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Boyle's Law

Note. Any convenient units can be used for pressure and volume, provided that the units for P₁ are the same as those for P₂, and that the units for V₁ are the same as those for V₂.

(Use g = 9.8 N kg^-1)     1 atm =  Atmospheric pressure = 100 000 Pa = 100 000 Nm^-2

1. A fixed mass of gas at constant temperature has a volume of 500 cm² at a pressure of 1 atm. What will its volume be at a pressure of 4 atm?  125 cm³

2. A gas has a volume of 600cm³ at a pressure of 3.0 x 10⁵ Pa.  What is its volume at a pressure of 6.0 x 10⁵ Pa?  300 cm³

3. A gas has a volume of 1000 cm³ at a pressure of 1 atm. At what pressure will it occupy 100 cm³?   10 atm

4. The pressure exerted by a gas is due to the molecules of the gas bombarding the walls of the container. Why does the pressure increase when the volume is decreased at constant temperature? Less volume, molecules closer together, more collisions etc

5. A cylinder of compressed air has a volume of 51 cm³ at a pressure of 8 atm. When the cylinder is opened, what volume of air will escape?                                           

P₁V₁ = P₂V₂

rearranging V₂ = P₁V₁/ P₂           

V₂ = 8 x 51/ 1 = 408 cm³ minus the 51cm³ left in the cylinder = 357 cm³

 

6. A diver is working in sea-water of density 1025 kg m^-3 on a day when atmospheric pressure is 100 450 Pa. A bubble from his mask is three times the volume when it reaches the surface. At what depth is he working? 20m

7. A lake is 92.7 m deep. A bubble at the bottom of the lake has a volume of 0.5 cm³. What will its volume be at the surface if a water barometer would read 10.3 m (i.e. atmospheric pressure is the same as the pressure at this depth)? 5cm³

8. A uniform cylinder 0.60 m long is sealed at one end. It is lowered open end downwards into a lake so that the mouth just touches the bottom. When retrieved the inside is wet up to 0.50 m from the mouth. Find the depth of the lake if a water barometer would read 10.4 m of water. 52.5m

9. A cylindrical diving bell 8 m high is lowered into water so that the top of the bell is 0.75 m below the surface. If the atmospheric pressure is the same as that exerted by a column of water 10.25 m high, find how far the water rises inside the bell. 6m

A vessel of volume 500 cm³ containing air at a pressure of 8.0 x 10⁴ Pa is connected by a very narrow tube fitted with a tap, to a vessel of volume 700 cm³ containing air at a pressure of 2.0 x 10⁵ Pa. What is the resulting pressure in the vessels when the tap is opened?                     1.5 x10⁵ Pa

A compression pump is connected to a vessel of volume 500 cm³. For each stroke of the pump the piston sweeps 50 cm³ of air at atmospheric pressure into the vessel. If the initial pressure in the vessel is 1 atm, find the pressure in the vessel after 2 strokes.

1.2 atm

An exhaust pump is connected to a flask of volume 100 cm³. The volume swept out by the piston is 25 cm³ for each stroke. The pressure in the vessel is originally 1 atm. By considering one stroke at a time, find the pressure in the vessel after two strokes. 0.64atm