The entropy of mixing ideal gases was treated already by Gibbs. The result is known as the Gibbs’ paradox. Several scientists were engaged with this paradox, among them Rayleigh, Lorentz, Einstein, and von Neumann 1[1,2].
The paradox states that the two gases can be as similar as possible, but not completely similar to exhibit an entropy of mixing. Gibbs’ paradox was tried to be explained in several ways. For example, it was stated that nature changes the properties in jumps, in other words, in quanta [3,p.163].
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Fink, J.K. (2009). Thermodynamic Paradoxes. In: Physical Chemistry in Depth. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01014-9_10
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