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.

**the thermodynamic state of gaseous system can be specified by its pressure**

*For example,***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.

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