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Electronic entropy is the entropy of a system attributable to electrons' probabilistic occupation of states. This entropy can take a number of forms. The first form can be termed a density of states based entropy. The Fermi–Dirac distribution implies that each eigenstate of a system, i, is occupied with a certain probability, p i. As the ...
R is the universal ideal gas constant: R = 8.314 462 618 153 24 J K −1 mol −1, T is the temperature in kelvins, z is the number of electrons transferred in the cell reaction or half-reaction, F is the Faraday constant, the magnitude of charge (in coulombs) per mole of electrons: F = 96 485.332 123 310 0184 C mol −1,
Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. [23] However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula.
Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states (microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the macrostate of the system. A useful illustration is the example of a sample of gas contained in a container.
R, gas constant, T, absolute temperature, ln, natural logarithm, Q r, reaction quotient (unitless), K eq, equilibrium constant (unitless), w elec,rev, electrical work in a reversible process (chemistry sign convention), n, number of moles of electrons transferred in the reaction, F = N A e ≈ 96485 C/mol, Faraday constant (charge per mole of ...
The Sackur–Tetrode constant, written S 0 /R, is equal to S/k B N evaluated at a temperature of T = 1 kelvin, at standard pressure (100 kPa or 101.325 kPa, to be specified), for one mole of an ideal gas composed of particles of mass equal to the atomic mass constant (m u = 1.660 539 068 92 (52) × 10 −27 kg [5]).
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0 .
Common values of b are 2, Euler's number e, and 10, and the unit of entropy is shannon (or bit) for b = 2, nat for b = e, and hartley for b = 10. [ 1 ] Mathematically H may also be seen as an average information, taken over the message space, because when a certain message occurs with probability p i , the information quantity −log( p i ...