**The Equation of State:**In order to describe the thermodynamic state of a system, certain variables are required. These variables, in general, are the mechanical variables supplemented by the thermal state of the system.

For example

**the thermodynamic state of the gaseous system can be specified by its pressure***,***P**, volume**V**& temperature**T**. But out of these three variables only two are independent variables & the third one may be considered as their function.See also:

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 the equation of state.

For example, the equation of state for an ideal gas in the 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.

**See Also:**

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