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Deriving one ideal gas law from the other two

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    If you know pressure is inversely proportional to volume then P = c/V
    and volume is proportional to temperature so V = kT
    then you can sub V = kT into P = c/V and you get
    P = c/kT 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?
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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:

     P = c/V is correct for constant temperature.

     V = kT 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:  PV = cT the problem here is you have 1 equation with 3 unknowns which you won't be able to solve.


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