Types of Properties

Thermodynamic properties are divided into two broad types:   intensive properties and extensive properties.

An extensive property is any property that depends on the size (or extent) of the system under consideration.   Volume is an example.  If you double the length of all edges of a solid cube, the volume increases by a factor of eight.  Mass is another.  The same cube will undergo an eight-fold increase in mass when the length of the edges is doubled. 

An intensive property is any property that can exist at a point in space.  Temperature, pressure and density are good examples.  You could imagine moving a thermometer about a room or a pressure sensor about a swimming pool so as to record the property at each location (point in space).  You also know that the density of the atmosphere is different from point to point, with air nearest the ground having the highest density and air far above the earth's surface having the lowest. 

On the other hand, it is silly to think of the volume of your swimming pool as being a property at a point.  It is a characteristic of the entire swimming pool and that makes it extensive.

A particularly important type of intensive property is the specific property, which is always given on a unit mass basis.  An example is specific volume, which has units of volume/mass, typically expressed as cubic feet per pound or cubic meters per kilogram.  Specific properties are intensive because they exist at a point.  For instance, specific volume is simply the reciprocal of density.

There is an important relationship between specific properties and extensive properties.  Consider the case where the intensive properties of a system are uniform, meaning they are the same at each point within the system.  The total volume V of the system (say in cubic feet) could be calculated from the mass M of the system (in pounds) and the specific volume v of the material comprising the system (in cubic feet per pound) by:

V = vM

This equation only works if the specific volume is constant throughout the system.  Although this is not always true, it is often sufficiently accurate to assume so.  For instance, if you wanted to know the mass of air in your bedroom, you could measure the volume of the room with a yardstick (to get V) and look up the specific volume of air (v) at ambient conditions and calculate M from V/v.  You would do this even though the air near the ceiling has a slightly different density than the air near the floor.

Notice that we used an upper case V to represent the extensive property volume and a lower case v to represent the intensive property specific volume.   We will continue to follow this convention.  Exceptions are temperature and pressure which are generally represented by upper case letters T and P, even though they are intensive properties.

You might wonder why we need to be concerned with both intensive and extensive properties.  It is because the expressions for the first and second laws of thermodynamics will be written in terms of extensive properties and the charts we use to look up property values will contain intensive properties.   So we will be using V=vM (and the analogous equations for properties other than V) to convert the chart properties to extensive variables for use in the equations.

Independence of Properties

There are a number of different intensive properties that are used to characterize material behavior.  We have already discussed temperature, pressure and density.  A few other examples are heat capacity, viscosity, thermal conductivity, and electrical conductivity.  Of particular importance is the question of how many of these properties can be regarded as independent variables.  In other words, how many properties can we specify before nature fixes the values of the rest of them?  Can we, for instance, specify that we want water that has a temperature of 50 oC, a pressure of 2 atm and a heat capacity of 1.0 cal/g oC?

It turns out that the magic number is 2 (observed experimentally and later verified theoretically).  To put it more formally:

For a pure substance existing in the form of a single phase (solid, liquid or gas), specifying the values of any two intensive variables will fix the values of all of the others.

This result will have some importance in the following pages, where we will discuss the relationship between pressure, specific volume and temperature for a pure substance.  Before moving on, let us summarize the important points about properties.


Important Points:

  • Extensive properties depend upon the size of the system.  Intensive properties apply at a point.  Specific properties are intensive properties that are on a "per unit mass" basis.

  • If properties are uniform throughout a system, specific volume v may be related to total volume V through V = Mv.

  • For a single phase of a pure substance, specifying values of any two variables fixes the remaining ones.


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