A climber carries an aneroid barometer and a sealed bag of crisps as she ascends a mountain from sea level to the summit at 3200 m altitude. At sea level th...
Question 1 Report
A climber carries an aneroid barometer and a sealed bag of crisps as she ascends a mountain from sea level to the summit at 3200 m altitude. At sea level the barometer reads 1.01 × 10⁵ Pa and the crisp bag is flat. As the climber gains altitude she notices that the crisp bag gradually inflates and becomes tight. At the summit the barometer reading is 0.69 × 10⁵ Pa. The air temperature at the summit is −8 °C compared with 24 °C at sea level. The sealed bag has a volume of 150 cm³ at sea level. The climber also notices that water boils at a lower temperature at the summit than at sea level.
(a) Explain why atmospheric pressure decreases with increasing altitude. [2]
(b) Explain, in terms of gas pressure, why the crisp bag inflates as the climber ascends. [2]
(c) Explain why water boils at a lower temperature at the summit. [2]
Answer Details
Marking Scheme
- (a) [2 marks]: At higher altitude there is less air above the climber [1]. The weight of the shorter air column pressing down is less, giving a lower atmospheric pressure [1].
- (b) [2 marks]: The gas inside the sealed bag was trapped at sea-level atmospheric pressure (1.01 × 105 Pa) [1]. As the external atmospheric pressure decreases with altitude, the higher internal pressure pushes the bag walls outward, causing it to expand (inflate) [1].
- (c) [2 marks]: Boiling occurs when the vapour pressure of the liquid equals the external atmospheric pressure [1]. At lower atmospheric pressure (the summit), this condition is met at a lower temperature, so water boils below 100 °C [1].
Explanation
Atmospheric pressure is caused by the weight of the air column above a given point. At sea level, the entire atmosphere presses down, producing about 1.01 × 105 Pa. At the summit (3200 m), a significant fraction of the atmosphere is below the climber, so there is less air above and the pressure drops to 0.69 × 105 Pa.
The crisp bag was sealed at sea level, trapping gas at the sea-level pressure of 1.01 × 105 Pa. As the climber ascends, the external pressure drops but the gas inside the sealed bag retains its original pressure. The net outward force (internal > external) pushes the flexible walls of the bag outward, making it inflate and become taut. This is a direct application of Boyle's law: at constant temperature, lower external pressure allows the trapped gas to expand.
Boiling is the process where bubbles of vapour form throughout a liquid. This happens when the vapour pressure inside a bubble equals the external atmospheric pressure pressing on the liquid surface. At sea level (1.01 × 105 Pa), water reaches this vapour pressure at 100 °C. At the summit (0.69 × 105 Pa), less vapour pressure is needed to match the lower external pressure, so the boiling point is reached at a lower temperature (roughly 90 °C at 3200 m). This is why cooking at high altitude takes longer: the water boils at a lower temperature and provides less thermal energy per unit time to the food.
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