A function may be state or path function depending on the dependence on path of the process or the end state.
(a) `text(State function or State variable)` : Variables like `P`, `V`, `T` are State Functions or State Variables because their values depend only on the present state of a system and not on how the state was reached.
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 `phi` is a state function
`int_A^B d phi = phi_B =phi_A`
It means change in `phi` depends only on end states and not on the path which it followed during the process.
(ii) If `phi` is a state function `int d phi = 0`
It implies, in cyclic integral as the end states are same, so `Delta phi` value will be zero.
(iii) If `phi= f(x, y)` is a state function, Euler's reciprocity theorem must be satisfied.
`del/(del y)[((del phi)/(delx))_y]_x =del/(del x)[((del phi)/(dely))_x]_y`
(b) `text(Path function)` : Functions which depend on the path means how the process is carried out to reach a state from another state depends on path e.g. work & heat.
`text(State function)` : Pressure, volume, temperature, Gibb's free energy, internal energy, entropy.
`text(Path function)` : Work, Heat, Loss of energy due to friction
`text(Note)` : `S`, `U`, `H`, `V`, `T` etc. are state function but `DeltaS`, `DeltaU`, `DeltaH`, `DeltaV`, `DeltaT`, etc. are not state function, in fact `Delta` terms are not function itself and it is very misleading and frequently asked in the exams.
A function may be state or path function depending on the dependence on path of the process or the end state.
(a) `text(State function or State variable)` : Variables like `P`, `V`, `T` are State Functions or State Variables because their values depend only on the present state of a system and not on how the state was reached.
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 `phi` is a state function
`int_A^B d phi = phi_B =phi_A`
It means change in `phi` depends only on end states and not on the path which it followed during the process.
(ii) If `phi` is a state function `int d phi = 0`
It implies, in cyclic integral as the end states are same, so `Delta phi` value will be zero.
(iii) If `phi= f(x, y)` is a state function, Euler's reciprocity theorem must be satisfied.
`del/(del y)[((del phi)/(delx))_y]_x =del/(del x)[((del phi)/(dely))_x]_y`
(b) `text(Path function)` : Functions which depend on the path means how the process is carried out to reach a state from another state depends on path e.g. work & heat.
`text(State function)` : Pressure, volume, temperature, Gibb's free energy, internal energy, entropy.
`text(Path function)` : Work, Heat, Loss of energy due to friction
`text(Note)` : `S`, `U`, `H`, `V`, `T` etc. are state function but `DeltaS`, `DeltaU`, `DeltaH`, `DeltaV`, `DeltaT`, etc. are not state function, in fact `Delta` terms are not function itself and it is very misleading and frequently asked in the exams.