Lets take a rectangular gas container of volume 
. There is a partition, somewhere in the middle, that makes the container divided into two chamber of volume $V_1$ and $V_2$. First we consider the case when partition is in place and first chamber is filled with one type of gas (mass of gas molecules $m_1$) while other chamber is filled with some other type of gas (mass of gas molecules $m_2$). When the partition is in, let the entropy of first type of gas is $S_1$ and second type of gas is $S_2$,
