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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 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.
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]
Clausius is the author of the sibyllic utterance, "The energy of the universe is constant; the entropy of the universe tends to a maximum." The objectives of continuum thermomechanics stop far short of explaining the "universe", but within that theory we may easily derive an explicit statement in some ways reminiscent of Clausius, but referring ...
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 first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes.The law distinguishes two principal forms of energy transfer, heat and thermodynamic work, that modify a thermodynamic system containing a constant amount of matter.
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]
For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. On the other hand, real-gas models have to be used near the condensation point of gases, near critical points , at very high pressures, to explain the Joule–Thomson effect , and in other less usual cases.