Combined Gas Law

I understand that it holds when one variable is held constant but how does that prove it when all three are variable?


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If you can derive the 3 gas laws from the combined gas law, then the combined law is valid.

Take F=ma

If I told you that a = F/m you would be happy. Yes?

1. If you keep m constant, a is proportional to F
2. If you keep F constant, a is inversely proportional to m

a = F/m combines both these statements 1 and 2

Hi everyone,

I need help trying to understand the compound gas law PV/T = constant. I understand that Boyle's law PV = constant with constant temperature, Gay-Lussac's law P/T with constant volume = constant and Charles's law V/T = constant with constant pressure are all empirical results, but what I cannot see is how you combine them. How do I combine them if each one keeps one of the other variables constant?

Thanks.

You could try a naive approach and simply multiply them all:

$PV = c_1$ with units $\text{Pa}\text{ l}$
$\frac{P}{T} = c_2$ with units $\frac{\text{Pa}}{\text{ K}}$
$\frac{V}{T} = c_3$ with units $\frac{\text{l}}{\text{ K}}$

So:

$PV \frac{P}{T} \frac{V}{T} = \frac{P^2 V^2}{T^2} = c_1c_2c_3$ with units $\frac{\text{Pa}^2\text{ l}^2}{\text{ K}^2}$

Since $P,V,T > 0$ we can take the positive square root to give:

$\frac{PV}{T} = \sqrt{c_1c_2c_3} = C$ with units $\frac{\text{Pa}\text{ l}}{\text{K}} = \frac{\text{N} m^{-2} m^3}{\text{K}} = \frac{\text{N} m}{K} = \frac{\text{J}}{\text{K}} = \text{J} \text{K}^{-1}$