# How does the ideal gas law confirm the laws of Boyle and Charles?

Dec 24, 2014

The ideal gas law encompasses all the simple gas law:

This means that we can derive any simple gas law starting from the ideal gas law. Let's try and see if we can formulate Boyle's law first.

According to Boyle's law, an inverse proportional relationship exists between a gas' pressure and its volume IF the amount of gas (the number of moles) and the temperature are kept constant. Starting from the ideal gas law expression $P V = n R T$, let's define two states for a gas at which

${P}_{1} {V}_{1} = {n}_{1} R {T}_{1}$ (1) and ${P}_{2} {V}_{2} = n R {T}_{2}$ (2).

If ${n}_{1} = {n}_{2} = n$ and ${T}_{1} = {T}_{2} = T$, we'd get

${P}_{1} {V}_{1} = n R T = {P}_{2} {V}_{2} \to {P}_{1} {V}_{1} = {P}_{2} {V}_{2}$ - this represents the mathematical expression of Boyle's law;

Charles' law states that a direct proportional relationship exists between a gas' volume and its temperature (in Kelvin) IF the amount of gas and the pressure are held constant.

Using the same (1) and (2) equations,but this time making sure that ${n}_{1} = {n}_{2} = n$ and ${P}_{1} = {P}_{2} = P$, we'd get

${V}_{1} / {T}_{1} = \frac{n R}{P} = {V}_{2} / {T}_{2} \to {V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$ - the mathematical expression for Charles' law.

Therefore, one could say that the ideal gas las confirms Boyle and Charles' laws, since both of these laws can be derived from it under specific conditions.