The equation of state Extensive and intensive properties

The ideal gas law, pV = is a relation between the four variables that describe the state of any gas. As such, it is an equation of state. The variables in this equation fall into two classes n and V are extensive variables (extensive properties), while p and T are intensive variables (intensive properties). 

The value of any extensive property is obtained by summing the values of that property in every part of the system. Suppose that the system is subdivided into many small parts, as in Fig. 2.3. Then the total volume of the system is obtained by adding together the volumes of each small part. Similarly, the total number of moles (or total mass) in the system is obtained by summing the number of moles in (or mass of) each part. By definition, such properties are extensive. It should be clear that the value obtained is independent of the way in which the system is subdivided. 

Intensive properties are not obtained by such a process of summation but are measured at any point in the system, and each has a uniform value throughout a system at equilibrium for example, T and p. 

The ratio of F to is not proportional to the mass, because in forming the ratio the mass drops out and F is an intensive variable. The ratio of any two extensive variables is always an intensive variable. 

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