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?

1 Answer
Nov 25, 2017

Answer:

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"#.