# An air compressor has a pressure of "5200 Torr" and contains "200 L" of compressed air. If the container ruptures, what is the volume of air that escapes through the rupture?

Nov 25, 2017

The volume of air that escapes through the rupture is $\approx \text{1000 L}$.

#### Explanation:

This is an example of Boyle's law, which states that the volume of a given amount of gas varies inversely with the applied pressure when temperature and mass are kept constant. This means that as the volume increases, the pressure increases, and vice-versa. The equation to use is:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$,

where:

$P$ is pressure and $V$ is volume.

We aren't given altitude, so I'm going to use the pressure at sea level for ${P}_{2}$. When the hose ruptured, the pressure would have been immediately decreased to that of the air pressure at the altitutde of the air compressor.

Organize data:

Known

${P}_{1} = \text{5200 torr}$

${V}_{1} = \text{200 L}$

${P}_{2} = \text{760.00 torr}$

Unknown

${V}_{2}$

Solution

Rearrange the equation to isolate ${V}_{2}$. Plug in the known data and solve.

${V}_{2} = \frac{{P}_{1} {V}_{2}}{{P}_{2}}$

V=(5200color(red)cancel(color(black)("torr"))xx200"L")/(760.00color(red)cancel(color(black)("torr")))="1000 L" to one significant figure due to $\text{200 L}$.