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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 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 ...
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]
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 German physicist Rudolf Clausius learned of Carnot's work through Clapeyron's memoir. Clausius corrected Carnot's theory by replacing the conservation of caloric with the work-heat equivalence (i.e., energy conservation). Clausius also put the second law of thermodynamics into mathematical form by defining the concept of entropy.
It goes on to say, however, that the exact equation is called the Clausius-Clapeyron equation in most texts for engineering thermodynamics and physics. (On the previous page, discussing the exact equation, the book said the exact version was called the Clapeyron equation, but said that it was also known as the Clausius-Clapeyron equation.)
Pages in category "Thermodynamic equations" The following 31 pages are in this category, out of 31 total. ... Clausius–Clapeyron relation; Compressibility equation; D.
The preceding equilibrium equations are typically applied for each phase (liquid or vapor) individually, but the result can be plotted in a single diagram. In a binary boiling-point diagram, temperature (T ) (or sometimes pressure) is graphed vs. x 1. At any given temperature (or pressure) where both phases are present, vapor with a certain ...