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The article reveals the error that in classical thermodynamics leads to theGibbs paradox. The essence of the error lies in the fact that the entropy of anideal gas is attributed to additive quantities, but it is not correct. Thevalue of an additive quantity for a whole object is equal to the sum of itsvalues for the parts of the object in any division of the object into parts.The entropy of an ideal gas in classical thermodynamics is expressed by theequation that contains the term Rnln(V/n), where n is the number of moles ofgas, V is the volume of gas, R is the universal gas constant, or by equationsequivalent to it. As a result, the entropy of an ideal gas is equal to the sumof the entropies of its parts only if the parts of the gas are in differentplaces (separated by an impermeable partition). If the parts of the gas form amixture, then the sum of the entropies of the parts is not equal to the entropyof the gas. Despite this, the entropy of an ideal gas is considered to be anadditive quantity. This gives rise to a series of inexplicable conclusionsknown as various formulations of the Gibbs paradox.

The Gibbs paradox in classical thermodynamics is a consequence of the erroneous attribution of the entropy of an ideal gas to additive quantities