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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.
For example, the Clausius–Mossotti relation is accurate for N 2 gas up to 1000 atm between 25 °C and 125 °C. [5] Moreover, the Clausius–Mossotti relation may be applicable to substances if the applied electric field is at a sufficiently high frequencies such that any permanent dipole modes are inactive. [6]
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 German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. [36] His formulation of the second law, which was published in German in 1854, is known as the Clausius statement:
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 ...
The saturation vapor pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. The boiling point of water is the temperature at which the saturated vapor pressure equals the ambient pressure.
Rudolf Julius Emanuel Clausius (German pronunciation: [ˈʁuːdɔlf ˈklaʊzi̯ʊs]; [1] [2] 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. [3]
The relationship between entropy, order, and disorder in the Boltzmann equation is so clear among physicists that according to the views of thermodynamic ecologists Sven Jorgensen and Yuri Svirezhev, "it is obvious that entropy is a measure of order or, most likely, disorder in the system."