The Ideal Gas Laws and the Equation of State

Gases are the simplest state of matter to model because their particles are far apart and interact only during brief collisions. This simplicity allows us to describe the behavior of a gas using just three macroscopic quantities: pressure $p$, volume $V$, and absolute temperature $T$. The relationships between these quantities are captured by the gas laws, which were discovered experimentally before being unified into a single equation of state for an ideal gas.

Before stating the laws, we need the idea of the mole and Avogadro's number. One mole of any substance contains a fixed number of particles equal to Avogadro's constant, $N_A \approx 6.02 \times 10^{23}$ particles per mole. This number is defined so that the mass of one mole in grams equals the relative molecular mass of the substa