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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 [3] [4] is a pragmatic mathematical expression of the relation between the vapor pressure and the temperature of pure liquid or solid substances. It is obtained by curve-fitting and is adapted to the fact that vapor pressure is usually increasing and concave as a function of temperature. The basic form of the equation is:
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 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]
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0 .
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 ...
[10] 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.