[tex]\frac{(P1)(V1)}{T1}=\frac{(P2)(V2)}{T2}[/tex] is directly related to the ideal gas law.
The ideal gas law states that:[tex]PV=nRT[/tex]. Rewriting this gives:[tex]\frac{PV}{T}=nR[/tex]. R is the universal gas constant, so its value is fixed. For a given sample, n is the number of moles of the gas, so its value would be fixed too. This means that the value of [tex]\frac{PV}{T}[/tex] would be a fixed constant as well. Therefore, whatever the initial value [tex]\frac{(P1)(V1)}{T1}[/tex] is, it should be equal to the final value [tex]\frac{(P2)(V2)}{T2}[/tex].
