Derivation of Ideal Gas Equation

The ideal gas equation is obtained by combining the three proportionalities of Boyle's, Charles's and Avogadro's laws. At constant $T$ and $n$, $V \propto 1/P$ (Boyle's law); at constant $P$ and $n$, $V \propto T$ (Charles's law); at constant $P$ and $T$, $V \propto n$ (Avogadro's law). Combining all three simultaneously gives $V \propto \frac{nT}{P}$, and introducing a single proportionality constant $R$ turns this into $V = \frac{RnT}{P}$, which rearranges to $PV = nRT$ -- the ideal gas equation, also called the equation of state for an ideal gas because, given any three of the four variables $P$, $V$, $n$, $T$, the fourth can always be calculated from it. $R$ is called the gas constant, and becau …