Definition E.2.1.
A macroscopic property is a measurable quantity that describes the collective behavior of a physical system without specifying the microscopic state if its individual constituents.
Section E.2 Physical Properties
Subsection E.2.1 Macroscopic Property
Subsection E.2.2 State Variables
Definition E.2.2.
A state variable is a measurable property of a physical system whose value depends only on the equilibrium state of the system and not on the path taken to reach that state.
Remark E.2.3.
State variables can be used to define path-independent changes in the macrostate of a system between two points in time.
Subsection E.2.3 Extensive vs. Intensive Properties
Extensive Properties.
Definition E.2.4.
An extensive property is a physical property whose value scales with the size or amount of material comprising the physical system.
Remark E.2.5.
If two identical systems \(A\) and \(B\) are combined, their extensive properties sum together. For an extensive property \(X\) this can be mathematically represented as
\begin{equation*}
X(A+B) = X(A) + X(B) \, .
\end{equation*}
Example E.2.6. Examples of Extensive Properties.
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Mass
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Volume
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Internal energy
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Entropy
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Number of particles
Intensive Properties.
Definition E.2.7.
An intensive property is a property whose value does not scale with the size of the system.
Remark E.2.8.
If two identical systems \(A\) and \(B\) are combined, their intensive properties do not change.
Example E.2.9. Examples of Intensive Properties.
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Temperature
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Pressure
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Density
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Concentration
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Chemical potential
Relation between extensive and intensive properties.
Rule of Thumb.
If the value of a property is doubled when the amount of material comprising the system is doubled, then it is an extensive property.
If the value of a property is unchanged when the amount of material comprising the system is doubled, then it is an intensive property
Remark E.2.10.
Often times, intensive properties are constructed from ratios or derivatives of extensive properties.
Example E.2.11.
Density (an intensive property) is the ratio of mass to volume (both extensive properties).
\begin{equation*}
\mathrm{density} = \frac{\mathrm{mass}}{\mathrm{volume}}
\end{equation*}
