1 Relate atmospheric pressure and the Boyle-Mariotte law Observe what happens to a bottle of water during a plane landing. Why does the bottle get crushed? • Inside the plane, the temperature remains constant. • There is gas above the water in the bottle. Some of it is water that has evaporated, and some of it is air that entered when we opened the bottle to drink. • During the descent, the atmospheric pressure inside the plane increases. This causes the volume occupied by the gas to decrease and the bottle is crushed. This is what the Boyle-Mariotte law predicts. SOLVED PROBLEM 2 A plane is flying at an altitude of 10 000 m and at 20 °C. Inside, there is a bottle partially filled with water. In the free space inside the bottle, 200 mL is occupied by a gas at a pressure of 750 hPa. On landing, without the temperature changing, the pressure reaches 1 atm. What volume does the gas in the bottle occupy? 1. Write down the two states of the gas with their quantities. p1 = 750 hPa V1 = 200 mL T1 = 20 °C p2 = 1 atm V2 = ? T2 = 20 °C 2. Identify the law to apply. For a transformation when T = constant, apply the Boyle-Mariotte law: p v p v 1 1 2 2 ⋅ = ⋅ . 3. Make V2 the subject. p V p V V p p V 1 1 2 2 2 1 2 1 ⋅ ⋅ → ⋅ = = 4. Before substituting the data, write all the amounts of each quantity in the same units. 1 atm 103.25 hPa 1 atm 1013 hPa ⋅ = v p p v 2 1 2 1 = ⋅ = = 750 hPa 1013 hPa 200 mL 148 mL The bottle when the plane is flying at 10 000 m. The bottle when the plane has landed. 5 WO R K W I T H T H E I M AG E . Push the piston of a syringe up to the first mark (A). Then cover the hole with one finger and push the piston with your thumb (B). You will notice that the piston goes quite far into the cylinder. Now, while still covering the hole, remove your thumb and let the piston move. You will see that it returns to its starting position. a) What is inside the syringe all the time? b) Does the amount of matter inside the syringe change during the experiment? c) What happens to the volume of that matter when you push the piston? Why? 6 A 6 L container is filled with nitrogen gas at a pressure of 5 atm. a) What volume will it occupy if we double the pressure without changing the temperature? b) What pressure should be exerted for the volume to reach 15 L? A C T I V I T I E S A B 13
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