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# Combined Gas Law watch

1. 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.
2. From pV/T = constant you get pV = constant x T
If T is constant
pV = a constant x a constant = a constant(which is Boyle's Law)
Do the same for the other two laws and it's clear that the general gas law combines the three laws.
3. 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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4. (Original post by Malabarista)
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
5. (Original post by Stonebridge)
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
Thanks very much, I can't believe I didn't see it like that, late nights must be getting to me or something. I am very grateful for your answer
6. (Original post by Malabarista)
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:

with units
with units
with units

So:

with units

Since we can take the positive square root to give:

with units
7. (Original post by atsruser)
You could try a naive approach and simply multiply them all:

with units
with units
with units

So:

with units

Since we can take the positive square root to give:

with units

I'm convinced! That demonstrates, for me, the validity of the general law from consideration of the individual laws.
My way was a case of reasoning in the other direction from the general to the individual.

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