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    Hi everyone,

    I need help trying to understand the compound gas law PV/T = constant. I understand that Boyle's law PV = constant with constant temperature, Gay-Lussac's law P/T with constant volume = constant and Charles's law V/T = constant with constant pressure are all empirical results, but what I cannot see is how you combine them. How do I combine them if each one keeps one of the other variables constant?

    Thanks.
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      From pV/T = constant you get pV = constant x T
      If T is constant
      pV = a constant x a constant = a constant(which is Boyle's Law)
      Do the same for the other two laws and it's clear that the general gas law combines the three laws.
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      I understand that it holds when one variable is held constant but how does that prove it when all three are variable?


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        (Original post by Malabarista)
        I understand that it holds when one variable is held constant but how does that prove it when all three are variable?


        This was posted from The Student Room's iPhone/iPad App
        If you can derive the 3 gas laws from the combined gas law, then the combined law is valid.

        Take F=ma

        If I told you that a = F/m you would be happy. Yes?

        1. If you keep m constant, a is proportional to F
        2. If you keep F constant, a is inversely proportional to m

        a = F/m combines both these statements 1 and 2
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        (Original post by Stonebridge)
        If you can derive the 3 gas laws from the combined gas law, then the combined law is valid.

        Take F=ma

        If I told you that a = F/m you would be happy. Yes?

        1. If you keep m constant, a is proportional to F
        2. If you keep F constant, a is inversely proportional to m

        a = F/m combines both these statements 1 and 2
        Thanks very much, I can't believe I didn't see it like that, late nights must be getting to me or something. I am very grateful for your answer
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        (Original post by Malabarista)
        Hi everyone,

        I need help trying to understand the compound gas law PV/T = constant. I understand that Boyle's law PV = constant with constant temperature, Gay-Lussac's law P/T with constant volume = constant and Charles's law V/T = constant with constant pressure are all empirical results, but what I cannot see is how you combine them. How do I combine them if each one keeps one of the other variables constant?

        Thanks.
        You could try a naive approach and simply multiply them all:

        PV = c_1 with units \text{Pa}\text{ l}
        \frac{P}{T} = c_2 with units \frac{\text{Pa}}{\text{ K}}
        \frac{V}{T} = c_3 with units \frac{\text{l}}{\text{ K}}

        So:

        PV \frac{P}{T} \frac{V}{T} = \frac{P^2 V^2}{T^2} = c_1c_2c_3 with units \frac{\text{Pa}^2\text{ l}^2}{\text{ K}^2}

        Since P,V,T > 0 we can take the positive square root to give:

        \frac{PV}{T} = \sqrt{c_1c_2c_3} = C with units \frac{\text{Pa}\text{ l}}{\text{K}} = \frac{\text{N} m^{-2} m^3}{\text{K}} = \frac{\text{N} m}{K} = \frac{\text{J}}{\text{K}} = \text{J} \text{K}^{-1}
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          (Original post by atsruser)
          You could try a naive approach and simply multiply them all:

          PV = c_1 with units \text{Pa}\text{ l}
          \frac{P}{T} = c_2 with units \frac{\text{Pa}}{\text{ K}}
          \frac{V}{T} = c_3 with units \frac{\text{l}}{\text{ K}}

          So:

          PV \frac{P}{T} \frac{V}{T} = \frac{P^2 V^2}{T^2} = c_1c_2c_3 with units \frac{\text{Pa}^2\text{ l}^2}{\text{ K}^2}

          Since P,V,T > 0 we can take the positive square root to give:

          \frac{PV}{T} = \sqrt{c_1c_2c_3} = C with units \frac{\text{Pa}\text{ l}}{\text{K}} = \frac{\text{N} m^{-2} m^3}{\text{K}} = \frac{\text{N} m}{K} = \frac{\text{J}}{\text{K}} = \text{J} \text{K}^{-1}

          I'm convinced! That demonstrates, for me, the validity of the general law from consideration of the individual laws.
          My way was a case of reasoning in the other direction from the general to the individual.
          I actually prefer your method.
         
         
         
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