Entropy formula11/28/2023 The microstates of such a thermodynamic system are not equally probable - for example, high energy microstates are less probable than low energy microstates for a thermodynamic system kept at a fixed temperature by allowing contact with a heat bath.įor thermodynamic systems where microstates of the system may not have equal probabilities, the appropriate generalization, called the Gibbs entropy, is: W is sometimes called the "thermodynamic probability" since it is an integer greater than one, while mathematical probabilities are always numbers between zero and one.īoltzmann's formula applies to microstates of the universe as a whole, each possible microstate of which is presumed to be equally probable.īut in thermodynamics it is important to be able to make the approximation of dividing the universe into a system of interest, plus its surroundings and then to be able to identify the entropy of the system with the system entropy in Classical thermodynamics. The "correction" in the denominator is due to the fact that identical particles in the same condition are indistinguishable. Where i ranges over all possible molecular conditions and ! denotes factorial. W can be counted using the formula for permutations (2) Boltzmann’s paradigm was an ideal gas of N identical particles, of which N i are in the i-th microscopic condition (range) of position and momentum. The value of W, specifically, is the Wahrscheinlichkeit, or number of possible microstates corresponding to the macroscopic state of a system - number of (unobservable) "ways" the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules. Boltzmann in his kinetic theory of gases." To quote Planck, "the logarithmic connection between entropy and probability was first stated by L. The equation was originally formulated by Ludwig Boltzmann between 1872 to 1875, but later put into its current form by Max Planck in about 1900.
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