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The best way to understand the nature of intensive and extensive quantities in thermodynamics is like this: Take a system of your interest. Make it into two portions (one large portion and the other a small portion) by using a partition, for example. Then see the property of interest of the two samples. Density of the two portions will be the same as the ...

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But what if the pressure in the balloon increases? Doesn't it make sense that the balloon would want to expand? That is, that as pressure increases, volume increases. This seems to contradict Boyle's Law. In simple words: If you increase the pressure in the balloon and let it expand, then the pressure in the balloon is not really increasing, as you are ...

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The two scenarios you mentioned both are correct, “the pressure $p$ has different sign from other generalized force, if we increase the pressure, the volume increases, whereas if we increase the force, $Y$, for all other cases, the extensive variable, $x$, decreases”.[1] There is no conflict between the two scenarios. [1] L.E.Reichl, A Modern Course in ...

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