Considering entropy (S) as a thermodynamic parameter, the criterion for the spontaneity of any process is

Here the volume of gas increase from V1 to V2 at constant temperature T. The total increase in entropy of the system and its surrounding during the spontaneous process of expansion considered above is, thus  Rln⁡V2V1 since V2 > V1 it is obvious that the spontaneous (irreversible) isothermal  expansion of a gas is accompanied by an increase in the entropy of the system and its surrounding considered together.  ΔSsystem +ΔSsurroundinys >0