For an N -particle gas, there are N! states which are identical in this sense, if one assumes that each particle is in a different single particle state. One can safely make this assumption provided the gas isn't at an extremely high density. Under normal conditions, one can thus calculate the volume of phase space occupied by the gas, by dividing Equation 1 by N!. Using the Stirling approximation again for large N, ln(N!) ≈ N ln(N) − N, the entropy for large N is: