If you know pressure is inversely proportional to volume then
and volume is proportional to temperature so
then you can sub into and you get
which says that pressure is inversely proportional to temperature but this is wrong as pressure is actually proportional to temperature.
What am I doing wrong?
Deriving one ideal gas law from the other two
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I believe your problem is arising from the fact you are trying to combine two equations which have different conditions on them:
is correct for constant temperature.
is correct for constant pressure.
You then try to combine the two which would only tell you a constant = constant, not a very significant answer.
You want to keep all P, V and T variable so the relation can only be simplified to: the problem here is you have 1 equation with 3 unknowns which you won't be able to solve.
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