In the following sequence of pictorials, the second law of thermodynamics will be illustrated by examining the state function entropy, S.  The following will use the same diagrams and sequence as used for the first law as a contrast.  Notice in the following, that S can change in an isolated system and depends upon what is happening inside the system.  If a system has a uniform temperature throughout then a small change in the entropy can be expressed by:

        dS  =  dq/T
 
 

tea pot before heating                                            tea pot being heated and S is increasing
  Start adding heat 
              Entropy is S1                                               Entropy is S2 so that S2 > S1
 

     Input of q increase overall S, but there is turbulence 
                                                                                    Entropy is S3  and S3  >   S2
Thus, at this point not all of the heat has been changed into an entropy term.  Rather some of the heat was use to create some internal energy.  Assume no time passes for the following operation.

Turning off heat and isolating the system - 
                                                                     Entropy is S4    and  S4  =  S3
 

The system is allowed to settle isolated 
                                                                  Entropy is S5 and  S5 > S4

Notice that in the last step the entropy increases without any external influence.  Notice also that this process will not reverse, i. e. the internal temperature will not spontaneously drop with an increase in turbulence.