4) Entropy of Mixing: Many practical problems deal with the mixing of two materials. It is not surprising that if you mix the contents of two bottles of different gases, or two beakers of different solutions , the total entropy will increase. Let's see how much. Start with two separated helium and argon gases , each with N atoms and 1volume V: Calculate the change in entropy if the partition is removed. Be sure to as- sume that atoms of a given type are identical, and use Stirling's Approximation, In N! N In N - N. S - S initial " nal S : entropy of mixing = (note: many terms cancel) Now calculate the change in entropy if the two gases were initially the same type (say He): S