Sort of... What you have is the same number of molecules attempting to take up more space.
*Taken from wiki*
Boyle's law states that P1V1=P2V2
Charle's law states that V1/T1=V2/T2
Gay-Lussac states that P1/T1=P2/T2
When you combine them you get (P1V1)/T1=(P2V2)/T2
P=pressure
V=volume
T=temperature
Using your example of running the gas through a Tee and each feed a 1 litre bottle. The hot gas will have a higher pressure and displace the water faster. However, as that gas cools the water would be sucked back into the bottle and show less gas.
Man, that sounds like a really cool high school science project.
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Some days I get the sinking feeling that Orwell was an optimist!