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

Abstract

The article reveals the error that in classical thermodynamics leads to the Gibbs paradox. The essence of the error lies in the fact that the entropy of an ideal gas is attributed to additive quantities, but it is not correct. The value of an additive quantity for a whole object is equal to the sum of its values 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 the equation that contains the term Rnln(V/n), where n is the number of moles of gas, V is the volume of gas, R is the universal gas constant, or by equations equivalent to it. As a result, the entropy of an ideal gas is equal to the sum of the entropies of its parts only if the parts of the gas are in different places (separated by an impermeable partition). If the parts of the gas form a mixture, then the sum of the entropies of the parts is not equal to the entropy of the gas. Despite this, the entropy of an ideal gas is considered to be an additive quantity. This gives rise to a series of inexplicable conclusions known as various formulations of the Gibbs paradox.