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I have just started thermodynamics (not with statistical approach but with macroscopic approach), in which the state postulate reads

Only two independent intensive properties of a simple compressible system are required to get all other properties necessary to describe the state .

So I was wondering that how this postulate may be justified . Since it is a postulate i think that it should feel like obvious (like a straight line is shortest path from one point to the other). But it is not so, therefore I am asking for a justification-

that how we know that this statement is indeed true Or if we can mathematically justify this through simpler (obvious) statements

A argument using macroscopic approach(not concerned with microscopic nature) is really what I am asking

However ,if it is too difficult to give such a justification then you can give a microscopic one. But former one would really help me.

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    $\begingroup$ I'm not sure what kind of justification you're looking for here. Take an ideal gas: You have temperature, pressure and volume as state variables for it, and one of the three depends on the other two through the ideal gas law, so in an axiomatic approach, we make that "two state variables" thing a postulate. $\endgroup$
    – ACuriousMind
    Mar 20, 2016 at 11:44
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    $\begingroup$ @ACuriousMind if i am not wrong any characteristic (smell colour ) would count as state variable (state changes as any one of these change)..then "How can we say that for a given value of P and V ..all other (uncountable) variables will have fixed values..so that they uniquely determine the state $\endgroup$ Mar 20, 2016 at 12:51
  • $\begingroup$ I think i shall use thermodynamic coordinates in place of variables $\endgroup$ Mar 20, 2016 at 12:53
  • $\begingroup$ @ACuriousMind Sorry i got it wrong..i think thermodynamic variables mean the properties necessary to uniquely describe a state of system ..and that is what i am asking .say for an IDEAL GAS - P and V are state variables (that's true) but how we know it -that all other properties (refractive index etc.) Will be specified and hence the state will be specified if WE HAVE A VALUE OF P and V.. $\endgroup$ Mar 20, 2016 at 13:05
  • $\begingroup$ Hi @lucas: Concerning your tag edit, please try to avoid the use of the laws-of-physics tag, which basically applies to all questions and therefore have no descriptive power. $\endgroup$
    – Qmechanic
    May 29, 2016 at 18:34

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