Modern Engineering Thermodynamics

2.4 System States and Thermodynamic Properties 37
that state was attained. Mass, volume, temperature, pressure, color, viscosity, magnetization, and so forth are all
possible properties.
The list of possible properties is quite long. Fortunately, not all properties are independent of each other. In fact,
a homogeneous system contains relatively few independent properties. The formula relating the dependent and
independent properties of a system is called a thermodynamic equation of state. Once the values of the independent
properties are known for a particular state, this formula can be used to calculate the values of all the
dependent properties at that state. The ideal gas formula, pv = RT, is an example of such an equation of state for
a simple system. In classical thermodynamics, there are two types of properties, intensive and extensive.
Most extensive properties can be converted into intensive properties by dividing the extensive property
by the system mass (or the number of moles) in the system. Intensive properties created in this way are called
specific properties. For example, the total volume of a system divided by the total mass of the system is the intensive
property called specific volume, and the total volume divided by the total number of moles of the system
is the intensive property called molar specific volume. To be able to tell the difference between extensive and
intensive properties in the formulae of this book, we adopt the notational scheme explained in the boxes.
Exceptions to this extensive property notation are uppercase T for temperature (which is an intensive property),
lowercase m for mass (which is an extensive property), and lowercase n for the number of moles (also an extensive
property). The letters T, m, andn for temperature, mass, and moles are the traditional symbols for these
quantities, and the symbols t, M, andN are the traditional symbols for time, molecular mass, and Avogadro’s
number, respectively.
INTENSIVE PROPERTY
An intensive property is any thermodynamic property of a homogenous system that is independent of mass. Examples are the
pressure, temperature, and density.
EXTENSIVE PROPERTY
An extensive property is any thermodynamic property of a homogenous system that depends on mass. Examples are the mass,
volume, and energy.
EXTENSIVE PROPERTY NOTATION
Extensive properties are symbolized by uppercase (capital) letters. For example, V, E, andU are the symbols for volume, 2
energy, and internal energy.
2 In this text, V represents total volume, and V represents the magnitude of velocity.
INTENSIVE PROPERTY NOTATION
Intensive mass-based properties are symbolized by lowercase letters, and intensive mole-based properties are symbolized
by lowercase letters with overbars. For example, v = V/m,, e = E/m,, u = U/m are the symbols for mass-based specific
volume, specific energy, and specific internal energy. Similarly, v, e, andu are the symbols for molar specific volume, molar
specific energy, and molar specific internal energy.
CRITICAL THINKING
If we chose the color of a system as a thermodynamic property, would it be an extensive or intensive property?