# The volume V of a gas varies inversely as pressure P is exerted. If V = 4 liters when P = 3 atmospheres, how do you find V when P = 7 atmospheres?

Aug 20, 2017

$V = \frac{12}{7} \text{litres}$

#### Explanation:

$\text{the relationship is } V \propto \frac{1}{P}$

$\text{to convert to an equation multiply by k the constant of}$
$\text{variation}$

$\Rightarrow V = \frac{k}{P}$

$\text{to find k use the given condition}$

$V = 4 \text{ when } P = 3$

$V = \frac{k}{P} \Rightarrow k = P V = 3 \times 4 = 12$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{V = \frac{12}{P}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } P = 7$

$\Rightarrow V = \frac{12}{7} \text{ litres}$