The Leaking Water Bottle
A student fills a 1.0 L plastic water bottle with 0.9 L of water and screws the cap on tightly. The bottle is left in a car on a hot day. The temperature inside the car rises from 20°C to 50°C. The student notices that the bottle feels firm and slightly bulged, and a small amount of water has leaked out around the cap. The student wonders why the bottle bulged and why water leaked even though the cap was tight. They know that the bottle is made of a flexible plastic that can stretch slightly, and that the cap has a rubber seal. The student has a thermometer and a balance available.
1. Explain why the bottle bulged and why water leaked, using ideas about particles and pressure. Include in your answer what would happen if the bottle were made of a rigid metal instead of flexible plastic.
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The bottle bulged because the water and the air trapped inside the bottle expanded when heated. As temperature increases, the particles move faster and spread out slightly (water expands a little) and the air expands much more. Since the bottle is sealed, the increased motion of particles leads to more frequent and forceful collisions with the inside walls, increasing the pressure inside the bottle. The flexible plastic stretches to accommodate the increased volume, causing the bulge. The leak occurred because the increased internal pressure forced water past the rubber seal at the cap. If the bottle were rigid metal, it would not stretch; instead, the pressure would continue to rise until the cap seal failed more dramatically or the bottle ruptured. The metal would conduct heat faster, possibly causing a quicker pressure increase, but the key difference is that a rigid container cannot expand to relieve pressure, so the seal or container would be more likely to fail suddenly.
2. The student claims that the water leaked because the bottle was overfilled. Evaluate this claim using the evidence given. What additional test could the student do to support or refute this claim?
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The claim is not well supported. The bottle was filled with 0.9 L in a 1.0 L bottle, leaving 0.1 L of air space. If the bottle had been completely full (no air), the expansion of water alone from 20°C to 50°C would be small: water's volume expansion coefficient is about 0.00021 per °C, so 0.9 L would expand by about 0.9 × 0.00021 × 30 = 0.0057 L (5.7 mL). That small increase might not cause a leak if there were no air. The presence of air, which expands much more (about 0.0037 per °C for air at constant pressure, but here volume is constrained), leads to a larger pressure increase. So overfilling is not the primary cause; the trapped air and the temperature rise are. To test, the student could repeat with the same amount of water but squeeze out the air before sealing, or use a rigid container with a pressure gauge, and compare leakage. They could also measure the mass of water lost to quantify leakage.