What are the Two Basic Concepts of Thermodynamic Variables?

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What are the Intensive and Extensive Variables in Thermodynamic?

Let us consider a wooden table and a wooden chair. The mass (m) and volume (V) of them are different because such properties depend on the whole body. These are the extrinsic thermodynamic properties. On the other hand, the density (ρ) is the same for both the bodies. This property does not depend on the whole body, but only on the material (in this case, wood) of the body. This is an Intrinsic thermodynamic property.

Generally, thermodynamic variables are of two types-

1. intensive variable and
2. extensive variable.

The variables which do not depend on the amount of matter or mass in a thermodynamic system are called intensive variables. Pressure, temperature, density, surface tension, etc., are intensive variables.

The variables which are proportional to the amount of matter or mass in a thermodynamic system are called extensive variables. Volume, magnetic moment, internal energy, entropy, etc., are extensive variables.

As an illustration we may consider some amount of gas of mass m, volume V, pressure p, temperature T and density ρ, enclosed in a container [Fig.]. Now we divide the gas into 4 equal parts. Clearly, mass, volume, pressure, temperature and density of each part are \(\frac{m}{4}\), \(\frac{V}{4}\), p, T and ρ, respectively. It means that m and V depend on the whole amount of gas; they are extensive variables. But ρ, p, T do not depend on the amount; they are intensive variables.

We consider a relation like mass = density × volume or, m = ρV. On the left-hand side, mass m changes proportionally with the amount of matter in a system. On the right hand side, volume V changes similarly. Thus, the two sides remain equal only if ρ remain the same. So, whereas m and V are extensive, ρ is intensive. In general, in a product of two or more thermodynamic properties, only one is an extensive variable and the others are intensive variables. So we can have a product like ρV which is extensive (V is extensive, but ρ is intensive). But a product like mV is not allowed, as both m and V are extensive.

Intensive and extensive variables in thermodynamic systems

Thermodynamic system	Intensive variables	Extensive variables
Stretched string	Tension, T	Length, l
Hydrostatic system	Pressure, p	Volume, V
Surface film	Surface tension, S	Area, A
Paramagnetic substance	Intensity of magnetic field, H	Magnetic moment, M.

State Function and Path Function

If a system is in equilibrium, the variables like its volume (V), pressure (p), temperature (T) etc. have definite values. So these values refer to the state of the system and do not depend on the path followed to reach that state. So the variables like volume, pressure, temperature etc. are called state functions or properties of the system.

On the other hand, the two functions-work (W) and heat (Q) are not related to any state of the system, rather they are relevant to any process of the system. A statement – W_A is the amount of work done in the state A-has no meaning. Rather the statement ‘W_AB is the amount of work done in the process A → B’ is meaningful. There can be various paths from the state A to the state B.

The values of W_AB or Q_AB in each path are different, i.e., these values depend on the paths between the states A and B. So W and Q are called path functions. They are not state functions. It is to be noted that if V_A and V_B are the volumes of the system in the states A and B respectively, then change in volume in the process A → B = V_B – V_A, remains the same. If does not depend on the path. So any change of a state function is independent of the path.