# Thermodynamic variables

Thermodynamic variables (or state variables) are easily measurable macroscopic quantities used to describe the state of a thermodynamic system. These quantities are different depending on the type of system we want to describe; it is not the same to describe the behavior of a magnet, a galaxy, or a living being. To describe each of these systems it is necessary to use a different set of quantities.

In the situations that we will discuss throughout these pages, we will assume that the system studied is in thermodynamic equilibrium:

It is the internal state of a system in which the thermodynamic variables that describe it do not undergo macroscopic changes.

In this situation, the thermodynamic variables that describe a system are well defined.

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When we analyze the processes undergone by a gas enclosed in a container, its state is described by the following quantities:

• Mass (m): expressed in kilograms (kg) or in number of moles (n).
• Volume (V): expressed in cubic meters (m3).
• Pressure (p): the one that exerts the gas on the walls of the container that contains it. Expressed in pascals (Pa).
• Temperature (T): Usually expressed in Kelvin (K) or in degrees Celsius (0C). You will find a brief summary of the International System of units on this page.

We can define other physical quantities called state functions from relationships between thermodynamic variables. These functions depend only on the state of a system and not on how the system arrived at this state.

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Thermodynamic variables are called extensive or intensive depending on how they depend on the size of the system they describe:

• Extensive variables: their value depends on the size of the system. For example: volume or mass,
• Intensive variables: their value is independent of the size of the system. For example: temperature, density, pressure.

A simple way to figure out if a variable is intensive or extensive is to carry out the following thought experiment: Imagine a gas enclosed in a container like the one shown in the figure above. The gas is at a pressure p, occupies a volume V and is at a temperature T. If you place a wall in the middle of the container, what will be the value of the variables on each side of the wall? If their value does not change, then the variable is intensive; otherwise it is extensive.

In a situation of thermodynamic equilibrium, the state variables (for example p, V, T) are related to each other by an equation of state. There is no single equation of state that would describe the behavior of all substances in all situations (or at least it has not been found yet). Therefore, it will be necessary to use a different equation of state depending on the system we want to study.

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