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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 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.
The Clausius theorem is a mathematical representation of the second law of thermodynamics. It was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. Clausius developed this in his efforts to explain entropy and define it quantitatively.
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.)
The Clausius–Clapeyron relation does not make sense for second-order phase transitions, [1] as both specific entropy and specific volume do not change in second-order phase transitions. Quantitative consideration
Clausius–Clapeyron equation: Calculus: Rudolf Clausius and Émile Clapeyron: Clausius–Mossotti equation: Physics: Rudolf Clausius and Ottaviano-Fabrizio Mossotti: Colebrook equation Colebrook–White equation: Fluid dynamics Fluid dynamics: C. F. Colebrook C. F. Colebrook and F. M. White: Competitive Lotka–Volterra equations: Population ...
The Joback method, often named Joback–Reid method, predicts eleven important and commonly used pure component thermodynamic properties from molecular structure only. It is named after Kevin G. Joback in 1984 [1] and developed it further with Robert C. Reid. [2] The Joback method is an extension of the Lydersen method [3] and uses very similar groups, formulas, and parameters for the three ...
These foundations enabled him to make substantive extensions of Clausius' work, including the formula, now known as the Clausius–Clapeyron relation, which characterises the phase transition between two phases of matter. He further considered questions of phase transitions in what later became known as Stefan problems.