Question

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?

Answer 1

The volume of air that escapes through the rupture is `~~"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_1V_1=P_2V_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="5200 torr"`

`V_1="200 L"`

`P_2="760.00 torr"`

Unknown

`V_2`

Solution

Rearrange the equation to isolate `V_2`. Plug in the known data and solve.

`V_2=(P_1V_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 `"200 L"`.