- #1
PFuser1232
- 479
- 20
How does one derive the combined gas law rigorously from Boyle's Law, Charle's Law and Gay-Lussac's law? I started out as follows (I will be using ##P## for pressure, ##T## for absolute temperature, and ##V## for volume - for constants I will use subscripts to denote the parameter on which the constant is dependent):
##PV = k_T = f(T)##
##P = k_V T = g(V)##
##V = k_P T = h(P)##
Multiplying those three equations together, one obtains:
##(PV)^2 = k_T k_V k_P T^2##
##\frac{PV}{T} = \sqrt{k_T k_V k_P}##
Now, where exactly do I go from here? I know it should equal ##Nk_B## (or ##nR##) but how do I show that?
In other words, how can I prove that the square root of the product of three functions of pressure, volume and temperature equals a function independent of pressure, volume, and temperature?
##PV = k_T = f(T)##
##P = k_V T = g(V)##
##V = k_P T = h(P)##
Multiplying those three equations together, one obtains:
##(PV)^2 = k_T k_V k_P T^2##
##\frac{PV}{T} = \sqrt{k_T k_V k_P}##
Now, where exactly do I go from here? I know it should equal ##Nk_B## (or ##nR##) but how do I show that?
In other words, how can I prove that the square root of the product of three functions of pressure, volume and temperature equals a function independent of pressure, volume, and temperature?