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The Clausius inequality is a consequence of applying the second law of thermodynamics at each infinitesimal stage of heat transfer. The Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir. [3]
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 ...
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]
It can be formulated in a variety of interesting and important ways. One of the simplest is the Clausius statement, that heat does not spontaneously pass from a colder to a hotter body. It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that
The first full statements of the law came in 1850 from Rudolf Clausius, [14] [15] and from William Rankine. Some scholars consider Rankine's statement less distinct than that of Clausius. Some scholars consider Rankine's statement less distinct than that of Clausius.
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–Duhem inequality can be expressed in integral form as () + .In this equation is the time, represents a body and the integration is over the volume of the body, represents the surface of the body, is the mass density of the body, is the specific entropy (entropy per unit mass), is the normal velocity of , is the velocity of particles inside , is the unit normal to the surface, is ...
In electromagnetism, the Clausius–Mossotti relation, named for O. F. Mossotti and Rudolf Clausius, expresses the dielectric constant (relative permittivity, ε r) of a material in terms of the atomic polarizability, α, of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof.