Concept of Entropy

Claussius Theorem

Claussium theorem states that any reversible cyclic path can be substituted by a reversible Zig-Zag path between the end states but the condition is that the zig zag path contains a reversible adiabatic process followed by a reversible isotherm and then a reversible adiabatic .The heat transfer in the real reversible process and substituted isothermal process must be same.

Consider a reversible process as shown.  According to Claussius theorem, we can divided it into many reversible process consisting of a reversible isotherm and followed by a reversible adiabatic.  If we closely examine the process, each closed zig zag lines can be called as a Carnot cycle.

So we can say that the reversible process is divided by a number of Carnot cycle.

Consider the process abcd.  there heat dQ₁, is absorbed reversibly at temperature T₁ and dQ₂ is rejected at temperature T₂.

      dQ₁      =    -dQ₂                    (-ve indicates dQ₂ is rejected)

        T₁                T₂

         dQ₁   +     dQ₂      =    O

           T₁             T₂

                 

 The equation shows that the cyclic integral of the ratio  for a reversible process is zero.                                                                    

But in practical a reversible cycle is never been  possible and the integral term  must have a value.                                                                                           

Classius call this value as entropy.  So entropy is the value of the integral

                 

So let us check it once more.

           

                      

So the application of entropy is that we can check how much irreversible a process is because if the value of entropy changes it indicates that the tendency of irreversibility