Question

Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 3 L, the pressure is 390 kPa (kilopascals). What is the volume when the pressure is 234 kPa?

Answer 1

V1/V2 =P1/P2 , so V2 = 1.8L

Answer 2

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

$\bf \stackrel{\textit{\underline{v}olume of a gas varies inversely with applied \underline{p}ressure}}{v=\cfrac{k}{p}} \\\\\\ \textit{we also know that } \begin{cases} v=3\\ p=390 \end{cases}\implies 3=\cfrac{k}{390}\implies 1170=k \\\\\\ therefore\qquad \boxed{v=\cfrac{1170}{p}} \\\\\\ \textit{when p = 234, what is \underline{v}?}\qquad v=\cfrac{1170}{234}$