  For an ideal gas consisting N molecules within a volume V, the volume
accessible to each molecule at an instantaneous time is V/N. The rest of the
volume, (N-1)(V/N), is occupied by other (N-1) molecules. The textbook
assumption that a molecule can access any location inside the volume V at one
instantaneous in time is wrong leading to the Gibbs paradox. By taking into
account the correct physical space for individual molecules, the partition
function for the N-molecule system is obtained without using any correction
factor which gives rise to the correct entropy of the system. There is thus no
need to argue about the distinguishability of molecules. Entropy of mixing two
quantities of ideal gasses is zero no matter the gasses are the same type or
different types. With the appropriate assignment of the phase space, the
entropy of the system has the expected property of being extensive and the
Gibbs paradox is removed.
