Question

The pressure of a gas p(v) varies inversely with the volume of the gas v. The pressure of a gas measures 25 kg/cm^2 when its volume is 200cm^2. Which equation can be used to find the pressure of the gas when the volume is changed?
A.p(v)=8/v
B.p(v)=8v
C.p(v)=5000/v
D.p(v)=5000v

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{\underline{p(v)} varies inversely with \underline{v}}}{p(v)=\cfrac{k}{v}}\qquad \textit{we also know that } \begin{cases} p(v)=25\\ v=200 \end{cases} \\\\\\ 25=\cfrac{k}{200}\implies 5000=k\qquad therefore\qquad \boxed{p(v)=\cfrac{5000}{v}}$