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In order to describe the thermodynamic state of a system, certain variables are required. These variables in general are the  mechanical variables supplemented by thermal state of the system.
For example, the thermodynamic state of gaseous system can be specified by its pressure P, volume V & temperature T. But out of these three variables only two are independent variables & third one may be considered as their function.
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If we fix two variables out of the three, the third one is automatically fixed, or in other words only two parameters are necessary & sufficient to specify uniquely the state of the system.
“The equation connecting the pressure, the volume & absolute temperature of a substance is called the Equation of State of the system”.
Thus for a gas forming the system, these three quantities are not independent & connected by a relationship, i.e.

               f( P, V, T ) = 0

which is called equation of state.
For example the equation of state for an ideal gas in static condition is represented as:
                   PV = RT
   
      where R = universal gas constant
                     = 8.314 Joule /gm
                     = 8314 J/Kg mol – K
                 
                 V = molar volume
For Vanderwall’s gas, the equation of state is:
                 {P + a / V2 }(V-b) = RT
         
Fig. Vanderwall’s equation of state.
         where a, b are Vanderwall’s constant.
For an equation of state, it should be noted that: –

1. Every thermodynamic system has its own equation of state independent of others.

2. An equation of state is not a theoretical deduction from thermodynamics but is an experimental addition to it.

3. The equation of state is not applicable to systems not in thermodynamic equilibrium.