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The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 900900 cubic centimeters when the pressure is 500500 millimeters of mercury​ (mm Hg), find the volume when the pressure is 450450 mm Hg.

Respuesta :

[tex]\bf \qquad \textit{ inverse proportional variation}\\\\ \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x} \\ &&\boxed{y=\cfrac{{{ k}}}{x}} \end{array}\\\\ -----------------------------\\\\ [/tex]

[tex]\bf \textit{V varies inversely with P}\implies V=\cfrac{k}{P} \\\\\\ \textit{we also know that } \begin{cases} V=900\\ P=500 \end{cases}\implies 900=\cfrac{k}{500} \\\\\\ 900\cdot 500=k\implies 450000=k\impliedby \textit{constant of variation} \\\\\\ \boxed{V=\cfrac{450000}{P}}\\\\ -----------------------------\\\\ \textit{what is V when P = 450?}\implies V=\cfrac{450000}{450}[/tex]

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