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If temprature is directly proportional to volume (Charles's law) and temperature is directly proportional to pressure (Gay-Lussac's law), then why is pressure and volume are inversely proportional?

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    $\begingroup$ By Boyale's law... $\endgroup$ – Zenix Dec 28 '19 at 16:48
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Given you know and understand Charles' and Gay-Lussac's laws, it's not about chemistry, rather, simple ratios:

$$ \begin{cases} T \propto V\\ T \propto p \end{cases} \implies p \propto \frac 1 V $$

which, as Zenix commented, is a math form of Boyle's law.

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