# What is the combined gas law?

For a given quantity of gas, $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$
Of course, when ${P}_{1} = {P}_{2}$, we get Charles' Law, ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$. And when ${T}_{1} = {T}_{2}$, we get Boyle's law, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$. Combining the two laws, we get $P V$ $=$ $k$. Once we introduce $n$, the molar quantity of gas, and a suitable constant, we get the Ideal Gas Law.