An isolated system is one that exchanges neither matter nor energy with the surroundings. What is the entropy criterion for spontaneous change in an isolated system? Give an example of a spontaneous process in an isolated system.

Video transcript

Hey everyone were asked what is the entropy condition for a spontaneous process in an isolated system where the system does not exchange matter or energy with its surroundings is the mixing of two ideal gasses inside a vessel. An example of a spontaneous process in an isolated system. To answer this question, we need to recall the second law of thermodynamics, which essentially tells us that the overall entropy of our system is equal to the entropy of our surroundings plus the entropy of our system. And as we know for a spontaneous process, our total change in entropy must be greater than zero. And in an isolated system the change in entropy of our surroundings must be equal to zero. So putting all this together for a spontaneous process in an isolated system, the total change in entropy is equal to the change in entropy of our surroundings plus the change of entropy of our system must be greater than zero. And since the change in entropy of our surroundings is equal to zero, this means that the total change in entropy is equal to the change in entropy of our system and this must be greater than zero. So now let's think about the system where the two ideal gasses are mixed inside a vessel that does not exchange matter nor energy with its surroundings. So that means we have an isolated system and when two ideal gasses also spontaneously mixed without the need of external forces of the system. That means we have a spontaneous process. So to answer this question, the entropy condition Is the change in entropy of our system is greater than zero. And yes, it is a spontaneous process. Now, I hope this made sense and let us know if you have any questions.