When we are dealing with a gaseous thermodynamic system, in books it's written that state of the system can be described by only two independent variables from the three (p,V,T) . But it's not written why or how? Why we have to choose only two independent variables, why not more or less? I've gone through some answers but still unable to understand.

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When we are dealing with a gaseous thermodynamic system, in books it&#039;s written that state of the system can be described by only two independent variables from the three (p,V,T) . But it&#039;s not written why or how? Why we have to choose only two independent variables, why not more or less? I&#039;ve gone through some answers but still unable to understand.

Cindy Walls · Accepted Answer

You can think of the state of a system as being some characteristics that determine that system uniquely. Properties of a system can be intensive (they don&#039;t depend on the mass of the system), or extensive (they depend on the mass of the system).You could describe a gaseous system using its enthalpy h and entropy s, for example, but it&#039;s more common to use pressure p, specific volume v and temperature T because they determine directly its molecular configuration.Take an ideal gas for example, if you know its temperature T and pressure p, you can calculate its specific mass using the ideal gas law  p  v  =  R  TIf only the pressure is known, you can think of the specific volume as a function of temperature (or vice-versa)  v  =  f  (  T  )  =            R      p        TAnd there&#039;s no unique pair (v,T) that satisfy the equation, but rather infinitely many (a piston under constant pressure can vary its temperature, varying therefore its specific volume as well).

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