I have broken the 2nd law of thermodynamics a person proclai

\"I have broken the 2nd law of thermodynamics!\" a person proclaims. He points at a sandcastle he has just built. \"This sand used to be just a disordered mess, randomly spread around the beach, but I have arranged it into this very orderly sandcastle. Therefore, I have decreased the entropy of the sand! But the 2nd low says that entropy only increases, so I have defeated the 2nd law!\" Is he right for once? If so, why is the 2nd law allowed to be broken in this situation? If he is wrong, it must be something else in the system had an increase in entropy to compensate for the drease in the sand\'s entropy, and you should explain how that happened.

Solution

There is a problem in the statement the person is making here. The statement of the second law of thermodynamics goes like this

\"  In any cyclic process the entropy will either increase or remain the same \"

Here, the term cyclic is very important. The process mentioned above is not a cyclic one. It is obviously possible for us to reduce the entropy of a particular system by doing some work on it. This process here is not a spontaneous one. The person has forcibly created the sand castle while doing some work on it. Hence its entropy reduces but once left to itself the spontaneous process will be the degradation of the sand castle into a heap of sand thus increasing its entropy. Hence we find that the entropy of a system can surely be reduced if we do some work on it. But that leads to an unstable state of the system which then gradually at equilibrium goes back to a high entropy state. Also if we consider the whole process of building a sand castle, we see that it started with a heap of sand, the person did work on it thus forcibly reducing its entropy and with time the castle crumbled back to a heap of sand again thus regaining the entropy again. So the entropy in the cyclic process does remain the same or increases. Second law never says that you cant reduce the entropy of the system by doing some work on it. The problem is that the on you do some work, the state to which you send that system is an inequilibrium one. So once left to itself it will come back to its equilibrium or high entropy state.