A mixture of classical ideal gases occupying a volume may be separated using semi-permeable membranes which are permeable to one gas but opaque to the others. The separation may be done reversibly using the membranes as pistons and keeping the whole system in contact with a reservoir at constant temperature[3]. To show that mixing has a thermodynamic effect, consider the following process restoring the mixture. After separation, each separated gas occupies the original volume alone. To return to the mixture, each gas is compressed to a volume (where is the concentration of the th gas). The compression requires work to be invested, and the entropy of the gas is reduced by . An increase in entropy of the same amount must then be associated with the mixing step of removing the partitions. This is the ‘mixing entropy’.