This arises from the fact that the real state ( T , V , p , n ) is in general not a valid ideal gas state, such that the ideal part of the property will be different depending on variable set. Take for example the chemical potential of a pure fluid: In a state ( T , V , p , n ) that does not satisfy the ideal gas law, but may be a real state for some real fluid. The ideal gas chemical potential computed as a function of temperature, pressure and mole number is