Question

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?

Answer 1

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

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