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Thermodynamic State Variables and Equation of State

Generally every equilibrium state of a thermodynamic system can be completely described by specific values of some macroscopic variables and they are called as state variables.
For example, an equilibrium state of a gas is completely specified by the values of pressure, volume, temperature, and mass.

The various state variables are not necessarily independent. The connection between the state variables is called as equation of state.

For example PV = µ RT. This is the equation of state for an ideal gas.

For a fixed amount of the gas i.e. given µ there are only two independent variables, say P and V or T and V.

The thermodynamic state variables can be classified into two categories.
  • Intensive
  • Extensive

Suppose we have two equal amounts of the same gas (n moles) in two different containers of the same volume V each and they are in equilibrium at a temperature T. Now the two containers mix together and the system becomes 2n moles.

The volume and internal energy of the system get doubled but the pressure and temperature remain the same.

Variables like volume (V) and internal energy (U), which are thus proportional to mass are called extensive variables and variables like pressure (P) and temperature (T) which do not depend on mass are called intensive variables.

The ratio of any two extensive parameters is an intensive parameter.

Table: Extensive and Intensive variables

Extensive Variables

Intensive Variables

Internal Energy

Specific Heat per Mole







Heat Capacity



We can check the consistency of thermodynamic equations using this classification.

∆Q = ∆U + P ∆V

In this equation quantities on both the sides are extensive. Actually Q is not a state variable but it is proportional to total mass of system and hence it is extensive.

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