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The second law of thermodynamics may be expressed in many specific ways, [23] the most prominent classical statements [24] being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms ...
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.
Clausius restated the two laws of thermodynamics to overcome this contradiction. This paper made him famous among scientists. (The third law was developed by Walther Nernst, during the years 1906–1912). Clausius's most famous statement of the second law of thermodynamics was published in German in 1854, [10] and in English in 1856. [11]
[1] [2] [3] A more fundamental statement was later labelled as the zeroth law after the first three laws had been established. The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium ...
and by factoring out Q, we have the following form, as was derived by Clausius: = Thus, for example, if Q was 50 units, T 1 was initially 100 degrees, and T 2 was 1 degree, then the entropy change for this process would be 49.5. Hence, entropy increased for this process, the process took a certain amount of "time", and one can correlate entropy ...
An example of a physical statement is that of Planck (1897/1903): It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.
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.
Clausius then points out the inherent difficulty in the mental comprehension of this law by stating: "although the necessity of this theorem admits of strict mathematical proof if we start from the fundamental proposition above quoted, it thereby nevertheless retains an abstract form, in which it is with difficulty embraced by the mind, and we ...