Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 7L, the pressure is 410 kPa (kilopascals). What is the volume when the pressure is 287 kPa?

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06-11-2017
Mathematics

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Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 7L, the pressure is 410 kPa (kilopascals). What is the volume when the pressure is 287 kPa?

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jdoe0001 jdoe0001 · Answer 1 · 2017-11-06T20:37:15+01:00

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \textit{"volume of a gas varies inversely with the pressure"}\quad v=\cfrac{k}{p} \\\\\\ \textit{we also know that } \begin{cases} v=7\\ p=410 \end{cases}\implies 7=\cfrac{k}{210}\implies 1470=k \\\\\\ thus\qquad \qquad \boxed{v=\cfrac{1470}{p}} \\\\\\ \textit{when p=287, what is \underline{v}?}\qquad v=\cfrac{410}{287}[/tex]