#ENTROPY EQUATION FREE#

#ENTROPY EQUATION FREE#

2.2 Relation to Gibbs free energy and enthalpy.

2.1 Proof that entropy is a state function.Since it requires more mathematical knowledge than the traditional approach based on Carnot engines, and since this mathematical knowledge is not needed by most students of thermodynamics, the traditional approach, which depends on some ingenious thought experiments, is still dominant in the majority of introductory works on thermodynamics. Carathéodory's work was taken up by Max Born, and it is treated in a few monographs. His axiom replaced the earlier Kelvin-Planck and the equivalent Clausius formulation of the second law and did not need Carnot engines. His theory was based on Pfaffian differential equations. Not satisfied with the engineering type of argument, the mathematician Constantin Carathéodory gave in 1909 a new axiomatic formulation of entropy and the second law of thermodynamics. For a system of about 10 23 particles, Ω is on the order of 10 10 23, that is the entropy is on the order of 10 23× k B ≈ R, the molar gas constant. The number Ω is the multiplicity of the macrostate for an isolated system, where the macrostate is of definite energy, Ω is its degeneracy. Ω is the number of different wave functions ('microstates') of the system belonging to the system's 'macrostate' (thermodynamic state). In the statistical approach the entropy of an isolated (constant energy) system is k B log Ω, where k B is Boltzmann's constant and the function log stands for the natural (base e) logarithm. The quantum statistical point of view, too, will be reviewed in the present article. Boltzmann's definition of entropy was furthered by John von Neumann to a quantum statistical definition. In 1877 Ludwig Boltzmann gave a definition of entropy in the context of the kinetic gas theory, a branch of physics that developed into statistical thermodynamics. The second law states that the entropy of an isolated system increases in spontaneous (natural) processes leading from one state to another, whereas the first law states that the internal energy of the system is conserved. In this approach, entropy is the amount of heat (per degree kelvin) gained or lost by a thermodynamic system that makes a transition from one state to another. The 'engineering' manner-by an engine-of introducing entropy will be discussed below. Carnot's work foreshadowed the second law of thermodynamics. The traditional way of introducing entropy is by means of a Carnot engine, an abstract engine conceived of by Sadi Carnot in 1824 as an idealization of a steam engine. The state variable 'entropy' was introduced by Rudolf Clausius in 1865, see the inset for his text, when he gave a mathematical formulation of the second law of thermodynamics.

I have deliberately constructed the word entropy to resemble as much as possible the word energy, since both quantities to be named by these words are so closely related in their physical meaning that a certain similarity in their names seems appropriate to me.

As I deem it better to derive the names of such quantities - that are so important for science - from the antique languages, so that they can be used without modification in all modern languages, I propose to call the quantity S the entropy of the body, after the Greek word for transformation, ἡ τροπή. Translation: Searching for a descriptive name for S, one could - like it is said of the quantity U that it is the heat and work content of the body - say of the quantity S that it is the transformation content of the body.

Entropy equation