What are the Mathmatical conditions for state functions or state variables?

 Mathematical Condition for a function to be a state function:-

There are three conditions that must be satisfied simultaneously for a function to be state      function.

(i) If ∆φ is a state function

        

    It means change in ∮ depends only on end states and not on the path which it followed       during the process.

(ii) If ∆φ is a state function

       

     It implies, in cyclic integral as the end states are same, so ∆φ value will be zero.

 (iii) If ∆φ = f(x, y) is a state function, Euler's reciprocity theorem must be satisfied.

           

                     If ∮dz=0 then, are we sure that z = 0 state function ?

   "Change in state function (z) is fixed in between two states so ∆z is also

      a state function example ∆P,∆T,∆V,∆H= state function is a wrong statement"

 

 

Related Questions:

What are the "State functions or State variables" ?