![]() the entropy of a pure substance at 298 K and 1 atm pressure). Standard molar entropies are listed for a reference temperature (like 298 K) and 1 atm pressure (i.e.The entropy of a substance has an absolute value of 0 entropy at 0 K. In fact, values for the "standard molar entropy" of a substance have units of J/mol K, the same units as for molar heat capacity. the rise in temperature is the heat capacity, it would seem that in some way, information about the heat capacity (and how it changes with temperature) would allow us to determine the entropy change in a system. Since the quantitative term that relates the amount of heat energy input vs. all the ice has melted or all the liquid has frozen) However, in both of the above situations, the energy change is not accompanied by a change in temperature (the temperature will not change until we no longer have an equilibrium condition i.e. Likewise if a small amount of energy is withdrawn from the system, the equilibrium will shift to the left (more ice).If a small amount of energy is input into the system the equilibrium will shift slightly to the right (i.e.At such a temperature and pressure we have a situation (by definition) where we have some ice and some liquid water.Vorlesungen über Gastheorie, Ludwig Boltzmann (1898) vol.Vorlesungen über Gastheorie, Ludwig Boltzmann (1896) vol.Ludwig Boltzmann: the Man who Trusted Atoms, Oxford University Press, Oxford UK, ISBN 9780198501541, p. "Über die Mechanische Bedeutung des Zweiten Hauptsatzes der Wärmetheorie". This article incorporates text from this source, which is available under the CC BY 3.0 license. Translation of Ludwig Boltzmann’s Paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium” Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. ^ Max Planck (1914) The theory of heat radiation equation 164, p.119.Eric Weisstein's World of Physics (states the year was 1872). ^ See: photo of Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.The probability distribution of the system as a whole then factorises into the product of N separate identical terms, one term for each particle and when the summation is taken over each possible state in the 6-dimensional phase space of a single particle (rather than the 6 N-dimensional phase space of the system as a whole), the Gibbs entropy The Boltzmann entropy is obtained if one assumes one can treat all the component particles of a thermodynamic system as statistically independent. This is exact for an ideal gas of identical particles that move independently apart from instantaneous collisions, and is an approximation, possibly a poor one, for other systems. ![]() The term Boltzmann entropy is also sometimes used to indicate entropies calculated based on the approximation that the overall probability can be factored into an identical separate term for each particle-i.e., assuming each particle has an identical independent probability distribution, and ignoring interactions and correlations between the particles. In every situation where equation ( 1) is valid,Įquation ( 3) is valid also-and not vice versa.īoltzmann entropy excludes statistical dependencies That is, equation ( 1) is a corollary ofĮquation ( 3)-and not vice versa. ![]() Gibbs gave an explicitly probabilistic interpretation in 1878.īoltzmann himself used an expression equivalent to ( 3) in his later work and recognized it as more general than equation ( 1). He interpreted ρ as a density in phase space-without mentioning probability-but since this satisfies the axiomatic definition of a probability measure we can retrospectively interpret it as a probability anyway.
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