Inversely proportional question


    (Original post by Fizzle-A)
    So, whenever there is an 'inversely proportional' question, whatever happens to the one side, the opposite happens to the other?
    Yes. The easiest way to see this, with equations which I would say are far easier to understand, is that if P = k (1/V), then multiplying by V, we get PV = k, or just PV = constant, which is the way that Boyle's law is usualy stated.

    If you start off with pressure P1 and volume V1, and end up with pressure P2 and volume V2, then P1V1 = k and P2V2 = k. Since k is a constant, it is easier to write P1V1 = P2V2. From this, it is easy to see that P2 = (V1 / V2) P1. So if V2 = 1.25 V1, then V1 / V2 = V1 / 1.25V1 = 1 / 1.25, and you get P2 = P1 / 1.25 straight away - no need to write an equation with a k in at any point.

    You can extend this to Charles' law (V1 / T1 = V2 / T2) and the pressure law (P1 / T1 = P2 / T2), and can even combine all three together to get P1V1 / T1 = P2V2 / T2. With these, you can solve all kinds of problems without having to worry about what the constants of proportionality actually are.

    In every case, there are certain physical conditions that have to be satisfied, such as the temperature having to be constant for Boyle's law to hold.
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