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For an ideal gas consisting N molecules within a volume V, the volumeaccessible to each molecule at an instantaneous time is V/N. The rest of thevolume, (N-1)(V/N), is occupied by other (N-1) molecules. The textbookassumption that a molecule can access any location inside the volume V at oneinstantaneous in time is wrong leading to the Gibbs paradox. By taking intoaccount the correct physical space for individual molecules, the partitionfunction for the N-molecule system is obtained without using any correctionfactor which gives rise to the correct entropy of the system. There is thus noneed to argue about the distinguishability of molecules. Entropy of mixing twoquantities of ideal gasses is zero no matter the gasses are the same type ordifferent types. With the appropriate assignment of the phase space, theentropy of the system has the expected property of being extensive and theGibbs paradox is removed.

Redefining the Phase Space for Ideal Gas Systems Resolves the Gibbs Paradox