Earlier this week, I took my water bottle out of the fridge and, without thinking, put it near the small heater we had running. In seconds it was spewing water all over the table!
I figured the heat made the air at the top expand, pushing the water out through the straw, but what I was really curious about was: Does the amount of air the bottle starts with change how much water is forced out?
Air follows the Ideal Gas Law, which is given by
where P is pressure, V volume, N number of molecules, k Boltzmann's constant, and T temperature in Kelvin. That last bit is important: We usually measure temperature in degrees Fahrenheit or Celsius, which can be negative. Kelvin on the other hand is only ever positive: 0 K corresponds to absolute zero. We can convert from Fahrenheit with
In our situation, the temperature rises, which increases the pressure the air applies to the surface of the water. This pushes water out, increasing the air's volume, and bringing the pressure down. At equilibrium then, we can set the initial and final pressures equal. Similarly, the number of molecules won't change, since no air is entering or exiting. Using that, we can write the ideal gas law for the initial and final states, then set them equal:
What we're really interested in though is the change in volume, since that tells how much of a mess we're making:
We can plot this for a couple different initial volumes over the temperature range from refrigerator to heater-adjacent:
The green line is half full for my water bottle, and will spit out a couple tablespoons worth! As I write this, Marika is using the Instant Pot for some dinner prep – I'm surrounded by pressure vessels ready to blow!
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