It is impossible to track and analyse each and every atom or molecule in a system. Fortunately, a set of state variables, namely the pressure p, volume V and temperature T, can be used to describe the state of the system. An equation used to model the relationship among the state variables (of a given amount of substance) is called an equation of state.
The equation of state for an ideal gas is
where n is the amount of substance in moles, and is the molar gas constant.
Since each mole contains particles (called the Avogadro’s number), the equation of state can also be written as
where N is the number of gas particles, and is the Boltzmann’s constant.
- When plugging numbers into this equation, one must ensure that p is the absolute pressure (not pressure relative to atmospheric pressure, aka gauge pressure), and T must be the thermodynamic temperature in Kelvin (not Celsius).
- Historically, the three empirical gas laws, namely
Boyle’s Law: at constant T
Charles’ Law: at constant p
Gay-Lussac’s Law: at constant V
were first combined into what’s called the
Combined Gas Law:
which is then combined with
Avogadro’s Law: at constant p and T
to finally arrive at