# How we combine two these equations P1V1 = k and P2 V2 = k , I need to know the combination method?

Aug 24, 2017

Well, if you notice, the constants are equal.

If ${P}_{1} {V}_{1} = k$ and ${P}_{2} {V}_{2} = k$, we must have

${P}_{1} {V}_{1} = k = {P}_{2} {V}_{2}$,

which is Boyle's law. It says that if ideal gas pressure increases at constant temperature and mols of gas, ideal gas volume decreases.

One could also derive this from the ideal gas law at constant temperature and mols of gas. Set an initial and final state:

${P}_{1} {V}_{1} = {\overbrace{n}}^{\text{constant"Roverbrace(T)^"constant}}$

${P}_{2} {V}_{2} = {\overbrace{n}}^{\text{constant"Roverbrace(T)^"constant}}$

$\implies \underline{{P}_{1} {V}_{1} = n R T = {P}_{2} {V}_{2}}$

Thus, $k = n R T$.