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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"
 
 
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