Gibbs paradox

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High Quality Content by WIKIPEDIA articles! In statistical mechanics, a simple derivation of the entropy of an ideal gas based on ...

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High Quality Content by WIKIPEDIA articles! In statistical mechanics, a simple derivation of the entropy of an ideal gas based on the Boltzmann distribution yields an expression for the entropy which is not extensive (is not proportional to the amount of gas in question). This leads to an apparent paradox known as the Gibbs paradox, allowing, for instance, the entropy of closed systems to decrease, violating the Second Law of Thermodynamics. The paradox is averted by recognizing the simple derivation implicitly assumed a constant number of particles, and that properly accounting for changing system size produces an extensive expression for entropy. Historically, many textbooks on the subject have instead attributed this correction to the quantum nature of fundamentally indistinguishable particles. The resulting equation for the entropy (of a classical ideal gas) is extensive, and is known as the Sackur-Tetrode equation.