TP: Ideal Gas Law and Equations of State

Ideal Gas Law


An equation of state relates the molar density (or specific molar volume) of a fluid (i.e., a vapor or a liquid) to the temperature and pressure of the fluid.

The most common and simplest equation of state is the ideal gas law:

$P=\frac{nRT}{V} = \frac{RT}{v}$


Interestingly, the ideal gas law can be derived from our molecular understanding of the properties T and P. This requires that we assume that gas molecules are infinitely small and interact only via collisions.


The ideal gas law is an approximation (!) that has only limited applicability. It is usually used for diatomic gas when (RT/P)>5 L/mol and for other gases when (RT/P) > 20 L/mol (i.e., at high specific volumes!).


Use equations of state to calculate unknown properties from measured properties