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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.
Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. 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 ...
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.
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 above derivation uses the first and second laws of thermodynamics. The first law of thermodynamics is essentially a definition of heat, i.e. heat is the change in the internal energy of a system that is not caused by a change of the external parameters of the system.
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.
Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics.
The thermodynamic equation for the Gibbs energy change accompanying mixing at constant temperature and (external) pressure is = A change, denoted by , is the value of a variable for a solution or mixture minus the values for the pure components considered separately.