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Gas Laws and Proportionalities?

Hello,

So in the combined gas law or ideal gas law, we know that:

PV
α T, so

P
α T

And we know that from Boyle’s law,

P α 1/V

and from Charles' law,

V α T


So if you increase the pressure, then volume decreases, but if you decrease the volume, temperature decreases, yet if temperature decreases, so does pressure?

This is more of a question about proportionalities than of gas laws, really. I’m not too good at them, so if I’m doing something wrong mathematically, please let me know.

Thanks!
With all these proportionalities you're assuming that everything else is staying constant. So yes, if you decrease temperature keeping volume constant, the pressure of your system will decrease.

Why not just work from the one law though, pV = nRT (the ideal gas law)?

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