The value of the slope dP/dT is given by the Clausius–Clapeyron equation for fusion (melting) [11] =, where ΔH fus is the heat of fusion which is always positive, and ΔV fus is the volume change for fusion.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
As a result, the latent heat of melting is zero, and the slope of the melting curve extrapolates to zero as a result of the Clausius–Clapeyron equation. [ 13 ] : 140 Thermal expansion coefficient
The extent of boiling-point elevation can be calculated by applying Clausius–Clapeyron relation and Raoult's law together with the assumption of the non-volatility of the solute. The result is that in dilute ideal solutions, the extent of boiling-point elevation is directly proportional to the molal concentration (amount of substance per mass ...
Pages in category "Thermodynamic equations" The following 31 pages are in this category, out of 31 total. ... Clausius–Clapeyron relation; Compressibility equation; D.
There are a number of methods for calculating the sublimation pressure (i.e., the vapor pressure) of a solid. One method is to estimate the sublimation pressure from extrapolated liquid vapor pressures (of the supercooled liquid), if the heat of fusion is known, by using this particular form of the Clausius–Clapeyron relation: [9]